A Two-Sided Laplace Inversion Algorithm with Computable Error Bounds and its Applications in Financial Engineering. (September 2014)

• Record Type: Journal Article
• Authors: Cai, Ning; Kou, S. G.; Liu, Zongjian
• Is Part Of: Advances in applied probability. Volume 46:Number 3(2014)
• Page Start: 766
• Page End: 789
• Publication Date: 2014-09
• Subjects: Laplace inversion, -- two-sided Laplace transform, -- option pricing, -- discretization error, -- truncation error; 91G20, -- 44A10; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1239/aap/1409319559
• Languages: English
• ISSNs: 0001-8678

Abstract

Abstract : 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.