A new computational tool for analysing dynamic hedging under transaction costs

Abstract

This paper highlights a framework for analysing dynamic hedging strategies under transaction costs. First, self-financing portfolio dynamics under transaction costs are modelled as being portfolio affine. An algorithm for computing the moments of the hedging error on a lattice under portfolio affine dynamics is then presented. In a number of circumstances, this provides an efficient approach to analysing the performance of hedging strategies under transaction costs through moments. As an example, this approach is applied to the hedging of a European call option with a Black–Scholes delta hedge and Leland's adjustment for transaction costs. Results are presented that demonstrate the range of analysis possible within the presented framework.

Keywords:

• Applied mathematical finance
• Arbitrage pricing
• Asset pricing
• Black–Scholes model
• Control and optimization
• Control of stochastic systems
• Derivatives hedging
• Derivatives analysis