Importance sampling applied to Greeks for jump-diffusion models with stochastic volatility

被引:0
作者
De Diego, Sergio [1 ]
Ferreira, Eva [1 ]
Nualart, Eulalia [2 ,3 ]
机构
[1] Univ Basque Country, Fac Ciencias Econ & Empresariales, Dept Econ Aplicada 3, Ave Lehendakari,Aguirre 83, Bilbao 48015, Spain
[2] Univ Pompeu Fabra, Dept Econ & Business, Ramon Trias Fargas 25-27, Barcelona 08005, Spain
[3] Univ Pompeu Fabra, Barcelona Grad Sch Econ, Ramon Trias Fargas 25-27, Barcelona 08005, Spain
关键词
option pricing; Esscher transform; Malliavin calculus; Robbins-Monro algorithm; LEVY PROCESSES; APPROXIMATION; CALCULUS; MARKET;
D O I
10.21314/JCF.2018.348
中图分类号
F8 [财政、金融];
学科分类号
0202 ;
摘要
We develop a variance reduction technique, based on importance sampling in conjunction with the stochastic Robbins-Monro algorithm, for option prices of jump-diffusion models with stochastic volatility. This is done by combining the work developed by Arouna for pricing diffusion models, and extended by Kawai for Levy processes without a Brownian component. We apply this technique to improve the numerical computation of derivative price sensitivities for general Levy processes, allowing both Brownian and jump parts. Numerical examples are performed for both the Black-Scholes and Heston models with jumps and for the Barndorff-Nielsen-Shephard model to illustrate the efficiency of this numerical technique. The numerical results support that the proposed methodology improves the efficiency of the usual Monte Carlo procedures.
引用
收藏
页码:79 / 105
页数:27
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