FINS4781 Continuous-Time Finance

Subject Code

FINS4781

Study Level

Undergraduate

Commencing Term

Term 3

Total Units of Credit (UOC)

Delivery Mode

On Campus

School

Banking & Finance

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The course outline is not available for current term. To view outlines from other year and/or terms visit the archives

1. Course Details

Given the ongoing COVID-19 restrictions in NSW, all Term 3 courses will be delivered online until at least Friday 22nd October and all assessment will be online throughout the term. The University remains hopeful that the situation will improve to allow for some on-campus activities later in Term 3 such as lab, practical and studio classes. UNSW will continue to review the situation regularly and keep students updated. For further information on how your study may be affected this term, please see FAQs here. See tab 8. Policies and Support in this course outline for tips on online study and assessment.

Summary of Course

The course consists of two major parts. The first one is a more technical prerequisite of the second, but it delivers its own insights into the modelling of financial problems. It deals with Stochastic Calculus as a basis to model the stochastic development of asset prices, interest rates or latent variables. At the end of this part students should be familiar with Ito's Lemma. Girsanov's Theorem, and stochastic differential equations. This part asks for a positive attitude of students towards a more formal reasoning. It will take up about 30% of the lectures. The second part deals with a number of classical continuous-time applications in Finance. First, three problems which areas based local on a no-arbitrage condition will be discussed: option pricing, structural models of credit risk, and the trade - off theory of the optimal capital structure. Second, portfolio theory and the characterization of expected asset returns in equilibrium will be analysed. These two problems were the first applications of the continuous-time finance approach. For the last topics, we have some flexibility: we can choose between several models that can be useful in a variety of settings, such as models with mean reversion, stochastic volatility, jumps, or regime switching. Alternatively, we could look at more sophisticated derivatives, such as term structure models, or models of credit default swaps.

Teaching Times and Locations

Please note that teaching times and locations are subject to change. Students are strongly advised to refer to the Class Timetable website for the most up-to-date teaching times and locations.

View course timetable

Course Policies & Support

The Business School expects that you are familiar with the contents of this course outline and the UNSW and Business School learning expectations, rules, policies and support services as listed below:

Program Learning Outcomes
Academic Integrity and Plagiarism
Student Responsibilities and Conduct
Special Consideration
Protocol for Viewing Final Exam Scripts
Student Learning Support Services

Further information is provided in the Assessment and Policies and Support sections.

Students may not circulate or post online any course materials such as handouts, exams, syllabi or similar resources from their courses without the written permission of their instructor.

Course Aims and Relationship to Other Courses

My goal for this course is to explain and in a sense “de-mystify” some of the more sophisticated models in Continuous-Time Finance. This should enable the student to read current research papers at a high level. In terms of modelling time series, we will discuss models with mean-reversion (such as the Ornstein-Uhlenbeck process and the square root process), stochastic volatility models (Heston in particular), Lévy processes and other jump processes, and continuous-time regime switching models.

These models describe the skewness and kurtosis of many financial time series more realistically than the standard models. In terms of derivative securities we will discuss equity derivatives, interest rate derivatives (based on the Heath-Jarrow-Morton approach as well as the Libor Market Model approach) and if time allows, credit derivatives. We also discuss portfolio optimization in continuous-time. All other chapters are designed to lead us to these topics.

The earlier chapters in this course will emphasize the following topics:

What is a filtration?

Why is it useful to consider the conditional expected value of a random variable to be also a random variable?

What are Markov Processes, Martingales, and Brownian Motions, and why are they so important to a dynamic Theory of Finance?

Why do we need a new integration theory (the Itô integral) to determine properly the gains of dynamic portfolio strategies?

Why do the rules of classical calculus no longer hold?

Why do stochastic differential equations help us to characterize changes of asset prices over small time intervals?

How do changes in probability measures (Girsanov’s theorem) make option pricing easier?

My approach is to include proofs to these results only if they’re relatively easy. This means that, even if the most general results will not be proved, sometimes simpler results can be proved. My hope is that the more a student understands about these results, the easier it will be for him/her to apply them, or even extend them.

This course will not require memorization. No assessment will be closed book. The lecture notes are fairly thorough, and will hopefully be a useful reference after the course is finished. In the spirit of full disclosure, let me also mention some topics that will not be discussed:

(a) discrete-time models (such as binomial models or GARCH)

(b) Monte Carlo methods

(d) estimation.

While all of these topics are important, students will have to learn these topics in other courses.

The course is a fourth year (Honours) and a Postgraduate (PhD) course. Participants should have a strong interest in asset pricing. The course FINS3635 (Options, Futures, and Risk Management) is a prerequisite. In addition, students would find it beneficial to have some background in probability theory.

Student Learning Outcomes

The Course Learning Outcomes (CLOs) are what you should be able to demonstrate by the end of this course, if you participate fully in learning activities and successfully complete the assessment items.

CLOs also contribute to your achievement of the Program Learning Outcomes (PLOs), which are developed across the duration of a program for all coursework students in the Business School. More information on PLOs is available under Policies and Support. PLOs are, in turn, directly linked to UNSW graduate capabilities and the aspiration to develop “globally focussed graduates who are rigorous scholars, capable of leadership and professional practice in an international community”.

