Mixed Lognormal Distributions for Derivatives Pricing and Risk-Management
AbstractMany 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
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Bibliographic InfoPaper provided by Society for Computational Economics in its series Computing in Economics and Finance 2004 with number 48.
Date of creation: 11 Aug 2004
Date of revision:
mixed lognormal distribution; jump-diffusion; stochastic volatility; Greeks; risk-management;
Find related papers by 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-08-16 (All new papers)
- NEP-FIN-2004-08-16 (Finance)
- NEP-RMG-2004-08-16 (Risk Management)
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