Statistical Methods in Finance 2018

Abstract

Statistical arbitrage of multiple asset under drawdown constraint and stochastic Sharpe's ratio

by Subhojit Biswas

We consider an investor who seeks to maximize his expected utility of the portfolio consisting of two risky assets and one risk free asset derived from the terminal wealth relative to the maximum wealth achieved over a fixed time horizon, and under a portfolio draw down constraint, in a market with local stochastic volatility. The two assets have been found out with the help of pairs trading. In the absence of closed form solution of the value function and the optimal strategy we obtain the approximates of these quantities using coefficient series expansion techniques and finite difference schemes. We utilize the risk tolerance factor function to ease our approximations of this value functions and the strategies. All the parameters were estimated from the triplets and all these parameters are put in the equation to illustrate and compare the stochastic volatility with the constant volatility situation, and how an investor can deploy different portfolio plans.

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