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A Two-Sided Laplace Inversion Algorithm with Computable Error Bounds and its Applications in Financial Engineering

Part of: Integral transforms, operational calculus Mathematical finance

Published online by Cambridge University Press:  22 February 2016

Ning Cai ,
S. G. Kou  and
Zongjian Liu
Ning Cai*
Affiliation:
The Hong Kong University of Science and Technology
S. G. Kou*
Affiliation:
National University of Singapore and Columbia University
Zongjian Liu*
Affiliation:
Columbia University
*
∗ Postal address: Department of Industrial Engineering and Logistics Management, The Hong Kong University of Science and Technology, Room 5551, Clear Water Bay, Kowloon, Hong Kong. Email address: ningcai@ust.hk
∗∗ Postal address: Risk Management Institute and Department of Mathematics, National University of Singapore, I3 Building #04-03, 21 Heng Mui Keng Terrace, Singapore 119613.
∗∗∗ Postal address: Columbia University, 313A S. W. Mudd Building, 500 W. 120th Street, New York, NY 10027, USA.
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Abstract

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Transform-based algorithms have wide applications in applied probability, but rarely provide computable error bounds to guarantee the accuracy. We propose an inversion algorithm for two-sided Laplace transforms with computable error bounds. The algorithm involves a discretization parameter C and a truncation parameter N. By choosing C and N using the error bounds, the algorithm can achieve any desired accuracy. In many cases, the bounds decay exponentially, leading to fast computation. Therefore, the algorithm is especially suitable to provide benchmarks. Examples from financial engineering, including valuation of cumulative distribution functions of asset returns and pricing of European and exotic options, show that our algorithm is fast and easy to implement.

Keywords

Laplace inversiontwo-sided Laplace transformoption pricingdiscretization errortruncation error

MSC classification

Primary: 91G20: Derivative securities
Secondary: 44A10: Laplace transform
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 46 , Issue 3 , September 2014 , pp. 766 - 789
Copyright
© Applied Probability Trust 

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