Abstract: This book presents an introduction to arbitrage theory and its applications to problems for financial derivatives. This second edition includes more advanced materials; appendices on measure theory, probability theory, and martingale theory; and a new chapter on the martingale approach to arbitrage theory. The chapters cover the binomial model, a general one period model, stochastic integrals, differential equations, portfolio dynamics, arbitrage pricing, completeness and hedging, parity relations and delta hedging, the martingale approach, incomplete markets, dividends, currency derivatives, barrier options, stochastic optimal control, bonds and interest rates, short rate models, forward rate models, and LIBOR and swap market models.

Keywords: arbitrage theory, financial derivatives, martingale approach