Implied parameter estimation for jump diffusion option pricing models: Pricing accuracy and the role of loss and evaluation functions

There is extensive literature on problems involved in estimating implied parameters in the Merton Jump Diffusion model. Using simulated data, we use weighted non-linear least squares to estimate implied parameters in the four parameter jump diffusion model (JD) and in an eight parameter jump diffusion model with convenience yield (JDC). We find reliable and accurate implied parameter estimates for the JD model but biased and unreliable estimates for some parameters in the JDC model. However, for both models we estimate accurate option prices, usually within several basis points. We also use Bitcoin real data to estimate parameters and test the out-of-sample performance of the JDC model.