Numerical Pricing and Hedging of Contingent Claims
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This chapter introduces numerical methods for calculating prices and replication strategies of contingent claims. Only a few options can be priced and hedged explicitly, for instance, call and put options. For path-dependent derivatives like barrier and average (Asian) options there does not exist any explicit formula, and a numerical approach is necessary to evaluate them. We will introduce techniques based on Monte Carlo simulations of the risk-neutral expectation defining the derivatives price, and so-called finite-difference methods which numerically solve the Black & Scholes partial differential equation (4.12). Both approaches work for claims with payoff of the form f(S(T)), while the former is also applicable for more general claims.1
KeywordsStock Price Finite Difference Method Payoff Function Call Option Contingent Claim
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