| Publisher | Goldman Sachs & Co. | ||
|---|---|---|---|
| Format | 520.0KB PDF, requires Acrobat Rdr 5 | Date added | 29 Oct 2003 |
| Topics | Online Trading | ||
| Downloads | 169 | ||
In this paper we present an arbitrage pricing framework for valuing and hedging contingent equity index claims in the presence of a stochastic term and strike structure of volatility. Starting from an initial set of index options prices and their associated local volatility surface, we show how to construct a family of continuous time stochastic processes which define the arbitrage-free evolution of this local volatility surface through time. The no-arbitrage conditions are similar to, but more involved than, the HJM conditions for arbitrage-free stochastic movements of the interest rate curve. They guarantee that even under a general stochastic volatility evolution the initial options prices, or their equivalent Black-Scholes implied volatilities, remain fair.
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