The following table shows how the CLOs for this course relate to the overall PLOs and indicates where each CLO and PLO is assessed:

Course Learning Outcomes	Program Learning Outcomes	Course Assessment Item
On successful completion of the course, you should be able to:	This course helps you to develop the following Program Learning Outcomes:	This learning outcome will be assessed in the following items:
Understand the basics of conditional expectation with respect to a filtration. As an example, we consider OLS regressions.	PLO 1: Research Excellence PLO 2: Academic Excellence	First Assignment
Understand how changing probability measures (e.g., producing the risk-neutral probability measure) can help with option pricing, and to understand the derivation of the Black-Scholes partial differential equation (PDE).	PLO 1: Research Excellence PLO 2: Academic Excellence	Second Assignment
Understand such applications of the Black-Scholes PDE as the models of risky debt due to Merton and Leland, barrier options and the Black-Cox model of risky debt, and the Brennan-Schwartz approach to real options.	PLO 1: Research Excellence PLO 2: Academic Excellence	Second Assignment Paper Review
Understand portfolio optimisation in continuous-time, including the derivation of the Hamilton-Jacobi-Bellman equation and its first order conditions. Understand how the first order conditions can lead to the Intertemporal CAPM model (ICAPM). Understand the approach due to Karatzas and others that can help with constrained optimisation.	PLO 1: Research Excellence PLO 2: Academic Excellence	Second Assignment Paper Review
Understand the benefits and uses of models with mean reversion.	PLO 1: Research Excellence PLO 2: Academic Excellence	Third Assignment Paper Review
Understand more advanced models, such as models with stochastic volatility, jumps, or regime-changes, OR, to understand more advanced option pricing models, such as term structure models or credit risk models.	PLO 1: Research Excellence PLO 2: Academic Excellence	Paper Review

2. Staff Contact Details

Position	Title	Name	Email	Location	Phone	Consultation Times
Course Coordinator	Dr			Room 367, Business School building - Ref E12	+61 9385 5851	Thursdays, 3-5pm or by appointment.

To get to Dr. Colwell’s office, please use the East wing elevator (closer to the bookstore), find the phone pad next to the glass door, hit the # key (i.e., “on”) and dial my extension: 55851. I’ll come open the door for you.

Email is also an excellent way to ask questions. For convenience, let me repeat my email address: d.colwell@unsw.edu.au. We should also be able to talk via Zoom or Teams as well, although I am still getting used to some of the technology.

3. Learning and Teaching Activities

Approach to Learning and Teaching in the Course

This course provides the basis to analyse and solve stochastic, dynamic problems in Finance at an advanced level. It is theoretically oriented with an enormous potential for practical application.

The course consists two two-hour lectures per week. The lecture notes will be available before class, so that students can have an overview of the topics in advance. During the lecture, we discuss the details of some proofs, and omit the details of others, leaving them for the interested student. We discuss the intuition behind results and continually refer to the “big picture” issues, of how each topic relates to other topics. Questions and discussion in class are welcome. Some practice problems will be available for most chapters, and doing these should help students prepare for the take-home assignments. The paper to be reviewed (see below) will be chosen by the student according to the student’s interests, but must be related to Continuous-Time Finance.

Learning Activities and Teaching Strategies

In order to obtain the full benefit from the course, students are expected to follow the following points below:

1. Read the relevant lecture notes before the lectures. This will make it easier for students to follow the lectures and to ask questions.

2. Attend class lectures.

3. Participate in the lectures, asking questions and answering the occasional questions posed by the lecturer.

4. Review the lectures after class.

5. Do the practice problems or take-home assignments when available.

6. Search the literature for a paper that interests you.

If any issues are still not clear, ask me, send me an e-mail, or arrange for a phone call or online meeting.

4. Assessment

Formal Requirements

In order to pass this course, you must:

achieve a composite mark of at least 50 out of 100;
meet any additional requirements described in the Assessment Summary section.

You are expected to attempt all assessment requirements in the course.

Assessment Structure

Assessment Task	Weighting	Length	Due Date
First Assignment	20%	–	Week 4
Second Assignment	20%	–	Week 7
Third Assignment	20%	–	Week 10
Paper Review	40%	5 to 10 pages	UNSW exam period
Total	100%	–	–

Assessment Summary

As a student at UNSW you are expected to display academic integrity in your work and interactions. Where a student breaches the UNSW Student Code with respect to academic integrity, the University may take disciplinary action under the Student Misconduct Procedure. To assure academic integrity, you may be required to demonstrate reasoning, research and the process of constructing work submitted for assessment.

To assist you in understanding what academic integrity means, and how to ensure that you do comply with the UNSW Student Code, it is strongly recommended that you complete the Working with Academic Integrity module before submitting your first assessment task. It is a free, online self-paced Moodle module that should take about one hour to complete.

The take-home assignments will involve applying the material learned in class to derive extensions of the results in class. For example, we may extend a calculation done in class to the case where the underlying asset exhibits mean-reversion. There will be roughly three or four questions per assignment. Your solutions can be hand-written, if your writing is clear. The assignment will be due at the beginning of class, in the week specified. I should be able to give you at least one week to finish each assignment.

