Summary
In Foreign Exchange Markets Compound options (options on options) are traded frequently. Instalment options generalize the concept of Compound options as they allow the holder to prolong a Vanilla Call or Put option by paying instalments 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 Instalment 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.
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Griebsch, S., Kühn, C., Wystup, U. (2008). Instalment Options: A Closed-Form Solution and the Limiting Case. In: Sarychev, A., Shiryaev, A., Guerra, M., Grossinho, M.d.R. (eds) Mathematical Control Theory and Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69532-5_12
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DOI: https://doi.org/10.1007/978-3-540-69532-5_12
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