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Delft University of Technology

1. Maree, S.C. (author). Numerical Pricing of Bermudan Options with Shannon Wavelet Expansions.

Degree: 2015, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:a080360d-9eeb-4b0d-9613-0c736f8769e5

This thesis is about pricing Bermudan options with the SWIFT method (Shannon Wavelets Inverse Fourier Technique). We reformulate the SWIFT pricing formula for European options to improve robustness, which allows us to heuristically select - and test the goodness - of all of the parameters a priori. Furthermore, we propose a simplified version of the SWIFT method, based on the Whittaker-Shannon sampling theory, which is an easy to implement method that posses algebraic convergence in the pricing of European and Bermudan options. The main contribution of this thesis is a new pricing method for Bermudan options by the SWIFT method, for exponential Levy processes using the Fast Fourier Transform. We compare the results of the SWIFT method to those of the COS method.

Delft Institute of Applied Mathematics

Electrical Engineering, Mathematics and Computer Science

Subjects/Keywords: option pricing; Bermudan options; exponential levy processes; wavelet series approximations; Shannon wavelets; Shannon-Whittaker sampling theory; Fourier transform inversion

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Maree, S. C. (. (2015). Numerical Pricing of Bermudan Options with Shannon Wavelet Expansions. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:a080360d-9eeb-4b0d-9613-0c736f8769e5

Chicago Manual of Style (16^{th} Edition):

Maree, S C (author). “Numerical Pricing of Bermudan Options with Shannon Wavelet Expansions.” 2015. Masters Thesis, Delft University of Technology. Accessed August 12, 2020. http://resolver.tudelft.nl/uuid:a080360d-9eeb-4b0d-9613-0c736f8769e5.

MLA Handbook (7^{th} Edition):

Maree, S C (author). “Numerical Pricing of Bermudan Options with Shannon Wavelet Expansions.” 2015. Web. 12 Aug 2020.

Vancouver:

Maree SC(. Numerical Pricing of Bermudan Options with Shannon Wavelet Expansions. [Internet] [Masters thesis]. Delft University of Technology; 2015. [cited 2020 Aug 12]. Available from: http://resolver.tudelft.nl/uuid:a080360d-9eeb-4b0d-9613-0c736f8769e5.

Council of Science Editors:

Maree SC(. Numerical Pricing of Bermudan Options with Shannon Wavelet Expansions. [Masters Thesis]. Delft University of Technology; 2015. Available from: http://resolver.tudelft.nl/uuid:a080360d-9eeb-4b0d-9613-0c736f8769e5

2. Yang, Fenghao. On Guaranteed Minimum Maturity Benefits and First-to-Default Type Problems.

Degree: PhD, Mathematics & Statistics, 2018, York University

URL: http://hdl.handle.net/10315/34554

A new class of exponential functionals arises when pricing certain equity-linked insurance products.We study the distribution of these exponential functionals using tools from Probability and Complex Analysis. In the case of the Kou process we obtain an explicit formula for the probability density function of the exponential functional and we apply this result to pricing equity-linked insurance products. As a by-product of this research we have also derived a new class of duality relations for hypergeometric functions.
In the second part of the thesis, we study correlation uncertainty in Credit Risk. The goal is to price analogues of first-to-default options under the assumption that the assets follow correlated stochastic processes with known marginal distributions and unknown dependence structure. We solve this problem using tools from Stochastic Analysis and Optimal Control Theory. We provide explicit solutions in some specific examples and numerical approximations in the more general case.
*Advisors/Committee Members: Salisbury, Thomas (advisor), Kuznetsov, Alexey (advisor).*

Subjects/Keywords: Finance; Levy processes; Kou processes; General exponential functional; Skew Brownian motion; Asymmetric local time; Mellin transform; Barnes- G function; Variable annuity guaranteed benefits; First to default; Uncertain correlation; Unknown dependence structure; Optimal control theory.

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Yang, F. (2018). On Guaranteed Minimum Maturity Benefits and First-to-Default Type Problems. (Doctoral Dissertation). York University. Retrieved from http://hdl.handle.net/10315/34554

Chicago Manual of Style (16^{th} Edition):

Yang, Fenghao. “On Guaranteed Minimum Maturity Benefits and First-to-Default Type Problems.” 2018. Doctoral Dissertation, York University. Accessed August 12, 2020. http://hdl.handle.net/10315/34554.

