Optimal Trading with Predictable Return and Stochastic Volatility

24 Pages Posted: 29 Jun 2015

See all articles by Patrick Chan

Patrick Chan

Princeton University - Program in Applied and Computational Mathematics

Ronnie Sircar

Princeton University - Department of Operations Research and Financial Engineering

Date Written: June 26, 2015

Abstract

We consider a class of dynamic portfolio optimization problems that allow for models of return predictability, transaction costs, and stochastic volatility. Determining the dynamic optimal portfolio in this general setting is almost always intractable. We propose a multiscale asymptotic expansion when the volatility process is characterized by its time scales of fluctuation. The analysis of the nonlinear Hamilton- Jacobi-Bellman PDE is a singular perturbation problem when volatility is fast mean-reverting; and it is a regular perturbation when the volatility is slowly varying. These analyses can be combined for multifactor multiscale stochastic volatility model. We present formal derivations of asymptotic approximations and demonstrate how the proposed algorithms improve our Profit & Loss using Monte Carlo simulations.

Keywords: Optimal trading, multiscale stochastic volatility, return predictability, Hamilton- Jacobi-Bellman equation

Suggested Citation

Chan, Patrick and Sircar, Ronnie, Optimal Trading with Predictable Return and Stochastic Volatility (June 26, 2015). Available at SSRN: https://ssrn.com/abstract=2623747 or http://dx.doi.org/10.2139/ssrn.2623747

Patrick Chan (Contact Author)

Princeton University - Program in Applied and Computational Mathematics ( email )

Princeton, NJ 08544
United States

Ronnie Sircar

Princeton University - Department of Operations Research and Financial Engineering ( email )

Princeton, NJ 08544
United States

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