Portfolio optimization under local-stochastic volatility: Coefficient taylor series approximations and implied sharpe ratio

Matthew Lorigt, Ronnie Sircar

Research output: Contribution to journalArticle

11 Scopus citations

Abstract

We study the finite horizon Merton portfolio optimization problem in a general local-stochastic volatility setting. Using model coefficient expan sion techniques, we derive approximations for both the value function and the optimal investment s trategy. We also analyze the "implied Sharpe ratio" and derive a series approximation for this quan tity. The zeroth order approximation of the value function and optimal investment strategy correspond to those obtained by [Merton, Rev. Econ. Statist., 51, pp. 247-257] when the risky asset follows a geometric Brownian motion. The first order correction of the value function can, for general utility functions, be expressed as a differential operator acting on the zeroth order term. For power utility functions, higher order terms can also be computed as a differential operator acting on the zeroth order term. While our approximations are derived formally, we give a rigorous accuracy bound for the higher order approximations in this case in pure stochastic volatility models. a number of examples are provided in order to demonstrate numerically the accuracy of our approximations.

Original languageEnglish (US)
Pages (from-to)418-447
Number of pages30
JournalSIAM Journal on Financial Mathematics
Volume7
Issue number1
DOIs
StatePublished - 2016

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Finance
  • Applied Mathematics

Keywords

  • Local volatility
  • Merton pr oblem
  • Portfolio optimization
  • Stochastic volatility

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