Variance reduction for Monte Carlo methods to evaluate option prices under multi-factor stochastic volatility models. (English) Zbl 1405.91692
Summary: We present variance reduction methods for Monte Carlo simulations to evaluate European and Asian options in the context of multiscale stochastic volatility models. European option price approximations, obtained from singular and regular perturbation analysis [the first author et al., Multiscale Model. Simul. 2, No. 1, 22–42 (2004; Zbl 1074.91015)], are used in importance sampling techniques, and their efficiencies are compared. Then, we investigate the problem of pricing arithmetic average Asian options (AAOs) by Monte Carlo simulations. A two-step strategy is proposed to reduce the variance where geometric average Asian options (GAOs) are used as control variates. Due to the lack of analytical formulas for GAOs under stochastic volatility models, it is then necessary to consider efficient Monte Carlo methods to estimate the unbiased means of GAOs. The second step consists in deriving formulas for approximate prices based on perturbation techniques, and in computing GAOs by using importance sampling. Numerical results illustrate the efficiency of our method.
MSC:
| 91G60 | Numerical methods (including Monte Carlo methods) |
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 65C05 | Monte Carlo methods |
Citations:
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