Analytical approximations of local‐Heston volatility model and error analysis
研究含局部波动率成分的随机波动率模型中期权价格的展开式，利用Malliavin微积分给出严格误差估计，并针对看涨看跌期权推导出隐含波动率的简单快速计算公式。
Abstract This paper studies the expansion of an option price (with bounded Lipschitz payoff) in a stochastic volatility model including a local volatility component. The stochastic volatility is a square root process, which is widely used for modeling the behavior of the variance process (Heston model). The local volatility part is of general form, requiring only appropriate growth and boundedness assumptions. We rigorously establish tight error estimates of our expansions, using Malliavin calculus. The error analysis, which requires a careful treatment because of the lack of weak differentiability of the model, is interesting on its own. Moreover, in the particular case of call–put options, we also provide expansions of the Black–Scholes implied volatility that allow to obtain very simple formulas that are fast to compute compared to the Monte Carlo approach and maintain a very competitive accuracy.