Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

OPTION HEDGING AND IMPLIED VOLATILITIES IN A STOCHASTIC VOLATILITY MODEL

OPTION HEDGING AND IMPLIED VOLATILITIES IN A STOCHASTIC VOLATILITY MODEL In the stochastic volatility framework of Hull and White (1987), we characterize the so‐called Black and Scholes implied volatility as a function of two arguments the ratio of the strike to the underlying asset price and the instantaneous value of the volatility By studying the variation m the first argument, we show that the usual hedging methods, through the Black and Scholes model, lead to an underhedged (resp. overhedged) position for in‐the‐money (resp out‐of the‐money) options, and a perfect partial hedged position for at the‐money options These results are shown to be closely related to the smile effect, which is proved to be a natural consequence of the stochastic volatility feature the deterministic dependence of the implied volatility on the underlying volatility process suggests the use of implied volatility data for the estimation of the parameters of interest A statistical procedure of filtering (of the latent volatility process) and estimation (of its parameters) is shown to be strongly consistent and asymptotically normal. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Finance Wiley

OPTION HEDGING AND IMPLIED VOLATILITIES IN A STOCHASTIC VOLATILITY MODEL

Renault, Eric; Touzi, Nizar
Mathematical Finance , Volume 6 (3) – Jul 1, 1996
Download PDF
24 pages

Loading next page...
 
/lp/wiley/option-hedging-and-implied-volatilities-in-a-stochastic-volatility-BUOHe2K0dN

References (43)

Publisher
Wiley
Copyright
Copyright © 1996 Wiley Subscription Services, Inc., A Wiley Company
ISSN
0960-1627
eISSN
1467-9965
DOI
10.1111/j.1467-9965.1996.tb00117.x
Publisher site
See Article on Publisher Site

Abstract

In the stochastic volatility framework of Hull and White (1987), we characterize the so‐called Black and Scholes implied volatility as a function of two arguments the ratio of the strike to the underlying asset price and the instantaneous value of the volatility By studying the variation m the first argument, we show that the usual hedging methods, through the Black and Scholes model, lead to an underhedged (resp. overhedged) position for in‐the‐money (resp out‐of the‐money) options, and a perfect partial hedged position for at the‐money options These results are shown to be closely related to the smile effect, which is proved to be a natural consequence of the stochastic volatility feature the deterministic dependence of the implied volatility on the underlying volatility process suggests the use of implied volatility data for the estimation of the parameters of interest A statistical procedure of filtering (of the latent volatility process) and estimation (of its parameters) is shown to be strongly consistent and asymptotically normal.

Journal

Mathematical Finance – Wiley

Published: Jul 1, 1996

There are no references for this article.