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 Modelers' Manifesto.
  • 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(s)
  • 林盈宏 Lin, Ying-Hung (Edward) (r01723029)
  • 陸裕豪 Lok, U Hou (d99922028)
  • 盧政良 Lu, Zheng-Liang (d00922011)
  • 助教時間
    • 週五 12:10~13:00，管理學院二館302教室（林盈宏，請先寄 email 通知）
    • 週三 15:00~17:00，資訊系 446 室（陸裕豪、盧政良）
  • CEIBA systems: 922 U0270 / 723 M9500

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, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014 ]

1. 2014.02.19
2. 2014.02.26
3. 2014.03.05
4. 2014.03.12 & 1st assignment due
5. 2014.03.19
6. 2014.03.26
7. 2014.04.02 No class & 2nd assignment due
8. 2014.04.09
9. 2014.04.16
10. 2014.04.23 & 3rd assignment due
11. 2014.04.30
12. 2014.05.07 & 4th assignment due
13. 2014.05.14
14. 2014.05.21
15. 2014.05.28 & 5th assignment due
16. 2014.06.04
17. 2014.06.11
18. 2014.06.18 6th assignment due

Programming Exercises

• You are expected to write your own codes and turn in your source code.
• Do not copy or collaborate with fellow students.
• Never ask your friends to write programs for you.
  • 哈佛：125學生集體作弊.
  • Harvard Students Fighting Allegations of Cheating on Exam.
• Never give your code to other students or publish your code because it may be copied and you in turn may be suspected of copying other's code! The graders will not attempt to sort out who the original coders are because we are not running a court here.

