Stochastic Finance

Abstract

Introduction Elements of Finance Price Arbitrage Time Value of Assets, Arbitrage and No-Arbitrage Assets Money Market, Bonds, and Discounting Dividends Portfolio Evolution of a Self-Financing Portfolio Fundamental Theorems of Asset Pricing Change of Measure via Radon-Nikodym Derivative Leverage: Forwards and Futures Binomial Models Binomial Model for No-Arbitrage Assets Binomial Model with an Arbitrage Asset Diffusion Models Geometric Brownian Motion General European Contracts Price as an Expectation Connections with Partial Differential Equations Money as a Reference Asset Hedging Properties of European Call and Put Options Stochastic Volatility Models Foreign Exchange Market Interest Rate Contracts Forward LIBOR Swaps and Swaptions Term Structure Models Barrier Options Types of Barrier Options Barrier Option Pricing via Power Options Price of a Down-and-In Call Option Connections with the Partial Differential Equations Lookback Options Connections of Lookbacks with Barrier Options Partial Differential Equation Approach for Lookbacks Maximum Drawdown American Options American Options on No-Arbitrage Assets American Call and Puts on Arbitrage Assets Perpetual American Put Partial Differential Equation Approach Contracts on Three or More Assets: Quantos, Rainbows and Friends Pricing in the Geometric Brownian Motion Model Hedging Asian Options Pricing in the Geometric Brownian Motion Model Hedging of Asian Options Reduction of the Pricing Equations Jump Models Poisson Process Geometric Poisson Process Pricing Equations European Call Option in Geometric Poisson Model Levy Models with Multiple Jump Sizes Appendix: Elements of Probability Theory Solutions to Selected Exercises References Index