A 'Coherent State Transform' Approach to Derivative Pricing
International Journal of Theoretical and Applied Finance
Posted: 25 Apr 2010 Last revised: 3 May 2010
Date Written: March 1, 2009
We propose an extension of the transform approach to option pricing introduced in Duffie, Pan and Singleton (Econometrica 68(6) (2000) 1343–1376) and in Carr and Madan (Journal of Computational Finance 2(4) (1999) 61–73). We term this extension the "coherent state transform" approach, it applies when the Markov generator of the factor process can be decomposed as a linear combination of generators of a Lie symmetry group. Then the family of group invariant coherent states determine the transform to price derivatives. We exemplify this procedure deriving a coherent state transform for affine jump-diffusion processes with positive state space. It improves the traditional FFT because inversion of the latter requires integration over an unbounded domain, while inversion of the coherent state transform requires integration over unit ball. We explicitly perform the pricing exercise for some contracts like the plain vanilla options on (credit) risky bonds and on the spread option.
Keywords: Coherent states, affine jump diffusion, Lie groups, Lie algebras
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