Chooser options ? chracteristics and metod of pricing

Boles?aw Borkowski, Monika Krawiec
Warsaw University of Life Sciences
Department of Econometrics and Statistics
e-mails: boleslaw_borkowski@sggw.pl, krawiec.monika@gmail.com
Possibilities of investing on European wheat market with the use of chooser
options Key words: wheat prices, stationarity, cointegration, error correction
model, chooser options Summary
The paper here presents the econometric analysis of interrelationships of
wheat prices in Poland and other important EU producers from 2004 through
2008. The first stage of research examined integration of considered
markets by the use of ADF and KPSS tests. To study the cointegration we
used the Johansen's method. Then for cointegrated time series we estimated
model with Error Correction Mechanism - ECM. We also considered
possibilities of applying derivatives, used within the EU, to reduce risk
on the Polish wheat market. We decided to test the chooser options as they
may be useful for inexperienced investors who are uncertain about the
direction of the market and do not know if they should buy a call or a put
option. We focused on Poland, Germany and France, because econometric
analysis presented in the paper revealed cointegration of wheat prices in
these countries. The research results proved that even though the choosers
options were more expensive than analogous vanilla options, it was possible
to gain profits from their application on the wheat markets in considered
European countries. 1. Introduction
In this paper we performed an analysis of correlation of consumption
wheat prices in Poland and other countries of European Union. We included
in the analysis the largest producers of consumption wheat, that is:
Germany, France, Poland, Spain, UK and Portugal. The analysis is based on
weekly data on consumption wheat prices from 27.12.2004 to 03.11.2008. The
data was collected within the Integrated System of Agricultural Information
and is still available at the website of Ministry of Agriculture and Rural
Development (www.minrol.gov.pl).
Mechanics of prices correlation and their transmission on various
markets were discussed over numerous works [Rembeza 2008]. Such analysis
allows to evaluate the efficiency of market mechanisms present on different
markets as well as their competitiveness. Other question is if the
integration of EU markets level the prices on the market because of the
flow of prices impulses [Syczewska 2007]. Here, we focused on studying
mutual prices relations between markets, integration of markets and their
competitiveness, mechanism of accommodation of grain prices in Poland to
the prices set by main producers of wheat within the EU and possibilities
of applying derivatives, used within the EU, to reduce risk on the Polish
wheat market.
All businesses are subject to a great variety of risks, but in the
case of agriculture some types of risk are more specific to it or affect it
to a greater extent than other sectors. According to Alizadeh, and Nomikos
(2005) the major types of risk in the agricultural sector are: asset risk
(associated with theft, fire and other loss or damage of equipment,
buildings and other agricultural assets used for production); production or
yield risks (often related to extreme weather events, but also include
risks like plant and animal diseases);. financial risks (related to
fluctuations in the cost of borrowing, insufficient liquidity and loss of
equity); price risk (which arises from falling output prices and/or rising
input prices after a production decision has taken place); institutional
and legal risks (which can be due to changes in regulatory and legal
environments that produces operate); ecological risks (related to pollution
and climate change or the result of management of natural resources);
market risks (which depend on output and input price variability) and
currency risk (that arises from fluctuation in exchange rates when costs
and revenues in agricultural business are in different currencies). Some of
this types of risk may be managed by the use of insurances, other by the
use of derivatives.
Derivative contracts are widely used for the purposes of price risk
management. The most popular derivatives used in hedging against price risk
are forwards, futures and options. Organized trading in agricultural
derivatives markets dates back to the mid 1860s with the opening of the
Chicago Board of Trade. Since then, the trading volume as well as the
variety of available futures contracts has increased dramatically. In
addition to the standard instruments, there are numerous other types of
derivatives which financial services providers can develop and offer to
farmers for the purpose of agricultural price risk management. Such
instruments are used extensively in the financial over-the-counter (OCT)
derivatives markets. Their migration to the agricultural derivatives
markets could be done relatively easy. Such instruments include, for
instance, barrier, lookback, Asian, binary, forward start or chooser
options.
Implementation of lookback options on commodity exchanges in Poland
was discussed by Krawiec (2003), while applications of Asian options in
managing risk related to price changes on the markets of fodder and porkers
in Poland were proposed by Borkowski and Krawiec (2007). This time we
decided to test the chooser options as they may be useful for inexperienced
investors who are uncertain about the direction of the market and do not
know if they should buy a call or a put option. It is common that someone
on financial market buys an option (for example, a vanilla call option) and
when it comes to exercising the option the person realizes that his
decision was totally wrong and whishes that a vanilla put option had been
purchased instead. For such a person, an option that gives the opportunity
to choose between a vanilla call option and a vanilla put option (a chooser
option) would serve as a useful and valuable instrument [Ravindran 1998]. 2. Methods of research
2.1 Cointegration analysis
Analysis of correlation of prices between markets is done through
various methods. The simplest methods of studying the correlation of prices
on different markets are limited to the analysis of Pearson's correlation
coefficients and linear regression models. Often in economical research we
deal with spurious regression rather than real long-term relations. We come
across this phenomenon mainly when we analyse time series characterized
with nonstationarity, autocorrelation and heteroscedasticity of error term.
In order to avoid spurious regression, firstly, we performed an analysis of
the order of integration of the studied time series. The definition of
integration as well as basic tests used to verify the level of variables
integration are discussed in many works [Charemza, Deadman 1997,
Kwiatkowski at al. 1992, Syczewska 2007, Johannes 1998]. In this work, to
study the variables integration we used two tests: augmented Dickey -
Fuller's test (ADF) and KPSS (Kwiatkowski - Philips - Schmidt - Shin's)
test. In the next step we examined the cointegration between the variables.
To do this two tests are most often employed: Engle - Granger's [Rembeza
2006] and Johannes' [Johansen 1991, Johannes 1998]. To study the
cointegration we used the Johansen's method, which is based on the Vector
Autoregressive Model (VAR) maximum likelihood estimation. We used VAR -
Vector Autoregressive Model with incrementation defined as follows:
[pic], (1)
where:
[pic] - first differences of variables,
[pic],
[pic] - matrix of model parameters,
[pic] - random error.
For cointegrated time series we calculated the model parameters with
Error Correction Mechanism - ECM, defined:
[pic], (2)
where :[pic] - residuals of cointegrational equation. 2.2 Chooser options - description and method of pricing
A chooser option is sometimes referred to "as you like it" option,
"you choose" option or "pay now/choose later" option. Chooser options,
being representatives of time-dependent options, came into existence in the
late eighties of XX century. They can be used to hedge exposures that may
or not may realize. Zahng (2006) suggests they are also useful for
speculating on changes in the volatility of the underlying asset.
The owner of a chooser option has the right to determine whether the
chooser option will become a call or a put option by a specified choice
date. After the choice date, the option becomes a plain vanilla call or
put, depending on the owner's choice. Since the holder of a chooser option
has the right to decide the nature of the option, the chooser option is
more to the advantage of the holder, and hence the holder should pay a
higher price than buying either the corresponding call or put option. Thus
a chooser option is more expensive than the corresponding call or put
option.
Chooser options are generally classified into simple chooser options
and complex chooser options. When the strike prices of the call and put
options are the same and the two options have the same time to maturity in
a chooser option, the chooser option is called a simple chooser option.
Otherwise, the chooser option is called a complex option. In the paper we
concentrate on European-style chooser options in a Black-Scholes
environment for transparency and easy comparisons with vanilla options.