**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.