Local and Stochastic Volatility Models

With the fast development of derivatives and structured products, advanced models are needed to improve the pricing and valuation accuracy as well as the hedging efficiency. As indicated in Sect. 14.5.4 , the P/L of a delta-hedged option is not flat but is related to the realized gamma and variance. Gamma-hedging improves the hedging P/L but makes the option’s price dependent on the implied volatility that changes during the hedging period. Stochastic volatility models (modelling implied volatility) offer a more consistent pricing and risk management framework compared to simple models such as the BSM that cannot capture the second order and cross derivatives impacts involving volatility.