Combining Options to Match a Desired Payoff Schedule
Munyaradzi Arnold Chiwara, Mohammad Sajjad Hossain
Abstract: This project was aimed at developing an algorithm which takes a payoff
function and current prices of available securities and propose an optimal investment
strategy to approximate this function. We proposed a linear programming and a quadratic
programming solution under two different error models. We have shown some promising results
using some standard spreads. At the end we have proposed a way to select a set of options from
a collection such that the probability of loss above a given threshold is minimized while making
maximum profit.
Tools used in the experiment
1. We used this program to get options from
Yahoo! finance. This list of all publically traded options (US) might be useful to you.
2. We submitted our problem to NEOS Server to get an answer.
We also used GLPK occassionally. Both of them support the same format of input and model files.
3. You can find the AMPL model file here.
4. We take options and payoff function as piecewise linear graph. This
program converts such graphs into SCIP parameter file which is submitted to NEOS Server (or GLPK) as a problem instance.
Results for some standard spreads
The texual description of the payoffs and options used here can be found in the appendix section of
our full report.
Results for a real dataset
We took 84 Microsoft options and could generate the following payoffs. Blue lines represent the desired payoffs and red lines represent what we produces.
Here are the options used:
Microsoft Options
Here are the payoffs used:
payoff #1
payoff #2
payoff #3
payoff #4
payoff #5