1. Write a program to calculate the relative change (in %) in the n-year spot rate if the n-year zero-coupon bond price moves from q% to (1+k%) *q%, where q% is the quoted price. Inputs: n (year), q (the n-year zero-coupon bond price as % of par), k (the increment in bond price, also as % of par). Output: the change in the n-year spot rate in %. For example, assume n=10, q=60, k=1. Then the change in the n-year spot rate is −1.9971%. Please send your source code, executable code, and a brief explanation file if necessary (e.g., how to run it?) using the CEIBA system (922 U0270)/CEIBA system (723 M9500) before 08:00 AM of March 12, 2014. Compress your files into a single file and name it StudentID_HW_1 for easy reference. Example: R91723054_HW_1. Even if you need to make an appointment with 盧政良 for demonstration because of the unusual software you use, you still have to submit the files before the deadline.
2. Write a binomial tree program to calculate the prices of a standard European put and an American put (which can be exercised only in the last quarter of the option's life). Inputs: S (stock price at time = 0), X (strike price ), s (annual volatility), t (maturity), n (the number of periods, a multiple of 4), d (continuous annualized dividend yield), r (interest rate). For example, suppose S = 100, X = 95, s = 0.4, t = 1, n = 1000, d = 0.02, and r = 0.06. The European option price is about 10.9611 and the American option price is about 11.2128. Please send your source code, executable code, and a brief explanation file if necessary (e.g., how to run it?) using the CEIBA system (922 U0270)/CEIBA system (723 M9500) before 08:00 AM of April 2, 2014. Compress your files into a single file and name it StudentID_HW_2 for easy reference. Example: R91723054_HW_2. Even if you need to make an appointment with 林盈宏 for demonstration because of the unusual software you use, you still have to submit the files before the deadline.
3. Write a program to price American-style arithmetic average-rate calls based on the CRR binomial tree. Please output the delta, too. The payoff function is max(average - X, 0). Of course, if the holder exercises early, then average means the average up to that node. Inputs: S (stock price at time = 0), X (strike price), t (maturity in years), s (%) (annual volatility), r (%) (continuously compounded annual interest rate), n (number of periods), and k (number of states per node). For example, when S = 100, X = 70, t = 2 (years), s = 20%, r = 5%, n = 40, and k = 5, the price is about 36.308 and the delta is about 0.9515. Please send your source code, executable code, and a brief explanation file if necessary (e.g., how to run it?) using the CEIBA system (922 U0270)/CEIBA system (723 M9500) before 08:00 AM of April 23, 2014. Compress your files into a single file and name it StudentID_HW_3 for easy reference. Example: R91723000_HW_3. Even if you need to make an appointment with 陸裕豪 for demonstration because of the unusual software you use, you still have to submit the files before the deadline.
4. Write a CRR binomial tree program to price European single-barrier knock-in calls on a dividend-paying stock and determine the relative error based on the call price using the formula (31) on p. 367 of the slides. Let c₁ be the price from the tree program, c₂ be the price from formula (31). Then the relative error is given by 100*[(c₁ -c₂)/c₂] (%). Inputs: S (stock price), X (strike price), H (barrier, smaller than S), t (year), s (volatility in %), r (interest rate in %), q (dividend yield in %), and n (number of periods). For example, the prices are c₁=5.3840 and c₂=5.3844 when S = 95, X = 100, H = 90, t = 1 (year), s = 25 (%), r = 15 (%), q = 5 (%), and n = 192. The relative error is -0.0083%. For another example, the prices are c₁=4.1270 and c₂=5.3844 when the inputs are the same except that n = 193. The relative error is -23.3527%. Please send your source code, executable code, and a brief explanation file (e.g., how to run it?) using the CEIBA system (922 U0270)/CEIBA system (723 M9500) before 08:00 AM of May 7, 2014. Compress your files into a single file and name it StudentID_HW_4 for easy reference. Example: R91723054_HW_4. Even if you need to make an appointment with 盧政良 for demonstration because of the unusual software you use, you still have to submit the files before the deadline.
5. Write a trinomial tree or a binomial-trinomial program to price European double-barrier knock-out calls. Inputs: S (stock price), X (strike price), H (high barrier), L (low barrier), t (year), s (volatility in %), r (continuously compounded interest rate in %), and n (number of periods). Assume L < S < H. For example, the price is about 1.457~1.4584 when t = 1 (year), r = 10 (%), S = 95, s = 25 (%), X = 100, L = 90, H = 140. See here for the binomial-trinomial tree outputs. See here for the convergence of binomial-trinomial tree vs that of trinomial tree. As comparison, write a Monte Carlo simulation program to price the same option. Inputs are the same (S, X, H, L, t, s, r, n) plus m (number of paths). Outputs are teh option price plus the sample standard deviation. Please send your source code, executable code, and a brief explanation file if necessary (e.g., how to run it?) using the CEIBA system (922 U0270)/CEIBA system (723 M9500) before 08:00 AM of May 28, 2014. Compress your files into a single file and name it StudentID_HW_5 for easy reference. Example: R91723054_HW_5. Even if you need to make an appointment with 林盈宏 for demonstration because of the unusual software you use, you still have to submit the files before the deadline.
6. Write a program to price an x-year American-style call option on a zero-coupon bond that matures at year y with a par value of 1 dollar. Use trees for the CIR model. Inputs: x (year), y (year), r (%) (initial short rate), b (%) and m (%), s (%) and number of partitions during the option's life n, and strike price X (% of par). For example, the option price is about 5.87267 (% of par) when x = 1, y = 2, r = 4 (%), b = 20 (%), m = 4 (%), s = 10 (%), n = 30 and X = 90 (%). Please send your source code, executable code, and a brief explanation file if necessary (e.g., how to run it?) using the CEIBA system (922 U0270)/CEIBA system (723 M9500) before 08:00 AM of June 18, 2014. Compress your files into a single file and name it StudentID_HW_6 for easy reference. Example: R91723054_HW_6. Even if you need to make an appointment with 陸裕豪 for demonstration because of the unusual software you use, you still have to submit the files before the deadline.

Enrollments

• Non-programmers will be strongly discouraged as the probability of passing this course is slim, if possible at all.
• It is not impossible to pick up programming skills before the first assignment.
• Financial knowledge is a plus, but again it can be picked up if you are motivated.