Approximate ordinary differential equations for the optimal exercise boundaries of American put and call options
- Citation data:
European Journal of Applied Mathematics, ISSN: 1469-4425, Vol: 25, Issue: 1, Page: 27-43
- Publication Year:
- Mathematics; approximate; put; american; boundaries; differential; exercise; options; optimal; equations; call; ordinary; Engineering; Science and Technology Studies
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. Copyright © Cambridge University Press 2013.