Risk management for derivatives in illiquid markets: A simulation study. (English) Zbl 1002.91031

Frey, Rüdiger; Patie, Pierre

Sandmann, Klaus (ed.) et al., Advances in finance and stochastics. Essays in honour of Dieter Sondermann. Berlin: Springer. 137-159 (2002).

Summary: We study the hedging of derivatives in illiquid markets. More specifically we consider a model where the implementation of a hedging strategy affects the price of the underlying security. Following earlier work we characterize perfect hedging strategies by a nonlinear version of the Black-Scholes PDE. The core of the paper consists of a simulation study. We present numerical results on the impact of market illiquidity on hedge cost and Greeks of derivatives. We go on and offer a new explanation of the smile pattern of implied volatility related to the lack of market liquidity. Finally we present simulations on the performance of different hedging strategies in illiquid markets.
For the entire collection see [Zbl 0986.00085].

MSC:

91B28	Finance etc. (MSC2000)
91B30	Risk theory, insurance (MSC2010)
91B26	Auctions, bargaining, bidding and selling, and other market models

Keywords:

option hedging; volatility; illiquid markets; nonlinear Black-Scholes equation; simulation study