TOWARDS A GENERAL THEORY OF GOOD DEAL BOUNDS

Tomas Björk
(joint work with Irina Slinko)

Abstract

We consider a Markovian factor model consisting of a vector price process for traded assets as well as a multidimensional random process for non traded factors. All processes are allowed to be driven by a general marked point process (representing discrete jump events) as well as by a standard multidimensional standard Wiener process. Within this framework we provide the following results.

1. We extend the Hansen-Jagannathan bounds for the Sharpe Ratio to the point process setting.

2. We study arbitrage free good deal pricing bounds for derivative assets along the lines of Cochrane and Saa-Requejo. Using martingale techniques we derive the relevant Hamilton-Jacobi-Bellman equation for the upper and lower good deal bound functions, thus extending the results from Cochrane and Saa-Requejo to the point process case.

3. In particular we study the case of a single price process driven by a scalar Wiener process as well as by a marked point process. For this case we provide a detailed analysis of the dynamic programming equation and the optimal market prices of risk. As a concrete application we present numerical results for the classic Merton jump-diffusion model.