Abstract
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, so that a jump in one market increases the intensities of more jumps in the same market and in other markets. Between jumps the intensities revert to their long-run means. 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 using Fourier transform methods. In total we calibrate the specifications to options data on three indexes; the SPX, the SX5E and the NKY, and investigate the effect of contagion on multi-asset derivatives prices. In order to reduce computational time, the calibration is performed in two steps. First, the parameters of the mutually exciting processes are calibrated for the indexes simultaneously to data for the shortest maturity options. Second, the stochastic volatility dynamics are calibrated to the whole option surface on each index independently. 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.
[PDF] Slides of the presentation.