Principles of Financial Computing

• Textbook
  • Y.-D. Lyuu, Financial Engineering & Computation: Principles, Mathematics, Algorithms. Cambridge University Press, 2002. Corrigenda. Taiwan representative is Catherine Shih. Book is available from Sci-Tech Publishing Company, Taipei.

• References
  • F. J. Fabozzi and T. D. Fabozzi (Ed.), The Handbook of Fixed Income Securities. 4th ed. Irwin, 1995.
  • J. C. Hull, Options, Futures, and Other Derivatives. 4th ed. Prentice-Hall, 1999.
  • R. Jarrow and S. Turnbull, Derivative Securities. South-Western, 1996.
  • P. Ritchken, Derivative Markets: Theory, Strategy, and Applications. HarperCollins, 1996.
  • S. M. Sundaresan, Fixed Income Markets and Their Derivatives. South-Western, 1997. Review.
• Internet Resources
  • The Financial Data Finder.
  • Don M. Chance Recommended Derivatives Reading List.
  • Term Structure and Interest Rate Derivatives Literature.
  • Financial Engineering Programs around the World.
• Teaching Assistant
  • 楊宗穆 Yang, Tsung-Mu.

To Students,

You will learn a perhaps different perspective on finance, especially as it pertains to pricing and software engineering. Our emphasis on computation should add a new dimension and toolbox to your existing knowledge and financial sense. (But see Enrollments below.)

It is your responsibility to learn to write in high-level programming languages. We cannot impart that skill in the class. If the mathematics proves hard going, you are expected to fill in the gap by self-reading. The technicalities are not beyond a motivated graduate student's reach.

• Time value of money
• Bonds, mortgages, and annuities
• Duration, convexity, and immunization
• Yield curve, forward rate, and spot rate
• Option pricing theory and its wide-ranging applications
• Black-Scholes analysis
• binomial option pricing model (BOPM)
• Futures, forwards, and other derivatives
• The combinatorics of random walks
• Martingale, Brownian motion, stochastic calculus, and Ito integral
• Risk-neutral valuation
• Risk management
• Fixed-income securities with embedded options and interest rate derivatives
• Mortgage-backed securities (MBS)
• Numerical methods
• Monte Carlo methods
• Variance reduction (efficiency-improving) techniques
• Least-squares technique
• Quasi-Monte Carlo method
• Solving partial differential equations
• Yield curve fitting
• GARCH models
• Interest rate models and calibration

Notes [ 2003, 2004 ]

• [slides 2005.02.23 (PDF)]

Programming Exercises

1. Write a program to calculate the spot rates and forward rates from coupon bond prices (% of par) and their coupon rates (%). All times are period-based for convenience. The complexity should be linear in n, the number of bonds. Inputs: coupon bond prices (% of par; the ith maturing at period i), period coupon rates (% of par). Outputs: spot rates (%), forward rates (%). For example, if the coupon rates are [ 0%, 10%, 10% ] and the corresponding bond prices are [ 92.5925, 90, 89 ], then the spot rates are [ 8.00%, 16.72%, 14.96% ], and the forward rates are [ 8.00%, 26.15%, 11.52% ]. Due: March 31, 2004. Please send your source code, executable code, and an explanation file (how to run it? what is the programming language used?) under a folder/directory to Mr Yang. Name your directory StudendID_Name_HomeworkNumber for easy reference. Example: R91723054_YourName_1. Even if you need to make an appointment with Mr Yang for demonstration because of the unusual software you use, you still have to submit the files before the deadline.
2. Write a quadratic-time program to price American calls and puts based on the CRR binomial tree. Observe its convergence behavior. You may want to incorporate fancy ideas to improve the convergence speed for your own pleasure. Inputs: S, X, tau (year), sigma (%), r (%), continuous dividend yield q (%), and n. Due: April 28, 2004 with on-site demonstration.
3. Write a quadratic-time program to price European double-barrier knock-out calls. You may use the CRR binomial tree or any other trees. Observe its convergence behavior. You may want to incorporate fancy ideas to improve the convergence speed. Inputs: S, X, high barrier H, low barrier L, t (year), s (%), r (%), and n. Assume L < S < H. For example, the price is about 1.458 when t = 1 (year), r = 10%, S = 95, s = 25%, X = 100, L = 90, H = 140. You are strongly urged to let your program take in the parameters in the above order to make the job easier for Ms Teng. Due: May 19, 2004.
4. Write a Monte Carlo simulation to price European calls based on the GARCH model (with c = 0). Inputs: S, X, t (days), daily r (%), H₀, b₀, b₁, b₂, and number of replications m. Recall that H_t+1 = b₀ + b₁ H_t + b₂ H_t ( e_t+1)². For example, the price is about 0.72 when S = 100, X = 100, t = 3 (days), r = 0%, H₀ = 0.0001096, b₀ = 0.000006575, b₁ = 0.9, b₂ = 0.04. You are strongly urged to let your program take in the parameters in the above order to make the job easier for Ms Teng. Due: June 9, 2004.

Enrollments

• Non-programmers will be strongly discouraged as the probability of passing this course is slim, if possible at all (measure zero, so to speak).
• It is not impossible to pick up programming skills before the first assignment.
• The above two statements are not contradictory.