G63.2792.001 Continuous Time Finance
Teaching assistant: Stanley Zhang
Office: Warren Weaver Hall, room 608
Phone: 646-894-1016
Email: stanley AT cims.nyu.edu
Office hours: TBD and by appointment

Prerequisites: Derivative Securities and Stochastic Calculus, or equivalent.

Content: This is a "second course" in arbitrage-based pricing of derivative securities.  We start by deriving the Black-Scholes-Merton model and its generalizations.  Topics we cover include equivalent martingale measures, the martingale representation theorem, the market price of risk, applications including change of numeraire and the analysis of quantos.  We see that in order to accounting for the volatility smile/skew one needs models incorporating jumps, local volatility models, and stochastic volatility models. As we turn to interest rate models, we discuss the Heath-Jarrow-Morton approach and its relation to short-rate models, affine models, and some applications including mortgage-backed securities.

Course requirements: There will be several homework sets, approximately one every other week. Collaboration on homework is encouraged but registered students must write up and turn in their solutions individually. If you work together, please list collaborators on your homework. There will be one in-class final exam. Your grade will be based on the final exam (70%) and homework (30%).

Communication:  All material, homework and announcements related to the class will be posted on the NYU Blackboard Course Site. The Blackboard Course Site has a message board for the class. Please post any questions related to the homework on that message board rather than emailing them to me or the TA. Of course, you may contact me directly for personal questions.

Textbook: Steven E. Shreve, Stochastic Calculus for Finance II: Continuous-Time Models, Springer, 2004. The book is available in hardcover only and copies can be purchased at the Campus bookstore.

Recommended reading (optional):
Martin Baxter and Andrew Rennie, Financial Calculus: An Introduction to Derivative Pricing, Cambridge University Press, 1996.

Tomas Bjork, Arbitrage Theory in Continuous Time, Oxford University Press, 2004.

Darrell Duffie, Dynamic Asset Pricing Theory, Princeton University Press, 2001.

Jessica James and Nick Webber, Interest Rate Modelling, Wiley, 2000.

Robert C. Merton, Continuous-Time Finance, Blackwell Pub, 1990.

Marek Musiela and Marek Rutkowski, Martingale Methods in Financial Modelling, Springer, 2007.

J. Michael Steele, Stochastic Calculus and Financial Applications, Springer, 2003.