Pricing and hedging of derivatives in contagious markets

It is well documented that stock markets are contagious. A negative shock to one market increases the probability of adverse shocks to other markets. We model this contagion effect by including mutually exciting jump processes in the dynamics of the indexes' log-returns. On top of this we add a stochastic volatility component to the dynamics. It is important to take the contagion effect into account if derivatives written on a basket of assets are to be priced or hedged. Due to the affine model specification the joint characteristic function of the log-returns is known analytically, and for two specifications we detail how the model can be calibrated efficiently to option prices. In total we calibrate over an extended period of time the specifications to options data on four US stock indexes, and show how the models achieve satisfactory pricing errors. We study the effect of contagion on multi-asset derivatives prices and show how for certain derivatives the impact is heavy. Moreover, we derive hedge ratios for European put and call options and perform a numerical experiment, which illustrates the impact of contagious jumps on option prices and hedge ratios. Mutually exciting processes have been analyzed for multivariate intensity modeling for the purpose of credit derivatives pricing, but have not been used for pricing/hedging options on equity indexes.