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...

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...

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...

Several principal component models of volatility smiles and skews have been based on daily changes in implied volatilities, by strike and/or by moneyness. Derman and Kamal (1997) analyze S&P500 and Nikkei 225 index options where the daily change in the volatility surface is specified by delta...

Equity hedge funds are thought to effectively operate market timing by implementing switching strategies conditional on market circumstances. In this paper we use only the reported monthly returns on a set of funds to infer the type of switching strategies they follow, if any, as well as their...

It is a common problem in risk management today that risk measures and pricing models are being applied to a very large set of scenarios based on movements in all possible risk factors. The dimensions are so large that the computations become extremely slow and cumbersome, so it is quite common...

This paper presents an empirical study of hedging the four largest US index exchange traded funds (ETFs). When hedging each ETF position with its own index futures we find that it is difficult to improve on the naïve 1:1 futures hedge, that hedging is less effective around the time of dividend...

Under the new capital accord stress tests are to be included in market risk regulatory capital calculations. This development necessitates a coherent and objective framework for stress testing portfolios exposed to market risk. Following recent criticism of stress testing methods our tests are...