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Mixed Lognormal Distributions for Derivatives Pricing and Risk-Management

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  • Dietmar Leisen

Abstract

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

Suggested Citation

  • Dietmar Leisen, 2004. "Mixed Lognormal Distributions for Derivatives Pricing and Risk-Management," Computing in Economics and Finance 2004 48, Society for Computational Economics.
    • Handle: RePEc:sce:scecf4:48
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    More about this item

    Keywords

    mixed lognormal distribution; jump-diffusion; stochastic volatility; Greeks; risk-management;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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