A 'Coherent State Transform' Approach to Derivative Pricing

International Journal of Theoretical and Applied Finance

Posted: 25 Apr 2010 Last revised: 3 May 2010

See all articles by Claudio Tebaldi

Claudio Tebaldi

Bocconi University - CAREFIN - Centre for Applied Research in Finance; Bocconi University - Department of Finance; Bocconi University - IGIER - Innocenzo Gasparini Institute for Economic Research

Ludovico Perissinotto

University of Verona, Department of Economics and Veneto Banca Holding

Date Written: March 1, 2009

Abstract

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

Suggested Citation

Tebaldi, Claudio and Perissinotto, Ludovico, A 'Coherent State Transform' Approach to Derivative Pricing (March 1, 2009). International Journal of Theoretical and Applied Finance, Available at SSRN: https://ssrn.com/abstract=1515462

Claudio Tebaldi (Contact Author)

Bocconi University - CAREFIN - Centre for Applied Research in Finance ( email )

Via Roentgen 1
Milan, 20136
Italy

Bocconi University - Department of Finance ( email )

Via Roentgen 1
Milano, MI 20136
Italy

Bocconi University - IGIER - Innocenzo Gasparini Institute for Economic Research ( email )

Via Roentgen 1
Milan, 20136
Italy

Ludovico Perissinotto

University of Verona, Department of Economics and Veneto Banca Holding ( email )

Via dell'Artigliere, 8
Verona, 37129
Italy

Here is the Coronavirus
related research on SSRN

Paper statistics

Abstract Views
334
PlumX Metrics