SFB 303 Discussion Paper No. B - 256
Author: Frey, Rüdiger, and Alexander Stremme
Title: Portfolio Insurance and Volatility - On the Robustness of the
Black-Scholes Option Pricing Model
Abstract: We shall investigate the feedback effect that dynamical hedging
strategies have on the price process of the underlying security, supposing
the investors who run these strategies believe in the Black-Scholes option
pricing theory. To this end we first construct within the general framework
introduced by H. Föllmer and M. Schweizer in [FS 93] an economic environment
in which security prices are given by the classical Black-Scholes model of
geometric Brownian Motion. Then we introduce portfolio insurance into that
model and study how the price process changes. It will turn out that the
change of volatility depends not only on the weight of portfolio insurers'
demand compared to total demand but also on the heterogeneity of the
distribution of insured option contracts.
Keywords: Black-Scholes Model, Portfolio Insurance, Volatility
JEL-Classification-Number: 026, 313, 314, 521
Creation-Date: September 1993
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