MA 366a: Introduction to Stochastic Finance
Credits: 3:0
Prerequisites :
- It is desirable to have taken MA 262 Introduction to Stochastic Processes and MA 361 Probability Theory or equivalent. Students who have not taken this course can also register for this course. They must then learn the introductory probability material covered in the first three chapters of Introduction to Stochastic Finance Vol II by Shreve before discrete time option pricing is covered in the course.
Financial market. Financial instruments: bonds, stocks, derivatives. Discrete Time Models: Single and multi-period Binomial no-arbitrage pricing model, Martingale methods for pricing. Interest rate-dependent assets: binomial models for interest rates, fixed income derivatives, forward measure and future. Capital asset pricing model (CAPM). Continuous time Models: geometric Brownian motion and Ito calculus. Option pricing and hedging in continuous time: Black-Scholes theory, risk-neutral pricing, fundamental theorem of asset pricing, Feynman-Kac formula and connections to partial differential equations, term-structure models, option pricing in incomplete markets: Merton’s jump diffusion and Heston’s models.
Suggested books and references:
- Shreve, S.E., Stochastic Calculus for Finance I : The Binomial Asset Pricing Model, Springer, 2005.
- Shreve, S.E., Stochastic Calculus for Finance II : The continous Time Models, Springer, 2004.
- Shiryaev, A.N., Essentials of Stochastic Finance, World Scientific, 1999.