Pricing European and American Installment Options

Joanna Goard and Mohammed AbaOud ()
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Joanna Goard: School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia
Mohammed AbaOud: Department of Mathematics and Statistics, Al Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia

Mathematics, 2022, vol. 10, issue 19, 1-27

Abstract: This paper derives accurate and efficient analytic approximations for the prices of both European and American continuous-installment call and put options. The solutions are in the form of series in time-to-expiry with explicit formulae for the coefficients provided. Unlike other solutions for installment options, no Laplace inverses are needed, and there is no need to solve complex, recursive systems or integral equations. The formulae provided fast yield and accurate solutions not just for the prices, but also for the critical boundaries. We also compare the solutions with those obtained using an existing method and show that it surpasses it delivering more correct option prices and critical stock prices.

Keywords: American continuous installment options; European continuous installment options; critical stock price; analytic approximations; free boundary problems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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