For the paper review, I would like each student first to find a fairly current, published paper that has something to do with continuous-time finance. Find a paper that interests you. Then I would like you to summarize the paper, somewhat briefly. Show me that you understand the paper and understand its contribution. Finally, I would like you to make some suggestions for future research. Your suggestion(s) may involve empirically testing the paper in some way, applying it to a different problem, or extending it in some way. I imagine this paper review/research proposal (or “report”) could be of about 5 to 10 typed pages in length. You are not expected to carry out original research, but I would like you to make a proposal that seems attainable. This paper review will be due, say, during the University Exam Period. You may discuss your choice of paper with me before you start writing.

Assignment Submission Procedure

Ordinarily, for a small class such as this, assessment items could be handed into me as hard copies during class. For online learning, it looks like you will have to scan your work and email it to me. One App that I've heard of, called CamScanner, is useful for taking a photo of your handwritten pages, and converting it to a good quality, readable photo. Then you can save it as a pdf file.

For the paper review, please email me a copy of your review together with a copy of the paper that you are reviewing.

Assessment Feedback

Feedback on student performance from formative and summative assessment tasks will be provided to students in a timely manner. Assessment tasks completed within the teaching period of a course, other than a final assessment, will be assessed and students provided with feedback, with or without a provisional result, within 10 working days of submission, under normal circumstances. Feedback on continuous assessment tasks (e.g. laboratory and studio-based, workplace-based, weekly quizzes) will be provided prior to the midpoint of the course.

Special Consideration

You can apply for special consideration when illness or other circumstances beyond your control interfere with your performance in a specific assessment task or tasks, including online exams. Special consideration is primarily intended to provide you with an extra opportunity to demonstrate the level of performance of which you are capable. To apply, and for further information, see Special Consideration on the UNSW Current Students page.

Special consideration applications will be assessed centrally by the Case Review Team, who will update the online application with the outcome and add any relevant comments. The change to the status of the application immediately sends an email to the student and to the assessor with the outcome of the application.

Please note the following:

Applications can only be made through Online Services in myUNSW. Applications will not be accepted by teaching staff. The lecturer-in-charge/course coordinator will be automatically notified when your application is processed.
Applying for special consideration does not automatically mean that you will be granted a supplementary exam or other concession.
If you experience illness or misadventure in the lead up to an exam or assessment, you must submit an application for special consideration, either prior to the examination taking place, or prior to the assessment submission deadline, except where illness or misadventure prevent you from doing so.
If your circumstances stop you from applying before your exam or assessment due date, you must apply within 3 working days of the assessment or the period covered by your supporting documentation.
Under the UNSW Fit To Sit/Submit rule, if you sit the exam/ submit an assignment, you are declaring yourself well enough to do so and are cannot subsequently apply for special consideration.
If you become unwell on the day of – or during – an exam, you must stop working on your exam, advise your course coordinator or tutor and provide a medical certificate dated within 24 hours of the exam, with your special consideration application. For online exams, you must contact your course coordinator or tutor immediately via email, Moodle or chat and advise them you are unwell and submit screenshots of your conversation along with your medical certificate and application.
If your online assessment is scheduled at a specific time in Sydney, Australian Eastern Standard Time (AEST), you must make yourself available at the time advised. Special consideration will not be awarded on the grounds that you are in a different time zone.
Special consideration requests do not allow the awarding of additional marks to students.

Further information on Business School policy and procedure can be found under “Special Consideration” on the Policies and Support page.

The School of Banking and Finance supports the concept to leave the course lecturer-in-charge to stipulate a penalty of 0 to 10% of the percentage weight of the assessment component or part thereof per day. Details of such penalties will be available on the course Moodle page.

Applications for extension are restricted to cases of serious illness, bereavement or misadventure and students must provide documentary evidence. Decisions on such applications will be based on policies that are consistent with the policies adopted by UNSW Business School for such cases.

Protocol for Viewing Final Exam Scripts

UNSW students have the right to view their final exam scripts, subject to a small number of very specific exemptions. The UNSW Business School has set a protocol under which students may view their final exam script. Individual schools within the Faculty may also set up a local process for viewing final exam scripts, so it is important that you check with your School. Further school-specific information may be included below.

Further to the Business School protocol for viewing final exam scripts:

A student must lodge a request to view their final exam script within 3 days immediately following the official release of overall course results. Applications must be made by completing the online form.
The School may fix a time at which all students wishing to see their exams will be permitted to do so, and the School may fix a time for each course on that day. The School may refuse to allow access to the exams at other times.

Protocol for Viewing Other Exam Scripts is the similar to that of viewing final exam scripts except the working days are defined with reference to the release date of specific assessment result.

Quality Assurance

The Business School is actively monitoring student learning and quality of the student experience in all its programs. A random selection of completed assessment tasks may be used for quality assurance, such as to determine the extent to which program learning goals are being achieved. The information is required for accreditation purposes, and aggregated findings will be used to inform changes aimed at improving the quality of Business School programs. All material used for such processes will be treated as confidential.

5. Course Resources

The website for this course is on Moodle.

The only materials that are required for this course are the lecture notes, which will be made available on Moodle in a timely manner.

The lecture notes are influenced by a wide variety of sources. The following is a list of some of those sources, and could be considered extra reading if the student needs more detail on a particular subject.

