A stochastic semidefinite programming approach for bounds on option pricing under regime switching

Roy Kwon () and Jonathan Li ()

Annals of Operations Research, 2016, vol. 237, issue 1, 75 pages

Abstract: We consider bounds for the price of a European-style call option under regime switching. Stochastic semidefinite programming models are developed that incorporate a lattice generated by a finite-state Markov chain regime-switching model as a representation of scenarios (uncertainty) to compute bounds. The optimal first-stage bound value is equivalent to a Value at Risk quantity, and the optimal solution can be obtained via simple sorting. The upper (lower) bounds from the stochastic model are bounded below (above) by the corresponding deterministic bounds and are always less conservative than their robust optimization (min-max) counterparts. In addition, penalty parameters in the model allow controllability in the degree to which the regime switching dynamics are incorporated into the bounds. We demonstrate the value of the stochastic solution (bound) and computational experiments using the S&P 500 index are performed that illustrate the advantages of the stochastic programming approach over the deterministic strategy. Copyright Springer Science+Business Media New York 2016

Keywords: Option pricing; Bounds on option prices; Stochastic programming; Semidefinite programming (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10479-014-1651-1

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