Most option pricing models assume all parameters except volatility are fixed; yet they almost invariably change on re‐calibration. This article explains how to capture the model risk that arises when parameters that are assumed constant have calibrated values that change over time and how to use...

This paper formalizes the class of scale-invariant volatility models and explores its hedging properties. A model is 'scale-invariant' if and only if its probability distribution of asset returns is independent of the current level of the asset price. We provide a set of equivalent properties...

The delta hedging performance of deterministic local volatility models is poor, with most studies showing that even the simple constant volatility Black-Scholes model performs better. But when the local volatility model is extended to capture stochastic dynamics for the spot volatility process,...

There are two unique volatility surfaces associated with any arbitrage-free set of standard European option prices, the implied volatility surface and the local volatility surface. Several papers have discussed the stochastic differential equations for implied volatilities that are consistent...

Different theoretical and numerical methods for calculating the fair-value of a variance swap give rise to systematic biases that are most pronounced during volatile periods. For instance, differences of 10-20 percentage points would have been observed on fair-value index variance swap rates...

Most research on option hedging has compared the performance of delta hedges derived from different stochastic volatility models with Black-Scholes-Merton (BSM) deltas, and in particular with the `implied BSM’ model in which an option’s delta is based on its own market implied volatility....

Conditional returns distributions generated by a GARCH process, which are important for many problems in market risk assessment and portfolio optimization, are typically generated via simulation. This paper extends previous research on analytic moments of GARCH returns distributions in several...