Aksamit, A., & Jeanblanc, M. (2017). Enlargement of filtration with finance in view. Switzerland: Springer.

Bachelier, L. (1900). Théorie de la spéculation. In Annales scientifiques de l'École normale supérieure (Vol. 17, pp. 21-86).

Bates, D.S., 1996, “Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options,” Review of Financial Studies, (Spring) Vol. 9, No. 1, 69-107.

Baxter, M. and Rennie, A., 1996, Financial Calculus: An Introduction to Derivative Pricing, Cambridge University Press.

Bielecki, T.R. and Rutkowski, M., 2002, Credit Risk: Modeling, Valuation and Hedging, Springer Finance.

Black, F. and Cox, J.C., 1976, “Valuing Corporate Securities: Some Effects of Bond Indenture Provisions,” Journal of Finance, 31 (May), 351-368.

Black, F., and Scholes, M., 1973, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, 81 (May-June), 637-654.

Bhar, R., & Chiarella, C. (1997). Transformation of Heath-Jarrow-Morton models to Markovian systems. The European Journal of Finance, 3(1), 1-26.

Bjerksund, P., & Stensland, G. (2014). Closed form spread option valuation. Quantitative Finance, 14(10), 1785-1794.

Brace, A., Gatarek, D., & Musiela, M. (1997). The market model of interest rate dynamics. Mathematical finance, 7(2), 127-155.

Brennan, M. and Schwartz, E., 1985, “Evaluating Natural Resource Investments,” Journal of Business, 58, 135-157

Brigo, D. and Mercurio, F. 2006, Interest Rate Models—Theory and Practice: With Smile, Inflation and Credit, 2nd Ed., Springer Finance.

Buchen, P.W., 2001, “Image Options and the Road to Barriers,” Risk Magazine, 14 (9), 127-130.

Buchen, P.W., 2012, An Introduction to Exotic Option Pricing, Chapman & Hall.

Caouette, Altman, and Narayanan, 1998, Managing Credit Risk: The Next Great Financial Challenge, Wiley.

Carr, P., & Madan, D. (1999). Option valuation using the fast Fourier transform. Journal of computational finance, 2(4), 61-73.

Chen, R. R., Cheng, X., Fabozzi, F. J., & Liu, B. (2008). An explicit, multi-factor credit default swap pricing model with correlated factors. Journal of Financial and Quantitative Analysis, 43(1), 123.

Chiarella, C., & Kwon, O. K. (2001). Forward rate dependent Markovian transformations of the Heath-Jarrow-Morton term structure model. Finance and Stochastics, 5(2), 237-257.

Colwell, D.B., Feldman, D. and Hu, W., 2015, “Non-Transferable Non-Hedgeable Executive Stock Option Pricing,” Journal of Economic Dynamics and Control, Vol. 53, April, pp. 161-191.

Colwell, D.B., Henker, T., Fong, K., and Ho, J., 2003, “Real Options Valuation of Australian Gold Mines and Mining Companies.” The Journal of Alternative Investments, 23-38.

Chung, K.L., 1974, A Course in Probability Theory, 2nd Ed., Academic Press.

Cochrane, J.H., 2001. Asset Pricing, Princeton University Press.

Cont, R. and Tankov, P., 2008, Financial Modelling with Jump Processes, 2nd Ed., Chapman and Hall.

Cox, J. C., & Huang, C. F., 1989, “Optimal consumption and portfolio policies when asset prices follow a diffusion process,” Journal of economic theory, 49(1), 33-83.

Cox, J.C., Ingersoll, J.E., and Ross, S.A., 1985, “A Theory of the Term Structure of Interest Rates,” Econometrica, 53, 385-407.

Cvitanić, J., and Karatzas, I., 1992, “Convex Duality in Constrained Portfolio Optimization,” Annals of Applied Probability, 2(4), 767-818.

Dempster, M., Medova, E., and Tang, K. (2008). Long term spread option valuation and hedging. Journal of Banking & Finance, 32(12):2530-2540.

Dixit, R. K., & Pindyck, R. S. (2012). Investment under uncertainty. Princeton university press.

Duffie, D., Pan J., and Singleton, K., 2000, “Transform Analysis and Asset Pricing for Affine Jump-Diffusions,” Econometrica, 1343-1376.

Elliott, R.J., 1982, Stochastic Calculus and Applications, Springer.

Elliott, R.J., Aggoun, L., and Moore, J.B., 1995, Hidden Markov Models: Estimation and Control, Springer.

Harrison, J.M., and Pliska, S., 1981, “Martingales and Stochastic Integrals in the Theory of Continuous Trading,” Stochastic Processes and their Applications, 11, 215-260.

Heath, D., Jarrow, R.A. and Morton, A., 1992, “Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation,” Econometrica, 60, 77-105.

Heston, S.L., 1993, “A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options”, Review of Financial Studies, 6, 327-343.

Ho, T.S.Y., and Lee, S.-B., 1986, “Term Structure Movements and the Pricing of Interest Rate Contingent Claims,” The Journal of Finance, 41, 1011-1029.

Hull, J.C., 2017, Options, Futures, and Other Derivatives, 9th Ed., Pearson.

