Most option pricing models assume all parameters except volatility are fixed; yet they almost invariably change on re-calibration. This paper 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...

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...

Fixed income analysts deal constantly with the challenge of mapping their expectations about the macroeconomic environment into movements of the yield curve. This paper assumes that an analyst is able to provide a forecast of a few benchmark yields or combinations of yields. Then it derives a...

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...

A price process is scale-invariant if and only if the returns distribution is independent of the price level. We show that scale invariance preserves the homogeneity of a pay-off function throughout the life of the claim and hence prove that standard price hedge ratios for a wide class of...

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 assumption that the probability distribution of returns is independent of the current level of the asset price is an intuitive property for option pricing models on financial assets. This ‘scale invariance’ feature is common to the Black-Scholes (1973) model, most stochastic volatility...

We derive the local volatility hedge ratios that are consistent with a stochastic instantaneous volatility and show that this ‘stochastic local volatility’ model is equivalent to the market model for implied volatilities. We also show that a common feature of all Markovian single factor...

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,...