Is there a better way to predict derivative prices? This research introduces derivative pricing and estimation tools for stochastic volatility models, exploiting the persistent nature of stock price volatility. An empirical analysis of S&P 500 index data confirms that volatility reverts slowly to its mean compared to index fluctuations, but fast when viewed over a derivative contract's timescale. Utilizing the distinction between these time scales, the researchers develop an asymptotic analysis of the partial differential equation for derivative prices. The theory identifies crucial group parameters—average volatility and the slope and intercept of the implied volatility line—essential for pricing and hedging European-style securities. This simplifies the estimation procedure, yielding stable estimates during periods of stationary volatility. The study suggests that other parameters, such as the growth rate of the underlying, asset price and volatility correlation, mean-reversion rate, and the market price of volatility risk, can be roughly estimated but aren't needed for asymptotic pricing formulas for European derivatives. The extension to American and path-dependent contingent claims is a topic for future research.
Published in the International Journal of Theoretical and Applied Finance, this research aligns with the journal's focus on financial modeling and derivative pricing. By presenting new tools for stochastic volatility models, the paper builds upon existing knowledge in financial economics. The study's empirical analysis and identification of key parameters are relevant to the journal's readership.
| Category | Category Repetition |
|---|---|
| Science: Mathematics | 1 |
| Science: Science (General) | 1 |