FRONT FIXING METHOD FOR SOLVING INSTALLMENT OPTION

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BEIRANVAND ALI; Ivaz Karim

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Seminar Paper

Paper Information

Seminar: SEMINAR OF MATHEMATICS AND HUMANITIES, FINANCIAL MATHEMATICS
Year:2016 | Issue:4

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Title

FRONT FIXING METHOD FOR SOLVING INSTALLMENT OPTION

Author(s)

BEIRANVAND ALI | Ivaz Karim | Issue Writer Certificate

Keywords

INSTALLMENT OPTION

BLACK-SCHOLES MODEL

FOREIGN CUR-RENCY

FRONT XING METHOD

FREE BOUNDARY PROBLEM

Abstract

IN THIS PAPER WE CONSIDER THE EUROPEAN CONTINUOUS INSTALLMENT CALL OPTION ON FOREIGN CURRENCY EXCHANGE RATE AS UNDER-LYING ASSET. BY ARBITRAGE PRICING THEORY, ONE CAN MODEL THE INSTALL-MENT OPTION UNDER BLACK-SCHOLES MODEL. THEREFORE, NON HOMOGE-NEOUS PARABOLIC PARTIAL DI ERENTIAL EQUATION GOVERNING INSTALLMENT OPTION IS DERIVED. THE NON HOMOGENEOUS TERM IN THIS PARABOLIC PARTIAL DI ERENTIAL EQUATION IS THE INSTALLMENT RATE THAT MUST BE PAID BY OPTION HOLDER. THE PRICING PROBLEM FOR INSTALLMENT OPTION ON FOREIGN CURRENCY EXCHANGE RATE IS PARABOLIC PARTIAL DI ERENTIAL EQUATION WITH INITIAL AN BOUNDARY CONDITIONS CALLED FREE BOUNDARY PROBLEM. THEN, TO DETERMINE THE VALUE OF THE EUROPEAN INSTALL-MENT OPTION AND THE LOCATION OF THE STOPPING BOUNDARY, THE FRONT XING METHOD WILL BE APPLIED. IN THIS METHOD, WE TRANSFORM THE FREE BOUNDARY PROBLEM TO A NONLINEAR PARABOLIC PARTIAL DI ERENTIAL EQUATION WITH XED KNOWN BOUNDARY. IN THE NEXT STEP, NITE DIF-FERENCE METHOD WILL BE APPLIED TO DISCRETIZE THE PROBLEM. HENCE ONE CAN GET FORMULA FOR NDING THE PRICE OF EUROPEAN CONTINUOUS INSTALLMENT CALL OPTION AND THE LOCATION OF THE STOPPING OR FREE BOUNDARY.

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APA: Copy

BEIRANVAND, ALI, & Ivaz, Karim. (). . . SID. https://sid.ir/paper/940319/en

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BEIRANVAND ALI, Ivaz Karim. . . Available from: https://sid.ir/paper/940319/en

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