Hull, J. and White, A., 1990, “Pricing Interest Rate Derivative Securities,” The Review of Financial Studies, 3, 573-592.

Jacod, J. and Shiryaev, A.N., 1987, Limit Theorems for Stochastic Processes, Springer.

Karatzas, I., and Kou, S.G. (1996): “On the Pricing of Contingent Claims Under Constraints,” The Annals of Applied Probability, Vol. 6, No. 2, 321-369.

Karatzas, I., Lehoczky, J.P., Shreve, S.E., 1987. Optimal portfolio and consumption decisions for a “small investor” on a finite horizon. SIAM Journal on Control and Optimization 25 (6) 1557-1586. Doi: 10.1137/0325086

Karatzas, I. and Shreve, S.E., (I) 1991, Brownian Motion and Stochastic Calculus, 2nd Ed., Springer.

Karatzas, I. and Shreve, S.E., (II) 1998, Methods of Mathematical Finance, Springer.

Kirk, E., & Aron, J. (1995). Correlation in the energy markets. Managing energy price risk, 1, 71-78.

Konstandatos, O., 2008, Pricing Path Dependent Exotic Options: A Comprehensive Mathematical Framework, VDM Verlag Dr. Mueller e.K.

Lee, R. W. (2004). Option pricing by transform methods: extensions, unification and error control. Journal of Computational Finance, 7(3), 51-86.

Leland, H.E., 1994, “Corporate Debt Value, Bond Covenants, and Optimal Capital Structure,” Journal of Finance, 49, No. 4, (Sept), 1213-1252.

Liptser, R.S. and Shiryaev, A.N 1977, Statistics of Random Processes I: General Theory, Springer-Verlag.

Lord, R., & Kahl, C. (2007). Optimal Fourier inversion in semi-analytical option pricing. (papers.ssrn.com)

Margrabe, W. (1978). The value of an option to exchange one asset for another. The journal of finance, 33(1), 177-186.

Merton, R. C., 1973, "An intertemporal capital asset pricing model." Econometrica: Journal of the Econometric Society, 867-887.

Merton, R.C., 1974, “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates,” Journal of Finance, 29, 449-470.

Merton, R.C., 1990, Continuous-Time Finance, Blackwell.

Musiela, M., & Rutkowski, M. (1997a). Continuous-time term structure models: Forward measure approach. Finance and Stochastics, 1(4), 261-291.

Musiela, M. and Rutkowski, M., (1997b), Martingale Methods in Financial Modelling, Springer.

Øksendal, B. (2003). Fractional Brownian motion in finance. Preprint series. Pure mathematics http://urn. nb. no/URN: NBN: no-8076.

Oksendal, B. (2013). Stochastic differential equations: an introduction with applications. Springer Science & Business Media.

Pikovsky, I., & Karatzas, I. (1996). Anticipative portfolio optimization. Advances in Applied Probability, 1095-1122.

Protter, P.E., 2005, Stochastic Integration and Differential Equations, Springer.

Revuz, D., and Yor, M., 1999, Continuous Martingales and Brownian Motion, 3rd Ed., Springer.

Rogers, L.C.G. and Williams D., 1994, Diffusions, Markov Processes and Martingales, Vol. 2: Ito Calculus, Cambridge University Press.)

Ross, S.M., 1980, Introduction to Probability Models, 2nd Ed., Academic Press.

Rouah, F. D. (2013). The Heston model and its extensions in Matlab and C. John Wiley & Sons.

Royden, H.L., 1968, Real Analysis, 2nd Ed., MacMillan.

Schachermayer, W., & Teichmann, J. (2008). How close are the option pricing formulas of Bachelier and Black–Merton–Scholes?. Mathematical Finance: An International Journal of Mathematics, Statistics and Financial Economics, 18(1), 155-170.

Schönbucher, 2003, Credit Derivatives Pricing Models: Models, Pricing and Implementation, Wiley Finance.

Schwartz, E., and Smith, J. E., 2000, “Short-term variations and long-term dynamics in Commodity Prices,” Management Science, 46(7), 893-911.

Shreve, S.E., 2004, Stochastic Calculus for Finance II, Springer.

Stein, E.M., and Stein, J.C., 1991, “Stock Price Distributions with Stochastic Volatility: An Analytic Approach,” Review of Financial Studies, Vol. 4, No. 4, 727-752.

Suchard, J. A. (2005). The use of stand alone warrants as unique capital raising instruments. Journal of Banking & Finance, 29(5), 1095-1112.

Vasicek, O.A., 1977, “An Equilibrium Characterization of the Term Structure,” Journal of Finance, 5, 177-188.

Wong, B., and Heyde, C.C., 2006, “On Changes of Measure in Stochastic Volatility Models,” Journal of Applied Mathematics and Stochastic Analysis, 1-13.

6. Course Evaluation & Development

Feedback is regularly sought from students and continual improvements are made based on this feedback. At the end of this course, you will be asked to complete the myExperience survey, which provides a key source of student evaluative feedback. Your input into this quality enhancement process is extremely valuable in assisting us to meet the needs of our students and provide an effective and enriching learning experience. The results of all surveys are carefully considered and do lead to action towards enhancing educational quality.

