Explain stochastic volatility

Question

Explain stochastic volatility.

Answer 1

Stochastic volatility: As volatility is not easy to measure, and seems to be forever changing, this is natural to model this as stochastic. The most admired model of this type is because of Heston. These models often have some parameters that can either be chosen to fit historical data or, more usually, chosen in order that theoretical prices calibrate to the market. Such volatility models are better at confining the dynamics of traded option prices better than deterministic models. Nonetheless, different markets behave differently. Part of this is due to the way traders look at option price. FX traders look at implied volatility versus delta and Equity traders look at implied volatility versus strike. Therefore it is natural for implied volatility curves to behave differently within these two markets. Due to this there have grown up the sticky strike and sticky delta, etc., models that model how the implied volatility curve changes when the underlying moves.