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The Little Heston Trap

The Little Heston Trap,Hansjorg Albrecher,Philipp Mayer,Wim Schoutens,Jurgen Tistaert

The Little Heston Trap   (Citations: 24)
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Abstract The role of characteristic functions in finance has been strongly amplified by the develop- ment of the general option pricing formula by Carr and Madan. As these functions are defined and operating in the complex plane, they potentially encompass a few well known numerical issues due to ”branching”. A number,of elegant publications have emerged tackling these effects specifically for the Heston model. For the latter however we have two specifications for the characteristic function as they are the solutions to a Riccati equation. In this article we put the i’s and cross the t’s by formally pointing out the properties of and relations be- tween both versions. For the first specification we show that for nearly any parameter choice, instabilities will occur for large enough maturities. We subsequently establish - under an addi- tional parameter restriction - the existence of a “threshold” maturity from which the complex operations become,a spoil-sport. For the second specification of the characteristic function it is proved that stability is guaranteed under the full dimensional and unrestricted parameter space. We blend the theoretical results with a few examples. 2
Published in 2006.
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