Skip to main content
Article thumbnail
Location of Repository

Applications of Laplace transform for evaluating occupation time options and other derivatives

By Gianluca Fusai


The present thesis provides an analysis of possible applications of the Laplace Transform (LT) technique to several pricing problems. In Finance this technique has received very little attention and for this reason, in the first chapter we illustrate with several examples why the use of the LT can considerably simplify the pricing problem. Observed that the analytical inversion is very often difficult or requires the computation of very complicated expressions, we illustrate also how the numerical inversion is remarkably easy to understand and perform and can be done with high accuracy and at very low computational cost.\ud \ud In the second and third chapters we investigate the problem of pricing corridor derivatives, i.e. exotic contracts for which the payoff at maturity depends on the time of permanence of an index inside a band (corridor) or below a given level (hurdle). The index is usually an exchange or interest rate. This kind of bond has evidenced a good popularity in recent years as alternative instruments to common bonds for short term investment and as opportunity for investors believing in stable markets (corridor bonds) or in non appreciating markets (hurdle bonds). In the second chapter, assuming a Geometric Brownian dynamics for the underlying asset and solving the relevant Feynman-Kac equation, we obtain an expression for the Laplace transform of the characteristic function of the occupation time. We then show how to use a multidimensional numerical inversion for obtaining the density function. In the third chapter, we investigate the effect of discrete monitoring on the price of corridor derivatives and, as already observed in the literature for barrier options and for lookback options, we observe substantial differences between discrete and continuous monitoring. The pricing problem with discrete monitoring is based on an appropriate numerical scheme of the system of PDE's.\ud \ud In the fourth chapter we propose a new approximation for pricing Asian options based on the logarithmic moments of the price average

Topics: HG, QA
OAI identifier:

Suggested articles


  1. (1996). Averaging Options, in 1. Nelken, The Handbook of Exotic Ophons,
  2. (1992). On some exponential functionals of Brownian Motion, doi
  3. (1992). Some Aspects of Brownian Motion. Part 1: Some Special Functionals. Birkhauser Verlag. Basel - doi
  4. (1992). Sur les lois des fonctionnelles exponentielles du mouvement brownien, consid6r6es en certains instants al6atoires,
  5. (1966). Numerical inversion of Laplace transforms using Laguerre functions, doi
  6. (1999). Algorithms for Parameter Selection in the Weeks Method for Inverting the Laplace Týransform, doi
  7. (1970). Generalization of Vlach's Method for the Numerical Inversion of the Laplace Týansform, doi
  8. (1961). The E-algorithm and operational formulas of numerical analysis, doi
  9. (1989). PaTtal Differential Equattons of Apphed Alathcmatic,, ý,
  10. (1997). Robust Numerical methods for PDE models of Asian options, doi
  11. (1997). PDE methods for barrier options, doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.