Optimal Time for Closing a Trading Position

Abstract

In this paper, trading rules (strategies) on a specified financial asset at some future time are interpreted as contingent claims (financial derivatives). Therefore, their fair values are computable using the binomial tree technique. However, traders pay the price of financial asset at the current time to enter to trading. Clearly, it is a loss for traders. In this paper, first, hedging strategies are proposed. Then, using three procedures the optimal time for closing the trading position are derived. Mentioned procedures are based on optimal stopping time and stochastic dynamic programming, state space and a practical procedure which uses an adds-in of Excel software. Indeed, optimal closing time and related trading strategies are applied in discrete time price processes and in the binomial tree setting. Markov decision process (MDP) solution to the problem is proposed. Simulation results are studied and finally, a conclusion section is given.

Keywords

• binomial tree
• fair value
• financial derivative
• excel
• hedging
• mdp
• optimal stopping
• state space model
• stochastic dynamic programming
• trading strategies