论文标题
通过Malliavin演算在一般随机波动式框架中明确的期权价格近似值
Explicit approximations of option prices via Malliavin calculus in a general stochastic volatility framework
论文作者
论文摘要
我们获得了具有时间相关参数的一般随机波动率模型中的欧洲PUT期权价格的显式近似公式。我们的方法涉及编写PUT期权价格作为对黑色choles公式的期望，对波动率过程进行重新聚光，然后进行许多扩展。这项工作的大部分是由于显式计算扩展程序引起的许多期望，我们通过吸引Malliavin Colculus的技术来实现。我们获得了扩展过程产生的误差的明确表示，并根据基础波动过程的功能矩进行束缚。在分段恒定参数的假设下，我们的近似公式变为封闭形式，此外，我们能够建立快速校准方案。此外，我们执行了数值敏感性分析，以研究所谓的随机Verhulst模型中近似公式的质量，并证明出于应用目的，这些误差符合可接受的范围内。
We obtain an explicit approximation formula for European put option prices within a general stochastic volatility model with time-dependent parameters. Our methodology involves writing the put option price as an expectation of a Black-Scholes formula, reparameterising the volatility process and then performing a number of expansions. The bulk of the work is due to computing a number of expectations induced by the expansion procedure explicitly, which we achieve by appealing to techniques from Malliavin calculus. We obtain the explicit representation of the error generated by the expansion procedure, and bound it in terms of moments of functionals of the underlying volatility process. Under the assumption of piecewise-constant parameters, our approximation formulas become closed-form, and moreover we are able to establish a fast calibration scheme. Furthermore, we perform a numerical sensitivity analysis to investigate the quality of our approximation formula in the so-called Stochastic Verhulst model, and show that the errors are well within the acceptable range for application purposes.
