Numerical Computation of Theta in a Jump-Diffusion Model by Integration by Parts
| Autor: | Delphine David, Nicolas Privault |
|---|---|
| Přispěvatelé: | Financial mathematics (MATHFI), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-École des Ponts ParisTech (ENPC)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12), INRIA, Inria, Rapport De Recherche |
| Jazyk: | angličtina |
| Rok vydání: | 2006 |
| Předmět: |
Mathematical optimization
Generalization Computation Jump diffusion [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH] Malliavin calculus 01 natural sciences 0502 economics and business Applied mathematics Integration by parts SENSITIVITY ANALYSIS 0101 mathematics JUMP-DIFFUSION MODELS Mathematics GREEKS 050208 finance Computational finance Mathematical finance 010102 general mathematics 05 social sciences Stochastic game [INFO.INFO-OH] Computer Science [cs]/Other [cs.OH] MALLIAVIN CALCULUS THETA General Economics Econometrics and Finance Finance |
| Zdroj: | [Research Report] RR-5829, INRIA. 2006, pp.32 |
| Popis: | Using the Malliavin calculus in time inhomogeneous jump-diffusion models, we obtain an expression for the sensitivity Theta of an option price (with respect to maturity) as the expectation of the option payoff multiplied by a stochastic weight. This expression is used to design efficient numerical algorithms that are compared with traditional finite-difference methods for the computation of Theta. Our proof can be viewed as a generalization of Dupire's integration by parts to arbitrary and possibly non-smooth payoff functions. In the time homogeneous case, Theta admits an expression from the Black–Scholes PDE in terms of Delta and Gamma but the representation formula obtained in this way is different from ours. Numerical simulations are presented in order to compare the efficiency of the finite-difference and Malliavin methods. |
| Databáze: | OpenAIRE |
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