Feedback from previous students indicated that the lecturer sometimes speaks too quickly. As a result of this feedback, the lecturer is careful about speaking slowly and clearly.

7. Course Schedule

Note: for more information on the UNSW academic calendar and key dates including study period, exam, supplementary exam and result release, please visit: https://student.unsw.edu.au/new-calendar-dates

Week	Activity	Topic	Assessment/Other
Week 1: 13 September	Lectures	Measure Theory & Stochastic Processes	–
Week 2: 20 September	Lectures	Stochastic Integration & Girsanov’s Theorem	–
Week 3: 27 September	Lectures	The Black-Scholes Partial Differential Equation (PDE)	–
Week 4: 4 October	Lectures	Applications of the Black-Scholes PDE	–
Week 4: 4 October	Assessment	–	First Assignment
Week 5: 11 October	Lectures	Portfolio Optimisation-Part 1	–
Week 6: 18 October	Lectures	No lectures this week.	–
Week 7: 25 October	Lectures	Portfolio Optimisation & Intertemporal CAPM	–
Week 7: 25 October	Assessment	–	Second Assignment
Week 8: 1 November	Lectures	Mean-reversion	–
Week 9: 8 November	Lectures	Jump Processes OR Stochastic Volatility	–
Week 10: 15 November	Lectures	Regime-Switching	–
Week 10: 15 November	Assessment	–	Third Assignment
Term Break: 22 November	–	–	–
Exam Period: 29 November	Assessment	–	Paper Review

8. Policies and Support

Information about UNSW Business School program learning outcomes, academic integrity, student responsibilities and student support services. For information regarding special consideration and viewing final exam scripts, please go to the key policies and support page.

Program Learning Outcomes

The Business School places knowledge and capabilities at the core of its curriculum via seven Program Learning Outcomes (PLOs). These PLOs are systematically embedded and developed across the duration of all coursework programs in the Business School.

PLOs embody the knowledge, skills and capabilities that are taught, practised and assessed within each Business School program. They articulate what you should know and be able to do upon successful completion of your degree.

Upon graduation, you should have a high level of specialised business knowledge and capacity for responsible business thinking, underpinned by ethical professional practice. You should be able to harness, manage and communicate business information effectively and work collaboratively with others. You should be an experienced problem-solver and critical thinker, with a global perspective, cultural competence and the potential for innovative leadership.

All UNSW programs and courses are designed to assess the attainment of program and/or course level learning outcomes, as required by the UNSW Assessment Design Procedure. It is important that you become familiar with the Business School PLOs, as they constitute the framework which informs and shapes the components and assessments of the courses within your program of study.

PLO 1: Business knowledge

Students will make informed and effective selection and application of knowledge in a discipline or profession, in the contexts of local and global business.

PLO 2: Problem solving

Students will define and address business problems, and propose effective evidence-based solutions, through the application of rigorous analysis and critical thinking.

PLO 3: Business communication

Students will harness, manage and communicate business information effectively using multiple forms of communication across different channels.

PLO 4: Teamwork

Students will interact and collaborate effectively with others to achieve a common business purpose or fulfil a common business project, and reflect critically on the process and the outcomes.

PLO 5: Responsible business practice

Students will develop and be committed to responsible business thinking and approaches, which are underpinned by ethical professional practice and sustainability considerations.

PLO 6: Global and cultural competence

Students will be aware of business systems in the wider world and actively committed to recognise and respect the cultural norms, beliefs and values of others, and will apply this knowledge to interact, communicate and work effectively in diverse environments.

PLO 7: Leadership development

Students will develop the capacity to take initiative, encourage forward thinking and bring about innovation, while effectively influencing others to achieve desired results.

These PLOs relate to undergraduate and postgraduate coursework programs. For PG Research PLOs, including Master of Pre-Doctoral Business Studies, please refer to the UNSW HDR Learning Outcomes

Business School course outlines provide detailed information for students on how the course learning outcomes, learning activities, and assessment/s contribute to the development of Program Learning Outcomes.

UNSW Graduate Capabilities

The Business School PLOs also incorporate UNSW graduate capabilities, a set of generic abilities and skills that all students are expected to achieve by graduation. These capabilities articulate the University’s institutional values, as well as future employer expectations.

UNSW Graduate Capabilities	Business School PLOs
Scholars capable of independent and collaborative enquiry, rigorous in their analysis, critique and reflection, and able to innovate by applying their knowledge and skills to the solution of novel as well as routine problems.	PLO 1: Business knowledge PLO 2: Problem solving PLO 3: Business communication PLO 4: Teamwork PLO 7: Leadership development
Entrepreneurial leaders capable of initiating and embracing innovation and change, as well as engaging and enabling others to contribute to change	PLO 1: Business knowledge PLO 2: Problem solving PLO 3: Business communication PLO 4: Teamwork PLO 6: Global and cultural competence PLO 7: Leadership development
Professionals capable of ethical, self-directed practice and independent lifelong learning	PLO 1: Business knowledge PLO 2: Problem solving PLO 3: Business communication PLO 5: Responsible business practice
Global citizens who are culturally adept and capable of respecting diversity and acting in a socially just and responsible way.	PLO 1: Business knowledge PLO 2: Problem solving PLO 3: Business communication PLO 4: Teamwork PLO 5: Responsible business practice PLO 6: Global and cultural competence

While our programs are designed to provide coverage of all PLOs and graduate capabilities, they also provide you with a great deal of choice and flexibility. The Business School strongly advises you to choose a range of courses that assist your development against the seven PLOs and four graduate capabilities, and to keep a record of your achievements as part of your portfolio. You can use a portfolio as evidence in employment applications as well as a reference for work or further study. For support with selecting your courses contact the UNSW Business School Student Services team.

