Does Model Misspecification Matter for Hedging? A Computational Finance Experiment Based Approach

To find out whether the model misspecification matters for hedging accuracy, we carefully select six increasingly complicated asset models, i.e., the Black-scholes (BS) model, the Merton model (M), the Heston (H) model, the Heston jump-diffusion model (HJ), the double Heston (dbH) model and the double Heston jump-diffusion model (dbHJ) model, and then impartially evaluate their performances in mitigating the risk of an option, under a controllable experimental market. In experiments, the $\mathbb{P}$ measure asset paths are piecewisely simulated by a hybrid-model (including the Black-Scholes type and the (double) Heston types, with or without jump-diffusion) with randomly given well-defined parameters. We access the hedging accuracy of six models under the dynamic hedging framework of He et al. (2006) and Kennedy et al. (2009), and apply the Fourier-COS-expansion method (COS formula, see F. Fang & C.W. Oosterlee (2008)), to price options and to calculate the Greeks. Extensive numerical results indicate that the model misspecification shows no significant impact on hedging accuracy, but the market fit does matter critically for hedging.