An integral representation approach for valuing American-style installment options with continuous payment plan
✍ Scribed by Pierangelo Ciurlia
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 334 KB
- Volume
- 74
- Category
- Article
- ISSN
- 0362-546X
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✦ Synopsis
In this paper, we present an integral equation approach for the valuation of Americanstyle installment derivatives when the payment plan is assumed to be a continuous function of the asset price and time. The contribution of this study is threefold. First, we show that in the Black-Scholes model the option pricing problem can be formulated as a free boundary problem under very general conditions on payoff structure and payment schedule. Second, by applying a Fourier transform-based solution technique, we derive a system of coupled recursive integral equations for the pair of free boundaries along with an analytic representation of the option price. Third, based on these results, we propose a unified framework which generalizes the existing methods and is capable of dealing with a wide range of monotonic payoff functions and continuous payment plans. Finally, by using the illustrative example of American vanilla installment call options, an explicit pricing formula is obtained for time-varying payment schedules.