Asset Pricing in the Derivatives Market

Derivative securities provide an important tool for the investors to protect themselves against market risks in the future. This course concentrates on the theory of pricing and hedging by means of the no-arbitrage theory introduced by Black and Scholes. We first study the case of finite discrete-time financial markets: after characterizing financial markets which contain no arbitrage opportunities, we study the minimal cost of super-hedging some given contingent claim, and we show that this solves the hedging, pricing, and portfolio allocation problems in the context of complete markets.
We next turn to continuous-time financial markets, which can be viewed as the limit of finite discrete-time markets when the time step shrinks to zero. This leads naturally to the Brownian motion as the continuous-time limit of the scaled random walk. We provide an introduction to the main concepts from stochastic calculus which are needed for the understanding of the Black-Scholes pricing and hedging model for Vanilla and barrier options, and we present an overview of the Gaussian Heath-Jarrow-Morton model for the term structure of interest rates.