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Instalment Options: A Closed-Form Solution and the Limiting Case

In: Mathematical Control Theory and Finance

Author

Listed:
  • Susanne Griebsch

    (Frankfurt School of Finance & Management)

  • Christoph Kühn

    (Goethe-University Frankfurt, Frankfurt MathFinance Institute)

  • Uwe Wystup

    (Frankfurt School of Finance & Management)

Abstract

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.

Suggested Citation

  • Susanne Griebsch & Christoph Kühn & Uwe Wystup, 2008. "Instalment Options: A Closed-Form Solution and the Limiting Case," Springer Books, in: Andrey Sarychev & Albert Shiryaev & Manuel Guerra & Maria do Rosário Grossinho (ed.), Mathematical Control Theory and Finance, pages 211-229, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69532-5_12
    DOI: 10.1007/978-3-540-69532-5_12
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