Instalment options: a closed-form solution and the limiting case - Susanne Griebsch; Christoph Kühn; Uwe Wystup (Frankfurt School of Finance & Management, Centre for Practical Quantitative Finance (CPQF), 2007)
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.
Keywords: C15; G12; 330; exotic options; Optionsgeschäft; Black-Scholes-Modell; Theorie