When a stochastic volatility model is calibrated?

Question

In an Investment Bank, how often a stochastic volatility model is calibrated ? Is it calibrated daily ? Is it calibrated whenever a pricing is required ?

Thanks.

Answer 1

This depends largely on the model as well as the market, so there is no one-size-fits-all approach. Let us take the Stochastic Alpha Beta Rho (SABR) model, which has four parameters, as an example:

• $\alpha$, the initial instantaneous volatility of an ATM option. This is calibrated frequently and often intra-day due to the importance of ATM options.
• $\beta$, which describes the backbone of volatility. This is often chosen a priori and not calibrated.
• $\rho$, which describes the correlation betweent the Brownian motions driving the forward process and its vol proces, respectivelty. This is not calibrated as frequently - perhaps once a week/month depending on the market.
• $\nu$, which is the vol of vol. This is not calibrated as frequently - perhaps once a week/month depending of the market.

Have a look at the initial paper by Pat Hagan et al. for more information!