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PRICING ASIAN OPTIONS FOR JUMP DIFFUSION
Author(s) -
Bayraktar Erhan,
Xing Hao
Publication year - 2011
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2010.00426.x
Subject(s) - jump diffusion , jump , sequence (biology) , mathematics , convergence (economics) , partial differential equation , parabolic partial differential equation , diffusion , asian option , differential equation , mathematical optimization , mathematical analysis , valuation of options , econometrics , economics , physics , genetics , biology , economic growth , quantum mechanics , thermodynamics
We construct a sequence of functions that uniformly converge (on compact sets) to the price of an Asian option, which is written on a stock whose dynamics follow a jump diffusion. The convergence is exponentially fast. We show that each element in this sequence is the unique classical solution of a parabolic partial differential equation (not an integro‐differential equation). As a result we obtain a fast numerical approximation scheme whose accuracy versus speed characteristics can be controlled. We analyze the performance of our numerical algorithm on several examples.