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oai:www.ideals.illinois.edu:2142/44400 2023-07-11 col_2142_5131 col_2142_16359 com_2142_5130 com_2142_16358 com_2142_234

Feng, Liming Feng, Liming Sreenivas, Ramavarapu S. Song, Renming Zhou, Enlu Chen, Zisheng 2013-05-24T22:14:48Z 2013-05-24T22:14:48Z 2015-05-24T10:01:03Z 2013-05 2013-05-24T22:14:48Z 2013-05 This dissertation is devoted to high performance numerical methods for option valuation and model calibration in L´evy process and stochastic volatility models. In the first part, a numerical scheme for simulating from an analytic characteristic function is developed. Theoretically, error bounds for bias are explicitly given. Practically, different types of options in commonly used L´evy process models could be priced through this method fast and accurately. Also, sensitivity analysis could be conducted through this approach effectively. Numerical results show that the schemes are effective for both options valuation and sensitivity analysis in L´evy process models. In the second part, a numerical scheme for Asian option pricing in jump-diffusion models is analyzed. Approximation errors are shown to decay exponentially. Numerical results show the speed and accuracy of the scheme. In the third part, for calibration purpose, certain numerical schemes are studied to price European and American options. For European options, error bounds are explicitly given. For American contracts, multiple options with different strikes and maturities could be priced simultaneously. Numerical results show that the combination of the above schemes with state-of-the-art optimization schemes makes efficient calibration of option pricing models possible. Item withdrawn by Alexis Thompson (athmpsn1@illinois.edu) on 2013-04-15T21:41:58Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Chen_Zisheng.pdf: 1584646 bytes, checksum: 575a7b2e2441f793afacb14197a5a703 (MD5) Made available in DSpace on 2013-05-24T22:14:48Z (GMT). No. of bitstreams: 2 Zisheng_Chen.pdf: 1584646 bytes, checksum: 575a7b2e2441f793afacb14197a5a703 (MD5) license.txt: 4061 bytes, checksum: 5ca6a2119ac27c36a8a1f3d5caea0d67 (MD5) Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Seth Robbins (srobbins@illinois.edu) on 2013-05-24T22:18:32Z Item is restricted until 2015-05-24T22:18:31Z Restriction data tranferred 2014-07-01T11:35:37-05:00 Original Data Group with Access UIUC Users [automated] Release Date: 2015-05-24 17:18:31 UTC Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system U of I Only Restriction Lifted for Item 44373 on 2015-05-24T10:01:03Z. http://hdl.handle.net/2142/44400 en Copyright 2013 Zisheng Chen option pricing model calibration analytic class characteristic function simulation inverse transform Topics on option valuation and model calibration text Industrial&Enterprise Sys Eng 1422 Industrial Engineering 0127 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Industrial Enginerng -UIUC 10KS0127PHD