Academic Integrity and Plagiarism

Academic Integrity is honest and responsible scholarship. This form of ethical scholarship is highly valued at UNSW. Terms like Academic Integrity, misconduct, referencing, conventions, plagiarism, academic practices, citations and evidence based learning are all considered basic concepts that successful university students understand. Learning how to communicate original ideas, refer sources, work independently, and report results accurately and honestly are skills that you will be able to carry beyond your studies.

The definition of academic misconduct is broad. It covers practices such as cheating, copying and using another person’s work without appropriate acknowledgement. Incidents of academic misconduct may have serious consequences for students.

Plagiarism

UNSW regards plagiarism as a form of academic misconduct. UNSW has very strict rules regarding plagiarism. Plagiarism at UNSW is using the words or ideas of others and passing them off as your own. All Schools in the Business School have a Student Ethics Officer who will investigate incidents of plagiarism and may result in a student’s name being placed on the Plagiarism and Student Misconduct Registers.

Below are examples of plagiarism including self-plagiarism:

Copying: Using the same or very similar words to the original text or idea without acknowledging the source or using quotation marks. This includes copying materials, ideas or concepts from a book, article, report or other written document, presentation, composition, artwork, design, drawing, circuitry, computer program or software, website, internet, other electronic resource, or another person's assignment, without appropriate acknowledgement of authorship.

Inappropriate Paraphrasing: Changing a few words and phrases while mostly retaining the original structure and/or progression of ideas of the original, and information without acknowledgement. This also applies in presentations where someone paraphrases another’s ideas or words without credit and to piecing together quotes and paraphrases into a new whole, without appropriate referencing.

Collusion: Presenting work as independent work when it has been produced in whole or part in collusion with other people. Collusion includes:

Students providing their work to another student before the due date, or for the purpose of them plagiarising at any time
Paying another person to perform an academic task and passing it off as your own
Stealing or acquiring another person’s academic work and copying it
Offering to complete another person’s work or seeking payment for completing academic work

Collusion should not be confused with academic collaboration (i.e., shared contribution towards a group task).

Inappropriate Citation: Citing sources which have not been read, without acknowledging the 'secondary' source from which knowledge of them has been obtained.

Self-Plagiarism: ‘Self-plagiarism’ occurs where an author republishes their own previously written work and presents it as new findings without referencing the earlier work, either in its entirety or partially. Self-plagiarism is also referred to as 'recycling', 'duplication', or 'multiple submissions of research findings' without disclosure. In the student context, self-plagiarism includes re-using parts of, or all of, a body of work that has already been submitted for assessment without proper citation.

To see if you understand plagiarism, do this short quiz: https://student.unsw.edu.au/plagiarism-quiz

Cheating

The University also regards cheating as a form of academic misconduct. Cheating is knowingly submitting the work of others as their own and includes contract cheating (work produced by an external agent or third party that is submitted under the pretences of being a student’s original piece of work). Cheating is not acceptable at UNSW.

If you need to revise or clarify any terms associated with academic integrity you should explore the 'Working with Academic Integrity' self-paced lessons available at: https://student.unsw.edu.au/aim.

For UNSW policies, penalties, and information to help you avoid plagiarism see: https://student.unsw.edu.au/plagiarism as well as the guidelines in the online ELISE tutorials for all new UNSW students: http://subjectguides.library.unsw.edu.au/elise. For information on student conduct see: https://student.unsw.edu.au/conduct.

For information on how to acknowledge your sources and reference correctly, see: https://student.unsw.edu.au/referencing. If you are unsure what referencing style to use in this course, you should ask the lecturer in charge.

Student Responsibilities and Conduct

Students are expected to be familiar with and adhere to university policies in relation to class attendance and general conduct and behaviour, including maintaining a safe, respectful environment; and to understand their obligations in relation to workload, assessment and keeping informed.

Information and policies on these topics can be found on the 'Managing your Program' website.

Workload

It is expected that you will spend at least ten to twelve hours per week studying for a course except for Summer Term courses which have a minimum weekly workload of twenty to twenty four hours. This time should be made up of reading, research, working on exercises and problems, online activities and attending classes. In periods where you need to complete assignments or prepare for examinations, the workload may be greater. Over-commitment has been a cause of failure for many students. You should take the required workload into account when planning how to balance study with employment and other activities.

We strongly encourage you to connect with your Moodle course websites in the first week of semester. Local and international research indicates that students who engage early and often with their course website are more likely to pass their course.

View more information on expected workload

Attendance and Engagement

Your regular attendance and active engagement in all scheduled classes and online learning activities is expected in this course. Failure to attend / engage in assessment tasks that are integrated into learning activities (e.g. class discussion, presentations) will be reflected in the marks for these assessable activities. The Business School may refuse final assessment to those students who attend less than 80% of scheduled classes where attendance and participation is required as part of the learning process (e.g. tutorials, flipped classroom sessions, seminars, labs, etc.). If you are not able to regularly attend classes, you should consult the relevant Course Authority.

