Steven L. Heston 的 随机波动率经典模型是期权定价最经典的理论模型，尤其重要的是对于标的资产波动率固定的假设：
1）期权的价格可以体现在隐含波动率中；
2）期权的隐含波动率一般是变化的；
3）行权价格和到期时间不同的期权合约，其隐含波动率通常也会不同。
4）从与B-S模型的假设不相符另外的视角提出问题和研究问题。

原文分享，以飧共同学习研究。



Abstract


I use a new technique to derive a closed-form solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spot-asset returns. I introduce stochastic interest rates and show how to apply the model to bond options and foreign currency options. Simulations show that correlation between volatility and the spot asset's price is important for explaining return skewness and strike-price biases in the Black-Scholes (1973) model. The solution technique is based on characteristic functions and can be applied to other problems.