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Stochastic Implied Trees: Arbitrage Pricing with Stochastic Term and Strike Structure of Volatility
Overview 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.
| Publisher | Goldman Sachs & Co. | File Format | PDF, requires Acrobat Rdr 5 |
|---|---|---|---|
| Date Published | October 2003 | Downloads | 63 |
| Format | White Papers | ||
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