Topics on option valuation and model calibration

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Industrial Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2013

Author dc:creator

• Chen, Zisheng

Contributors dc:contributor

• Feng, Liming
• Sreenivas, Ramavarapu S.
• Song, Renming
• Zhou, Enlu

• option pricing
• model calibration
• analytic class
• characteristic function
• simulation
• inverse transform

Statement dc:rights

• Copyright 2013 Zisheng Chen

Language dc:language

en

Handle dc:identifier

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

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/44400