A two-dimensional, two-sided Euler inversion algorithm with computable error bounds and its financial applications

In this paper we propose an inversion algorithm with computable error bounds for two-dimensional, two-sided Laplace transforms. The algorithm consists of two discretization parameters and two truncation parameters. Based on the computable error bounds, we can select these parameters appropriately to...

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Vydané v:Stochastic systems Ročník 4; číslo 2; s. 404 - 448
Hlavní autori: Ning Cai, Chao Shi
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Institute for Operations Research and the Management Sciences (INFORMS) 01.03.2015
Predmet:
computable error bounds
discretization errors
Euler inversion
exotic options
option pricing
truncation errors
Two-dimensional Laplace inversion
two-sided Laplace transforms
ISSN:1946-5238, 1946-5238
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Shrnutí:In this paper we propose an inversion algorithm with computable error bounds for two-dimensional, two-sided Laplace transforms. The algorithm consists of two discretization parameters and two truncation parameters. Based on the computable error bounds, we can select these parameters appropriately to achieve any desired accuracy. Hence this algorithm is particularly useful to provide benchmarks. In many cases, the error bounds decay quickly (e.g., exponentially), making the algorithm very efficient. We apply this algorithm to price exotic options such as spread options and barrier options under various asset pricing models as well as to evaluate the joint cumulative distribution functions of related state variables. The numerical examples indicate that the inversion algorithm is accurate, fast and easy to implement.
ISSN:1946-5238
1946-5238
DOI:10.1214/12-SSY094