Modelling volatility derivatives using neural networks

Abstract

Several papers over the past few years have addressed the pricing and potential usefulness of derivatives based on volatility. The Chicago Board Options Exchange (OEX) introduced an index on stock market volatility beginning in 1986. This volatility index is based on the implied volatility of eight different OEX options and is a measure that attempts to provide a reliable estimate of the market's consensus forecast of short-term volatility. It also provides a standard upon which volatility derivatives can be based. In this paper, we construct a similar measure for the market's short-term forecast of Deutschemark volatility. We evaluate the index's time series properties, explore a closed-form solution for valuing derivative instruments based on the index, and employ neural network methods to price options based on the index. Lastly, we explore a practical example of using futures on the index to hedge the volatility risk of a portfolio of Deutschemark options. For this project, neural net technology has been applied in two different areas. One neural net has been used to forecast the volatility index. A second neural net has been used to obtain prices of options traded on this contract. It has been shown that commercial neural net-based systems can outperform the systems based on classical techniques in time series processing and digital signal processing applications. Also, neural nets have been applied to many financial applications, including mutual fund performance forecasting.