Bio-Mathematics

• J. Eisenfeld & C.-H. Han, "On Sharp Interval Bounds, Parametric Identification and the Diagrams of Compartmental System", May 1999. (In memory of Professor Jerome Eisenfeld)

Numerical Linear Algebra and Control

• W.-W. Lin, C.-S. Wang & C.-H. Han, "Continuation Methods for Solving Discrete-Time Algebraic Riccati Equations", IEEE Tran. Automatic Control, Vol. 40, No. 5, May 1995.
• C.-H. Han, W.-W. Lin & C.-S. Wang, "Existence of Homotopy Methods for Solving Modified Algebraic Riccati Equations", April 1994.
• Master Thesis: Homotopy Methods for Solving the Modified Algebraic Riccati Equations, National Tsing-Hua University, June 1994.

My talks

• Variance Reduction for Monte Carlo Methods to Evaluate Option Prices under Multi-factor Stochastic Volatility Models, March. 26, 2004, Ford Motor Company, Detroit, MI.
  Part I (PowerPoint) Part II (PDF)
• Variance Reduction for Monte Carlo Methods to Evaluate Option Prices under Multi-factor Stochastic Volatility Models, March. 24, 2004, IMA, University of Minnesota.
  
• (1) Pricing Volatility-Dependent Optinos under Stochastic Volatility, Feb. 3, 2004, Mathematics Institute,Acamedia Sinica, Taiwan.
  (2) Reduction of Asian Options: from the aspect of financial engineering, Feb. 3, 2004, Mathematics Institute,Acamedia Sinica, Taiwan.
• Pricing Volatility-Dependent Optinos under Stochastic Volatility: from the aspect of financial engineering, Dec. 5, 2003, Department of Mathematics, University of Minnesota.
• An Epsilon-Martingale Approach for the Pricing and Hedging of Volatility Contracts, July 23, 2003, NCTS, Taiwan.
• Pricing Asian Options with Stochastic Volatilities, July 21, 2003, NCTS, Taiwan.
• "Time Scales in Stochastic Volatility Models" July 16, 2003, NCTS, Taiwan.

Abstracts: A motivation for stochastic volatility(SV) models will be given in the first part of this talk. Then we introduce variogram analysis and use this tool to capture the appearance of a short or fast time scale in SV models. In particular, we examine TAIEX (Taipei Stock Exchange Capitalization Weighted Stock Index) of high frequency data form May 2002 to May 2003. Combining with range-based estimation, the existence of a short time scale appears as the rate of mean reversion is about 2 days. In the end, we review the price approximation to European option prices and related calibration issues.
• Pricing Asian options and Variance Swaps with Volatility Scales, Stochastic Computation Final Workshop, June 28, 2003, SAMSI.

Abstract: In this talk, we first present a dimension reduction technique for pricing arithmetic average Asian options in the context of multiscale-factor stochastic volatility models. This technique is very useful to reduce computational efforts comparing to the usual higher dimensional Asian pricing problems. In particular, the price approximation derived from the multiscale asymptotic analysis allows relevant parameters to be calibrated from the implied volatility surface. We then turn to a similar subject: pricing volatility contracts but the SV model is restricted to one fast mean-reverting factor. We show that applying the Feynman-Kac formula may lead to a degenerate pricing PDE. A particular contract "corridor" is considered, and we show that the price of this contract should take account the local time appearing around boundaries of the corridor.
• "Short time scale in S&P 500 and option price," Stochastic Computation Mid-Term Workdays, Feb 20, 2003, SAMSI.

Abstract: The presence of a short time-scale in S&P 500 can be identified by use of the empirical structure function, or variogram, of the high-frequency log absolute returns. Jumps in the model can not effect the rate of mean reverting process. Instead, it amplifies the level of noise in the variogram. We also show that a well-separated longer time-scale can be ignored under the pricing measure but not for short time-scale. Option pricing problem under fast-scale volatility is dealt by asymptotic analysis such that the approximated option price takes into account the skew of implied volatility.
• "Graduate Student Recruiting Weekend: Financial Mathematics", Mathematics Department, NCSU, March, 1, 2003, NC.