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Installment options; a closed-form solution and the limiting case. (English) Zbl 1153.91500

Sarychev, Andrey (ed.) et al., Mathematical control theory and finance. Proceedings of the workshop, Lisbon, April 10–14, 2007. Berlin: Springer (ISBN 978-3-540-69531-8/hbk). 211-229 (2008).
Summary: In Foreign Exchange Markets Compound options (options on options) are traded frequently. Installment options generalize the concept of Compound options as they allow the holder to prolong a Vanilla Call or Put option by paying installments of a discrete payment plan. We derive a closed-form solution to the value of such an option in the Black-Scholes model and prove that the limiting case of an installment option with a continuous payment plan is equivalent to a portfolio consisting of a European Vanilla option and an American Put on this Vanilla option with a time-dependent strike.
For the entire collection see [Zbl 1143.91005].

MSC:

91G10 Portfolio theory
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