MLA Handbook (7^{th} Edition):

Yang, Fenghao. “On Guaranteed Minimum Maturity Benefits and First-to-Default Type Problems.” 2018. Web. 12 Aug 2020.

Vancouver:

Yang F. On Guaranteed Minimum Maturity Benefits and First-to-Default Type Problems. [Internet] [Doctoral dissertation]. York University; 2018. [cited 2020 Aug 12]. Available from: http://hdl.handle.net/10315/34554.

Council of Science Editors:

Yang F. On Guaranteed Minimum Maturity Benefits and First-to-Default Type Problems. [Doctoral Dissertation]. York University; 2018. Available from: http://hdl.handle.net/10315/34554

3.
Hackmann, Daniel.
Analytical Methods For *Levy* *Processes* With Applications To Finance.

Degree: PhD, Mathematics & Statistics, 2015, York University

URL: http://hdl.handle.net/10315/30132

This dissertation is divided into two parts: the first part is a literature review and the second describes three new contributions to the literature. The literature review aims to provide a self-contained introduction to some popular Levy models and to two key objects from the theory of Levy processes: the Wiener-Hopf factors and the exponential functional. We pay special attention to techniques and results associated with two “analytically tractable” families of processes known as the meromorphic and hyper-exponential families. We also demonstrate some important numerical techniques for working with these families and for solving numerical integration and rational approximation problems.
In the second part of the dissertation we prove that the exponential functional of a meromorphic Levy process is distributed like an infinite product of independent Beta random variables. We also identify the Mellin transform of the exponential functional, and then, under the assumption that the log-stock price follows a meromorphic process, we use this to develop a fast and accurate algorithm for pricing continuously monitored, fixed strike Asian call options. Next, we answer an open question about the density of the supremum of an alpha-stable process. We find that the density has a conditionally convergent double series representation when alpha is an irrational number. Lastly, we develop an effective and simple algorithm for approximating any process in the class of completely monotone processes –some members of this class include the popular variance gamma, CGMY, and normal inverse Gaussian processes – by a hyper-exponential process. Under the assumption that the log-stock price follows a variance gamma or CGMY process we use this
approximation to price several exotic options such as Asian and barrier options. Our algorithms are easy to implement and produce accurate prices.
*Advisors/Committee Members: Kuznetsov, Alexey (advisor).*

Subjects/Keywords: Applied mathematics; Mathematics; Finance; Levy processes; Exotic options; Meromorphic processes; Hyper-exponential processes; Mathematical finance; Analytical methods; Mellin transform; Laplace transform; Exponential functional; Wiener-Hopf factors; Asian options; Barrier options; Stable processes

…*exponential*
functional for specific L´
evy *processes*.
By “approximating” we mean that we usually… …precisely
the family of hyper-*exponential* *processes* and its generalization, the family of… …and
those on completely monotone *processes* and hyper-*exponential* *processes* will inform our… …apply this result
for hyper-*exponential* *processes* and *processes* with jumps of rational… …technique to determine
the distribution of the *exponential* functional for meromorphic *processes*…

Record Details Similar Records

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Hackmann, D. (2015). Analytical Methods For Levy Processes With Applications To Finance. (Doctoral Dissertation). York University. Retrieved from http://hdl.handle.net/10315/30132

Chicago Manual of Style (16^{th} Edition):

Hackmann, Daniel. “Analytical Methods For Levy Processes With Applications To Finance.” 2015. Doctoral Dissertation, York University. Accessed August 12, 2020. http://hdl.handle.net/10315/30132.

MLA Handbook (7^{th} Edition):

Hackmann, Daniel. “Analytical Methods For Levy Processes With Applications To Finance.” 2015. Web. 12 Aug 2020.

Vancouver:

Hackmann D. Analytical Methods For Levy Processes With Applications To Finance. [Internet] [Doctoral dissertation]. York University; 2015. [cited 2020 Aug 12]. Available from: http://hdl.handle.net/10315/30132.

Council of Science Editors:

Hackmann D. Analytical Methods For Levy Processes With Applications To Finance. [Doctoral Dissertation]. York University; 2015. Available from: http://hdl.handle.net/10315/30132