Paper Info
Title
Pricing Barrier and Bermudan Style Options Under Time-Changed Lévy Processes: Fast Hilbert Transform Approach.
Abstract
We construct efficient and accurate numerical algorithms for pricing discretely monitored barrier and Bermudan style options under time-changed Levy processes by applying the fast Hilbert transform method to the log-asset return dimension and quadrature rule to the dimension of log-activity rate of stochastic time change. Some popular stochastic volatility models, like the Heston model, can be nested in the class of time-changed Levy processes. The computational advantages of the fast Hilbert transform approach over the usual fast Fourier transform method, like exponential decay of errors with regard to the truncation level in the transform and avoidance of recovering option prices at the monitoring time instants, can be extended to pricing barrier and Bermudan style options under time-changed Levy processes. We compute the fair value of a dividend-ruin model with both embedded reflecting (dividend) barrier and absorbing (ruined) barrier. We also consider pricing of Bermudan options in conjunction with the determination of the associated critical asset prices. Our numerical tests demonstrate a high level of accuracy, efficiency, and reliability of the fast Hilbert transform approach when compared to other numerical schemes in the literature.
Year
DOI
Venue
2014
10.1137/130922495
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Keywords
Field
DocType
fast Hilbert transform,time-changed Levy processes,barrier options,dividend-ruin model,Bermudan options
Stochastic volatility,Mathematical optimization,Dividend,Exponential decay,Heston model,Fast Fourier transform,Hilbert transform,Lévy process,Gaussian quadrature,Mathematics
Journal
Volume
Issue
ISSN
36
3
1064-8275
Citations 
PageRank 
References 
4
0.52
9
Authors
2
Name
Order
Citations
PageRank
Pingping Zeng140.86
Yue Kuen Kwok2325.03