o10 Mathematics of financial derivatives 1999-2000

This is the home page for the o10 course on financial derivatives, 1999-2000 version (from 2000 the course will be given by Dr Hambly and the new home page for the course is here). The synopsis for the course is on the global synopses page accessible from the Mathematical Institute pages.

o10 students studying the course text (Financial Times 25/1/2000).

Click here for the exercises in pdf format (this version does not include the past schools questions).

Further information on rate modelling can be found on Saurav Sen's website .

  • The file greeks.mws is a Maple worksheet that lets you calculate and plot the greeks for vanilla call and put options. The files exotics.mws and barrier.mws let you calculate and plot digital call and put values, and down-and-out barrier call values. You may need to right click when downloading these files to stop Netscape from trying to open them, and offer you the option of saving them instead. I do not know what other browsers will do to them.

    Here are some Excel spreadsheets to illustrate parts of the course. Please note that they are beta versions, not for public release and (disclaimer!) are for demonstration purposes only. They were largely written by Jeff Dewynne, who retains the copyright. (These files are only accessible from .ox addresses. As with Maple files, you may need to be careful downloading them.)

    You will need a full install of Excel for some of these programs. If your college does not have Excel the University has a site licence, contact OUCS for details. The spreadsheets are not yet fully commented, but in most cases it is self-evident what you have to do: if it all goes horribly wrong just exit without saving!

    Please e-mail comments and suggestions for improvements to Sam Howison, howison@maths.ox.ac.uk.

  • The files ANData.xls (23 Kb) and IBM.xls (24 Kb) contain vanilla option data puts and calls, and plots.

  • There is a selection of binomial tree programs. The most basic is bin.xls (63 Kb) which calculates a call option value: try changing the inputs, while call-hedgeb.xls (178 Kb) simulates a random walk through the tree and lets you see the balance sheet of someone following a delta-hedge strategy.

  • The (large) files BARC2.xls (576 Kb) and FTSE.xls (1.15 Mb) contain analyses of market data: price histories, histograms of the distribution of returns, and plots showing how the mean and variance of returns scale with the time period (for models based on Brownian motion, the latter should be as the square root of the time period).

  • The file randomwalk.xls (276 Kb) lets you simulate discrete random walks in which the increments are normally distributed (generated by the subroutine zgauss). You can do Brownian motion, geometric Brownian motion and a mean-reverting process. On the Brownian motion sheet, you can alter the scaling of the variance of the increments with the timestep by changing the three exponents at the top left (one for each of the three simulations on the graph). They are currently set to be below 1/2, equal to 1/2 (Brownian motion) and above 1/2; make the timestep smaller and observe how the three random walks behave.

  • The file BS.xls (123 Kb) contains plots of the values and various Greeks for vanilla and digital call and put options.

  • The files DeltaH.xls (53 Kb) and GammaH.xls (53 Kb) illustrate what happens if you delta-hedge (or delta- and gamma-hedge) a call option at discrete time intervals, using geometric Brownian motion between rehedges and the Black-Scholes hedge ratios. Note the effect of a smaller time step. The file Hedgesim2.xls (1.3 Mb) simulates this discrete delta-hedging (replication) strategy for a call option many times, and plots the outcome as a scatter plot.

  • The files binEuroP.xls (63 Kb) and binAmerP.xls (63 Kb) contain binomial tree valuations of European and American style put options.

    This page last modified by Sam Howison (howison@maths.ox.ac.uk)
    4 October 2000