Chapter 2: FAQs 163
Stochastic volatility models have greater potential for
capturing dynamics, but the problem, as always, is
knowing which stochastic volatility model to choose and
how to find its parameters. When calibrated to market
prices you will still usually find that supposed constant
parameters in your model keep changing. This is often
the case with calibrated models and suggests that the
model is still not correct, even though its complexity
seems to be very promising.
Jump-diffusion models allow the stock (and even the
volatility) to be discontinuous. Such models contain
so many parameters that calibration can be instan-
taneously more accurate (if not necessarily stable
through time).
References and Further Reading
Gatheral, J 2006The Volatility Surface. John Wiley & Sons
Javaheri, A 2005Inside Volatility Arbitrage. John Wiley & Sons
Taylor, SJ & Xu, X 1994 The magnitude of implied volatility
smiles: theory and empirical evidence for exchange rates.
The Review of Futures Markets 13
Wilmott, P 2006Paul Wilmott On Quantitative Finance, second
edition. John Wiley & Sons
