University of Illinois Urbana-Champaign

Topics on option valuation and model calibration

Chen, Zisheng

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Zisheng_Chen.pdf

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https://hdl.handle.net/2142/44400

Description

Title
Topics on option valuation and model calibration
Author(s)
Chen, Zisheng
Issue Date
2013-05-24T22:14:48Z
Director of Research (if dissertation) or Advisor (if thesis)
Feng, Liming
Doctoral Committee Chair(s)
Feng, Liming
Committee Member(s)
  • Sreenivas, Ramavarapu S.
  • Song, Renming
  • Zhou, Enlu
Department of Study
Industrial&Enterprise Sys Eng
Discipline
Industrial Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2013-05-24T22:14:48Z
Keyword(s)
  • option pricing
  • model calibration
  • analytic class
  • characteristic function
  • simulation
  • inverse transform
Abstract
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.
Graduation Semester
2013-05
Permalink
http://hdl.handle.net/2142/44400
Copyright and License Information
Copyright 2013 Zisheng Chen

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