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External barrier options are two-asset options with stochastic variables where the payoff depends on one underlying asset and the barrier depends on another state variable. The barrier state variable determines whether the option is knocked in or out when the value of the variable is above or below some prescribed barrier level. This paper derives the explicit analytic solution of the chained option with an external single or double barrier by utilizing the probabilistic methods - the reflection principle and the change of measure. Before we do this, we examine the closed-form solution of the external barrier option with a single or double-curved barrier using the methods of image and double Mellin transforms. The exact solution of the external barrier option price enables us to obtain the pricing formula of the chained option with the external barrier more easily.
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참고문헌 (18)
참고문헌 신청
P. Buchen / 2001 / Image Options and the road to barriers / Risk Magazine 14(9):127~130
P. Buchen / 2009 / A new approach to pricing double-Barrier options with arbitrary payoffs and exponential boundaries / Appl. Math. Finance 16(6):497~515
P. Carr / 1995 / Two extensions to barrier option valuation / Appl. Math. Finance 2:173~209
A. Chen / 2012 / Rainbow over Paris
E. Hassan / 2007 / A note on Mellin transform and partial differential equations / International J. Pure Appl. Math 34(4):457~467
P. Buchen / 2009 / A new approach to pricing double-Barrier options with arbitrary payoffs and exponential boundaries / Appl. Math. Finance 16(6):497~515
P. Carr / 1995 / Two extensions to barrier option valuation / Appl. Math. Finance 2:173~209
A. Chen / 2012 / Rainbow over Paris
E. Hassan / 2007 / A note on Mellin transform and partial differential equations / International J. Pure Appl. Math 34(4):457~467
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