Stochastic Finance An Introduction with Market Examples Chapman and Hall/CRC Financial Mathematics Series

Stochastic Finance: An Introduction with Market Examples presents an introduction to pricing and hedging in discrete and continuous time financial models without friction, emphasizing the complementarity of analytical and probabilistic methods. It demonstrates both the power and limitations of mathematical models in finance, covering the basics of finance and stochastic calculus, and builds up to special topics, such as options, derivatives, and credit default and jump processes. It details the techniques required to model the time evolution of risky assets.

The book discusses a wide range of classical topics including Black?Scholes pricing, exotic and American options, term structure modeling and change of numéraire, as well as models with jumps. The author takes the approach adopted by mainstream mathematical finance in which the computation of fair prices is based on the absence of arbitrage hypothesis, therefore excluding riskless profit based on arbitrage opportunities and basic (buying low/selling high) trading.

With 104 figures and simulations, along with about 20 examples based on actual market data, the book is targeted at the advanced undergraduate and graduate level, either as a course text or for self-study, in applied mathematics, financial engineering, and economics.

Assets, Portfolios, and Arbitrage, Discrete-Time Model. Pricing and Hedging in Discrete Time. Brownian Motion and Stochastic Calculus. The Black-Scholes PDE. Martingale Approach to Pricing and Hedging. Estimation of Volatility. Exotic Options. American Options. Change of Numéraire and Forward Measures. Forward Rate Modeling. Pricing of Interest Rate Derivatives. Credit Default. Stochastic Calculus for Jump Processes. Pricing and Hedging in Jump Models. Basic Numerical Methods. Appendix. Exercise Solutions. References. Index.