Stochastic finance : an introduction with market examples

Preface This text is an introduction to pricing and hedging in discrete and continuous time financial models without friction (i.e. without transaction costs), with an emphasis on the complementarity between analytical and probabilistic methods. Its contents are mostly mathematical, and also aim at making the reader aware of both the power and limitations of mathematical models in finance, by taking into account their conditions of applicability. The book covers a wide range of classical topics including Black-Scholes pricing, exotic and american options, term structure modeling and change of num eraire, as well as models with jumps. It is targeted at the advanced undergraduate and graduate level in applied mathematics, financial engineering, and economics. The point of view adopted is that of mainstream mathematical finance in which the computation of fair prices is based on the absence of arbitrage hypothesis, therefore excluding riskless pro t based on arbitrage opportunities and basic (buying low/selling high) trading. Similarly, this document is not concerned with any "prediction" of stock price behaviors that belong other domains such as technical analysis, which should not be confused with the statistical modeling of asset prices. The text also includes 104 gures and simulations, along with about 20 examples based on actual market data. The descriptions of the asset model, self- nancing portfolios, arbitrage and market completeness, are first given in Chapter 1 in a simple two time-step setting. These notions are then reformulated in discrete time in Chapter 2. Here, the impossibility to access future information is formulated using the notion of adapted processes, which will play a central role in the construction of stochastic calculus in continuous time.