Bayes推断和神经网络求解美式回望期权的隐含波动率

Solving Implied Volatility of American Lookback Options byBayesian Inference and Neural Network

首先,用原始对偶活跃集方法求解期权定价正问题,将相应的数值解作为监督学习的输出,然后用训练好的神经网络替代期权定价正问题模型.其次,结合Bayes推断与神经网络进行Metropolis-Hastings采样,求解隐含波动率反问题.该方法减少了采样过程中正问题计算量庞大的问题,从而加速了反问题求解过程.

Firstly,we used the original dual active set method to solve the forward problem of option pricing,with the corresponding numerical solutions as the output for supervised learning,and then replaced the forward problem model of option pricing with a well-trained neural network.Secondly,we combined Bayesian inference with neural networks for Metropolis-Hastings sampling to solve the inverse problem of implied volatility.This method reduced the problem of large computational complexity of the forward problem during the sampling process,thereby accelerating the solution process for the inverse problem.