Topics on option valuation and model calibration

Chen, Zisheng

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

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

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

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

Copyright and License Information

Copyright 2013 Zisheng Chen

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