Market Volatility and Feedback Effects from Dynamic Hedging

In the paper we analyse in what way the implementation of dynamic hedging strategies affects the volatility of the underlying asset. To this end we first construct an economy where equilibrium prices are given by the classical Black- Scholes model of geometric Brownian Motion. Then we add program traders running dynamic hedging strategies into the model and study the resulting change of the diffusion process describing equilibrium asset prices. We derive an explicit formula for the transformation of market volatility under the impact of hedging. It turns out that volatility increases and becomes price-dependent. Moreover we discuss in what sense hedging strategies calculated under the assumption of constant volatility are still appropriate for the hedging of written option contracts even if the feedback effect of their implementation on prices is taken into account