Abstracts

In this paper we consider the problem of hedging a portfolio of options with the help of standardized options and futures. For this problem we propose a stochastic programming (SP) hedging model which minimizes a portfolio risk measure and at the same time penalizes transaction costs in order to produce a cost effective hedge. We evaluate the hedging model using historical market data from the Swedish index options market. In order to evaluate the model under realistic market conditions all transactions occur at the observed bid and ask prices for the options and futures.
To be able to accurately measure the risk in the option portfolio we need to have a good representation of the distribution of the risk factors that affect option prices. We use historical innovations for the empirically estimated local volatility surface in order to determine the risk factors that the option portfolio is exposed to. With the help of principal component analysis (PCA) for innovations of the empirical local volatility surfaces we can build an arbitrage-free stochastic process for a collection of option prices and thereby determine an optimal hedge with the SP model. In order to extract the true dynamics via the PCA it is vital that we have a method that can estimate local volatility surfaces of high quality. To this end we estimate local volatility surfaces with the help of a novel non-parametric estimation method , which produces local volatility surfaces that are stable over time.
We perform an evaluation that studies the hedging result with respect to risk and costs and compare the results with those obtained with traditional methods such as delta and delta-vega hedging. Tests show that we are able to come up with an effective hedge to a low hedging cost compared to the traditional methods.