Accounting for Risk Aversion in Derivatives Purchase Timing
Mathematics & Financial Economics, 2012
24 Pages Posted: 5 Sep 2011 Last revised: 5 Mar 2012
Date Written: January 4, 2012
We study the problem of optimal timing to buy/sell derivatives by a risk-averse agent in incomplete markets. Adopting the exponential utility indifference valuation, we investigate this timing flexibility and the associated delayed purchase premium. This leads to a stochastic control and optimal stopping problem that combines the observed market price dynamics and the agent's risk preferences. Our results extend recent work on indifference valuation of American options, as well as the authors' first paper (Leung and Ludkovski, SIAM J. Fin. Math., 2011). In the case of Markovian models of contracts on non-traded assets, we provide analytical characterizations and numerical studies of the optimal purchase strategies, with applications to both equity and credit derivatives.
Keywords: sequential purchase timing, indifference pricing, exponential utility, stochastic control with optimal stopping
JEL Classification: G12, G13, C68
Suggested Citation: Suggested Citation