Mixed Lognormal Distributions for Derivatives Pricing and Risk-Management

Many derivatives prices and their Greeks are closed-form expressions in the Black-Scholes model; when the terminal distribution is a mixed lognormal, prices and Greeks for these derivatives are then a weighted average of these closed-form) expressions. They can therefore be calculated easily and efficiently for mixed lognormal distributions. This paper constructs mixed lognormal distributions that approximate the terminal distribution in the Merton model (Black-Scholes model with jumps) and in stochastic volatility models. Main applications are the pricing of large portfolio positions and their risk-management