NEWS:

• Final Exam
  You can bring a cheat sheet: letter size, 2-sided, must be handwritten
  topics for final and problems
  solutions
• Exam 2 was on Monday, Dec. 5.
  Solution
  corrected version: Topics and practice problems ,   solutions
• Matlab m-files:
  • binomial tree model based on YEARLY data: ybinom_eu.m
  • Black-Scholes option prices for European call/put options: BlackScholes.m
    We can use this to find the implied volatility from call option prices using fzero, see the course notes and the example just below.
    To find the implied volatility from put option prices: Use BlackScholesPut.m
  • Example for using stock and option prices in Matlab, computing implied volatility (m-file)
    uses the following m-files (UPDATED version from Oct. 25):
    get current option prices: getOptionPrices.m
    plot option prices: option_plot.m
• Practice problems for Exam 1
  solution
• Exam 1 is on Mon, Oct. 17
  Solution of Exam
  It covers the following topics:
  • Present Value Analysis (Section 2 in the notes)
    write Matlab code to find answer (payment or interest rate)
    You may need fzero command.
  • Probability: expectation, variance, conditional expectation (Sections 3.1-3.10)
  • No Arbitrage Principle, Comparison principle (Sections 4.6)
  • Option pricing with risk-neutral measure (Sections 4.9,4.10)
  • Binomial tree model, trinomial tree model (Sections 4.1,4.2)
  • Option pricing algorithm for binomial tree model, Delta hedging (Sections 4.11, Conclusion on p.36, 4.17-4.20)
  • Properties of option prices (Section 5)
• Assignment 2 is due on Wed, Oct. 12, 9pm
  Solution of problem 1, m-file a2p1ab.m
  Solution of problem 2, m-files: xbinom_eu_put.m, xbinom_am_put.m, xbinom_am_call.m
  Hand in printouts of all m-files you used (unless they are exactly the m-files which I provided). Use publish in Matlab. I need to see all code and the generated output and graphics.
• Option pricing with binomial trees in Matlab (see course notes):
  binom_eu.m, binom_am.m, xbinom_eu_call.m
• Download the m-file xbinom_eu_call.m. Then run the example from section 4.19 in the class notes:
      S0=10; K=11; [V,av] = xbinom_eu_call(.01,S0,1.1,.9,10,K,3);
• Course notes (Nov. 2), Appendix: Convex separation theorem
• Solution of Assignment 1, m-file Please look at this solution and make sure that you understand the Matlab code.
  In particular look at the Matlab code for "Problem 3(a), Method 2" where I use vectors in Matlab. You will need this for future assignments.
• Assignment 1, due Wed Sept. 14 at 9pm
• Use the links below to find the price for an Apple (AAPL) put option and call option with strike price $100 and maturity June 2017.
• If you are not familiar with Matlab do the following NOW:
  • Read the "gentle introduction to Matlab" below
    
  • Read the first 10 pages of the Matlab Primer (see below) AND TRY OUT THE COMMANDS ON A COMPUTER.
  • Figure out how to write, run, and publish an m-file.

AAPL option prices in Sept. 2011 for three different maturities

Course information

SYLLABUS: Information about exams, homeworks, grades

Additional Course Material

• Stock prices (current and historical) and option prices (current only) are available online, e.g. from Yahoo Finance: E.g.,
  • real time IBM stock price with bid and ask prices (Nasdaq and NYSE data is really real time, data from some other exchanges is delayed)
  • historical IBM stock prices
  • IBM option prices (how to read an options table)
• Example for call and put option prices for different maturities
• Are actual options American style or European style?
  Options on stocks like IBM or GE are American style options. Most options on indices (like S&P 500) are European style, but there are a few exceptions: E.g, OEX options on the S&P 100 index are American style (there exists also a European style version called XEO).
• "Short position": How to have a negative amount of assets in your portfolio
• How to get stock prices into Matlab:
  • Download the files get_stock.m and get_stock_plot.m and put it in the same directory as your other m-files.
  • To get e.g. Apple (AAPL) stock prices from Aug.1 2001 to Jan.1 2004 use

    [sopen,sclose,shigh,slow,svol] = get_stock('AAPL',[2001 8],2004)

    Type help get_stock for more information.
  • For S&P 500 index use the symbol '^GSPC'.

Matlab programming

We will use Matlab for all computations.

• Matlab can be downloaded for free from TERPware.
• Gentle introduction to Matlab (also explains how to use the Matlab interface, how to publish)
  Note that we will NOT use SYMBOLIC Matlab commands like sym, syms, ezplot in this class.
• Matlab Primer gives a concise summary of the most important Matlab commands (This was written for an older version of Matlab. The flops command no longer exists, but all other commands still work in the same way).

How to hand in Matlab results for homeworks:

• You have to write an m-file for each problem. (Typing commands at the >> prompt and printing this out is not allowed)
• You have to hand in the m-file together with the output and graphics.
  The easiest way is to use the publish command in Matlab (if you call additional m-files, you have to print them out separately).
• How to use the publish command in Matlab:
  Example: this m-file shows how to format each problem. This is the generated output.
  More information about publishing markup