Rikard Davidsson  presenterar sitt examensarbete

Option Pricing in Equity-Linked Notes

Abstract

This thesis focus on the initial pricing of the Equity Linked Note
(ELN). This is being done by comparing prices between an issued ELN
and the synthetic equivalent, i.e. creating a theoretical ELN with the
same characteristics as the issued ELN, consisting of a bond and a
long call option. Absence of arbitrage would give the same price on
the two. This would also indicate fair pricing on the market and
conclude absence of "hidden fees". However a synthetic equivalent is
impossible to create on the market, due to limitations in the supply
of options and matching problems in issuing dates and maturity dates
between options and bonds. ELNīs often have a lifetime which span of
three to five years while option lifetime is most common measured in
months. One might suggest the use of warrants, which have the same
characteristics as an option but a greater life span, instead of
options however they are not as many or liquid as options now and even
worse in 1995 when the ELN s used in this study where issued. The main
task of this thesis therefor is to calculate the an accurate price of
the option.


Calibration - The Weighted Least Squares technique proved to be
successful in most cases when calibrating the option data. The faults
or poor performance occurred during days with little or bad data. One
reason for this is of course the lack of data during some trading days
but also the di culties of extracting and calculating correct expected
dividend yields. In some cases the dividend yield was actually
negative proposing a very unlikely scenario. Another complication when
calibrating is the over pricing of options with short time to
maturity, a problem which could have a solution in giving different
maturities different weights.


Pricing - The results from the four different stock price models is
surprisingly negative. Not in the sense of giving a incorrect answer
but in the sense of the complex and more sophisticated models been out
performed by the most simple model, Black-Scholes. Theory implicates
that the other models should give a better prediction of the option
price, which could not be confirmed in this study. At the same time
one should bare in mind that the Black-Scholes formula is far more
used then the others which could have an impact on market prices.


Participation rate - This part of the study is not just depending of
the option price but also on data and calculations around the
bond. Prior studies have utilized a type of corporate bond, with a
higher risk and therefor also higher yield. This would have had a
positive influence on the pr calculated to the synthetic ELN. In this
part the ad hoc solution of estimating a mean of expected dividend
yield came in place. Since absence of dividends have a great impact on
the results when pricing options with maturities of several years, it
proves the importance of being able to make a fair estimate to them.