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Approximate ordinary differential equations for the optimal exercise boundaries of American put and call options

Journal Article


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Abstract


  • 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.

Publication Date


  • 2014

Citation


  • Rodrigo, M. R. (2014). Approximate ordinary differential equations for the optimal exercise boundaries of American put and call options. European Journal of Applied Mathematics, 25 (1), 27-43.

Scopus Eid


  • 2-s2.0-84898478707

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=2806&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/1797

Number Of Pages


  • 16

Start Page


  • 27

End Page


  • 43

Volume


  • 25

Issue


  • 1

Abstract


  • 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.

Publication Date


  • 2014

Citation


  • Rodrigo, M. R. (2014). Approximate ordinary differential equations for the optimal exercise boundaries of American put and call options. European Journal of Applied Mathematics, 25 (1), 27-43.

Scopus Eid


  • 2-s2.0-84898478707

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=2806&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/1797

Number Of Pages


  • 16

Start Page


  • 27

End Page


  • 43

Volume


  • 25

Issue


  • 1