跳跃扩散的智能扩展和快速标定
Smart expansion and fast calibration for jump diffusion
摘要：
利用Malliavin演算技术，我们得到了一个解析的欧式期权的价格公式，对于任何模型，包括局部波动率和泊松跳跃过程。我们表明，该公式的准确性取决于支付函数的光滑性。我们的方法依赖于小扩散和小跳跃频率/大小相关的渐近展开。我们的公式具有很好的精度（对于不同的执行价格和到期日，看涨期权的隐含Black-Scholes波动率误差小于2 bp）。此外，模型校准变得非常迅速。
英文摘要：
Using Malliavin calculus techniques, we derive an analytical formula for the price of European options, for any model including local volatility and Poisson jump process. We show that the accuracy of the formula depends on the smoothness of the payoff function. Our approach relies on an asymptotic expansion related to small diffusion and small jump frequency/size. Our formula has excellent accuracy (the error on implied Black-Scholes volatilities for call option is smaller than 2 bp for various strikes and maturities). Additionally, model calibration becomes very rapid.
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