Determining the Cheapest-to-Deliver Bonds for Bond Futures ppt

Determining the Cheapest-to-Deliver Bonds

for Bond Futures

Marlouke van Straaten

March 2009

Master’s Thesis

Utrecht University

Stochastics and Financial Mathematics

March 2009

Master’s Thesis

Utrecht University

Stochastics and Financial Mathematics

Supervisors

Michel Vellekoop Saen Options

Francois Myburg Saen Options

Sandjai Bhulai VU University Amsterdam

Karma Dajani Utrecht University

Abstract

In this research futures on bonds are studied and since this future has several bonds as its un￾derlyings, the party with the short position may decide which bond it delivers at maturity of the

future. It obviously wants to give the bond that is the Cheapest-To-Deliver (CTD). The purpose

of this project is to develop a method to determine, which bond is the CTD at expiration of

the future. To be able to compare the underlying bonds, with different maturities and coupon

rates, conversion factors are used.

We would like to model the effects that changes in the term structure have on which bond is

cheapest-to-deliver, because when interest rates change, another bond could become the CTD.

We assume that the term structure of the interest rates is stochastic and look at the Ho-Lee

model, that uses binomial lattices for the short rates. The volatility of the model is supposed

to be constant between today and delivery, and between delivery and maturity of the bonds.

The following questions will be analysed:

• Is the Ho-Lee model a good model to price bonds and futures, i.e. how well does the model

fit their prices?

• How many steps are needed in the binomial tree to get good results?

• At what difference in the term structure is there a change in which bond is the cheapest?

• Is it possible to predict beforehand which bond will be the CTD?

• How sensitive is the futures price for changes in the zero curve?

• How stable are the volatilities of the model and how sensitive is the futures price for

changes in these parameters?

To answer these questions, the German Euro-Bunds are studied, which are the underlying bonds

of the Euro-Bund Future.

Acknowledgements

This thesis finishes my masters degree in ‘Stochastics and Financial Mathematics’ at the Utrecht

University. It was a very interesting experience to do this research at Saen Options and I hope

that the supervisors of the company, as well as my supervisor and second reader at the univer￾sity, are satisfied with the result.

There are a few persons who were very important during this project, that I would like to

express my appreciation to. First I would like to thank my manager Francois Myburg, who is

a specialist in both the theoretical and the practical part of the financial mathematics. Unlike

many other scientists, he has the ability to explain the most complex and detailed things within

one graph and makes it understandable for everyone. It was very pleasant to work with him,

because of his involvement with the project.

Also, I would like to express my gratitude to Michel Vellekoop, who has taken care of the

cooperation between Saen Options and the university. He proposed an intermediate presentation

and report, so that the supervisors of the university were given a good idea of the project. He

was very helpful in explaining the mathematical difficulties in detail and in writing this thesis.

He always had interesting feedback, which is the reason that this thesis has improved so much

since the first draft. Although the meetings with Francois and Michel were sometimes difficult

to follow, especially in the beginning when I had very little background of the subject, it always

ended up with some jokes and above all, many new ideas to work with.

In addition, I would like to thank Sandjai Bhulai, who was my supervisor at the university.

Although from the VU University Amsterdam and the subject of this thesis is not his expertise,

he was excited about the subject from the start of the project and he has put a lot of effort into

it. It was very pleasant to work with such a friendly professor.

I also want to thank Karma Dajani, who was the second reader, and who was so enthusiastic

that she wanted to read and comment all the versions I handed in.

Finally I would like to thank my family and especially Joost, who was very patient with me and

always supported me during the stressful moments.