Valuing Exotic Options and Estimating Model Risk

A common approach to valuing exotic options involves choosing a model and then determining its parameters to fit the volatility surface as closely as possible. We refer to this as the model calibration approach (MCA). This paper considers an alternative approach where the points on the volatility surface are features input to a neural network. We refer to this as the volatility feature approach (VFA). We conduct experiments showing that VFA can be expected to outperform MCA for the volatility surfaces encountered in practice. Once the upfront computational time has been invested in developing the neural network, the valuation of exotic options using VFA is very fast. VFA is a useful tool for the estimation of model risk. We illustrate this using S&P 500 data for the 2001 to 2019 period.