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Tomas Björk, Irina Slinko, Towards a General Theory of Good-Deal Bounds, Review of Finance, Volume 10, Issue 2, 2006, Pages 221–260, https://doi.org/10.1007/s10679-006-8279-1
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Abstract
We consider an incomplete market in the form of a multidimensional Markovian factor model, driven by a general marked point process (representing discrete jump events), as well as by a standard multidimensional Wiener process. Within this framework, we study arbitrage-free gooddeal pricing bounds for derivative assets, thereby extending the results by Cochrane and Saá Requejo (2000) to the point process case, while, at the same time, obtaining a radical simplification of the theory. To illustrate, we present numerical results for the classic Merton jump-diffusion model. As a by-product of the general theory, we derive extended Hansen-Jagannathan bounds for the Sharpe Ratio process in the point process setting.