Mixed Lognormal Distributions for Derivatives Pricing

D.P.J. Leisen (Germany)

Keywords

mixed lognormal distribution, jump-diffusion, stochastic volatility, Greeks, risk-management.

Abstract

Many derivatives prices are closed-form expressions in the Black-Scholes model; when the terminal distribution is a mixed lognormal, prices for these derivatives are then a weighted average of these (closed-form) expressions. They can therefore be calculated easily and ef´Čüciently for mixed lognormal distributions. For illustration this paper con structs mixed lognormal distributions that approximate the terminal distribution in the Merton model (Black-Scholes model with jumps).

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