View more information on attendance

General Conduct and Behaviour

You are expected to conduct yourself with consideration and respect for the needs of your fellow students and teaching staff. Conduct which unduly disrupts or interferes with a class, such as ringing or talking on mobile phones, is not acceptable and students may be asked to leave the class.

View more information on student conduct

Health and Safety

UNSW Policy requires each person to work safely and responsibly, in order to avoid personal injury and to protect the safety of others.

View more information on Health and Safety

Keeping Informed

You should take note of all announcements made in lectures, tutorials or on the course web site. From time to time, the University will send important announcements to your university e-mail address without providing you with a paper copy. You will be deemed to have received this information. It is also your responsibility to keep the University informed of all changes to your contact details.

Student Support and Resources

The University and the Business School provide a wide range of support services and resources for students, including:

Business School Learning Support Tools
Business School provides support a wide range of free resources and services to help students in-class and out-of-class, as well as online. These include:

Academic Communication Essentials – A range of academic communication workshops, modules and resources to assist you in developing your academic communication skills.
Learning consultations – Meet learning consultants who have expertise in business studies, literacy, numeracy and statistics, writing, referencing, and researching at university level.
PASS classes – Study sessions facilitated by students who have previously and successfully completed the course.
Educational Resource Access Scheme – To support the inclusion and success of students from equity groups enrolled at UNSW Sydney in first year undergraduate Business programs.

The Nucleus - Business School Student Services team
The Nucleus Student Services team provides advice and direction on all aspects of enrolment and graduation. Level 2, Main Library, Kensington 02 8936 7005 / https://nucleus.unsw.edu.au/en/contact-us

Business School Equity, Diversity and Inclusion
The Business School Equity, Diversity and Inclusion Committee strives to ensure that every student is empowered to have equal access to education. The Business School provides a vibrant, safe, and equitable environment for education, research, and engagement that embraces diversity and treats all people with dignity and respect. BUSEDI@unsw.edu.au

UNSW Academic Skills
Resources and support – including workshops, individual consultations and a range of online resources – to help you develop and refine your academic skills. See their website for details.
academicskills@unsw.edu.au

Student Support Advisors
Student Support Advisors work with all students to promote the development of skills needed to succeed at university, whilst also providing personal support throughout the process.
John Goodsell Building, Ground Floor.
advisors@unsw.edu.au
02 9385 4734

International Student Support
The International Student Experience Unit (ISEU) is the first point of contact for international students. ISEU staff are always here to help with personalised advice and information about all aspects of university life and life in Australia.
Advisors can support you with your student visa, health and wellbeing, making friends, accommodation and academic performance.
International.student@unsw.edu.au
02 9385 4734

Equitable Learning Services
Equitable Learning Services (formerly Disability Support Services) is a free and confidential service that provides practical support to ensure that your health condition doesn't adversely affect your studies. Register with the service to receive educational adjustments.
Ground Floor, John Goodsell Building.
els@unsw.edu.au
02 9385 4734

UNSW Counselling and Psychological Services
Provides support and services if you need help with your personal life, getting your academic life back on track or just want to know how to stay safe, including free, confidential counselling.
Level 2, East Wing, Quadrangle Building.
counselling@unsw.edu.au
02 9385 5418

Library services and facilities for students
The UNSW Library offers a range of collections, services and facilities both on-campus and online.
Main Library, F21.
02 9065 9444

Moodle eLearning Support
Moodle is the University’s learning management system. You should ensure that you log into Moodle regularly.
externalteltsupport@unsw.edu.au
02 9385 3331

UNSW IT
UNSW IT provides support and services for students such as password access, email services, wireless services and technical support.
UNSW Library Annexe (Ground floor).
02 9385 1333

Support for Studying Online

The Business School and UNSW provide a wide range of tools, support and advice to help students achieve their online learning goals.

The UNSW Guide to Online Study page provides guidance for students on how to make the most of online study.

We recognise that completing quizzes and exams online can be challenging for a number of reasons, including the possibility of technical glitches or lack of reliable internet. We recommend you review the Online Exam Preparation Checklist of things to prepare when sitting an online exam.

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Accreditation

FINS4781 Continuous-Time Finance - 2021

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1. Course Details

Summary of Course

Teaching Times and Locations

Course Policies & Support

Course Aims and Relationship to Other Courses

Student Learning Outcomes

2. Staff Contact Details

3. Learning and Teaching Activities

Approach to Learning and Teaching in the Course

Learning Activities and Teaching Strategies

4. Assessment

Formal Requirements

Assessment Structure

Assessment Summary

Assignment Submission Procedure

Assessment Feedback

Special Consideration

Protocol for Viewing Final Exam Scripts

Quality Assurance

5. Course Resources

6. Course Evaluation & Development

7. Course Schedule

8. Policies and Support

UNSW Graduate Capabilities

Plagiarism

Cheating

Workload

Attendance and Engagement

General Conduct and Behaviour

Health and Safety

Keeping Informed

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