Instantaneous Mean-Variance Hedging and Sharpe Ratio Pricing in a Regime-Switching Financial Model

Lukasz Delong*, Antoon Pelsser

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We study hedging and pricing of claims in a non-markovian regime-switching financial model. Our financial market consists of a bank account and a risky asset whose dynamics are driven by a brownian motion and a multivariate counting process with stochastic intensities. The counting process is used to model the switching behavior for the states of the economy. We assume that the trajectory of the risky asset is continuous between the transition times for the states of the economy and that the value of the risky asset jumps at the time of the transition. We find the hedging strategy that minimizes the instantaneous mean-variance risk of the hedger’s surplus, and we set the price so that the instantaneous sharpe ratio of the hedger’s surplus equals a predefined target. We discuss key properties of our optimal price and optimal hedging strategy.
Original languageEnglish
Pages (from-to)67-97
JournalStochastic Models
Volume31
Issue number1
DOIs
Publication statusPublished - 2 Jan 2015

Keywords

  • No-good-deal pricing
  • Counting process
  • Backward stochastic differential equations
  • Model ambiguity
  • Instantaneous Sharpe ratio
  • Instantaneous mean-variance risk

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