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A systematic approach for valuing European-style installment options with continuous payment plan


  • Pierangelo Ciurlia


In this paper we present an integral equation approach for the valuation of European-style installment derivatives when the premium payments, made continuously throughout the contract’s life, are assumed to be a function of the asset price and time variables. The contribution of this study is threefold. First, we show that in the Black-Scholes framework the option pricing problem can be formulated as a free boundary problem under very general conditions on payo structure and installment payment plan. Second, by applying a Fourier transform-based solution technique, we derive a recursive integral equation for the free boundary along with a general integral representation for the option initial premium. Third, within this systematic treatment of the European installment options, we propose a unified and easily applicable method to deal with a broad range of monotonic payo functions and continuous payment plans depending on the time variable only. Finally, by using the illustrative example of European vanilla installment call options, an explicit valuation formula is obtained for the class of linear time-varying installment payment functions.

Suggested Citation

  • Pierangelo Ciurlia, 2010. "A systematic approach for valuing European-style installment options with continuous payment plan," Departmental Working Papers of Economics - University 'Roma Tre' 0115, Department of Economics - University Roma Tre.
  • Handle: RePEc:rtr:wpaper:0115

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    More about this item


    Installment options; free boundary problem; Fourier transform; integral representations;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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