Pricing Barrier and Average Options Under Stochastic Volatility Environment
Pricing Barrier and Average Options Under Stochastic Volatility Environment
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DOI：
10.2139/ssrn.1491937
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发表时间：
2009-10
期刊：
影响因子：
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通讯作者：
Kenichiro Shiraya;Akihiko Takahashi;M. Toda
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文献类型：
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作者：
Kenichiro Shiraya;Akihiko Takahashi;M. Toda
利用渐近展开方法，给出了随机波动率环境下障碍期权和平均期权定价的一种新的近似方法。特别是，一般的多维扩散过程的高阶展开格式是有效的应用。此外，本文结合静态套期保值方法和渐近展开方法对障碍期权进行定价。最后，数值算例表明，四阶或五阶渐近展开格式提供了足够准确的近似下的Aprida-SABR和SABR模型。
This paper proposes a new approximation method of pricing barrier and average options under stochastic volatility environment by applying an asymptotic expansion approach. In particular, a high-order expansion scheme for general multi-dimensional diffusion processes is effectively applied. Moreover, the paper combines a static hedging method with the asymptotic expansion method for pricing barrier options. Finally, numerical examples show that the fourth or fifth-order asymptotic expansion scheme provides sufficiently accurate approximations under the lambda-SABR and SABR models.