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Dual pricing of multi-exercise options under volume constraints. (English) Zbl 1303.91167
Summary: In this paper, we study the pricing problem of multi-exercise options under volume constraints. The volume constraint is modelled by an adapted process with values in the positive integers, which describes the maximal number of rights to be exercised at a given time. We derive a representation of the marginal value of an additional \(n\)th right as a standard single stopping problem with a modified cash-flow process. This representation then leads to a dual pricing formula, which generalizes a result by N. Meinshausen and B. M. Hambly [Math. Finance 14, No. 4, 557–583 (2004; Zbl 1169.91372)] from the standard multi-exercise option (with at most one right per time step) to general constraints. We also state an explicit Monte Carlo algorithm for computing confidence intervals for the price of multi-exercise options under volume constraints and present numerical results for the pricing of a swing contract in an electricity market.

MSC:
91G20 Derivative securities (option pricing, hedging, etc.)
60G40 Stopping times; optimal stopping problems; gambling theory
91G60 Numerical methods (including Monte Carlo methods)
65C05 Monte Carlo methods
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