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black–scholes kernel

European Journal of Applied Mathematics (1)

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1 results

Approximate ordinary differential equations for the optimal exercise boundaries of American put and call options
MARIANITO R. RODRIGO
Journal:

European Journal of Applied Mathematics / Volume 25 / Issue 1 / February 2014

Published online by Cambridge University Press:

15 August 2013, pp. 27-43
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We revisit the American put and call option valuation problems. We derive analytical formulas for the option prices and approximate ordinary differential equations for the optimal exercise boundaries. Numerical simulations yield accurate option prices and comparable computational speeds when benchmarked against the binomial method for calculating option prices. Our approach is based on the Mellin transform and an adaptation of the Kármán–Pohlausen technique for boundary layers in fluid mechanics.