Page 72 - DMGT513_DERIVATIVES_AND_RISK_MANAGEMENT

Unit 6: Introduction to Options

exercised at any moment prior to maturity (expiration). A third form of exercise, which is Notes
occasionally used with OTC (over the counter) options, is Bermudan exercise. A Bermuda option
can be exercised on a few specific dates prior to expiration. The name 'Bermuda' was chosen
perhaps because Bermuda is half way between America and Europe.

Example: On March 1, the price of Wheat $ 1800 per tonne. A apprehends a rise in price
and buys an American option on June Wheat (maturity date June 15) at a strike price of $1800.
The prices subsequently are as follows:
May 15:$ 2100
June 15: $ 1700

As the option is an American option, A exercise it on May 15, and sells the Wheat at a profit of
$300 per tonne.

Example: All the other facts are as above, but the option is a European option. In this
case A cannot exercise the option on May 15 because he only has the right to do so on the
maturity date. He therefore does not have the profit opportunity that he had in the previous
example.
It will be clear that an American option has a greater profit potential than a European option for
the buyer. Thus leads to premia being higher for American options.

There are hundreds of different types of options which differ in their payoff structures, path-
dependence, and payoff trigger and termination conditions. Pricing some of these options
represent a complex mathematical problem. Let us briefly discuss the various other types of
options.

6.4.1 Call Options

The following example would clarify the basics on Call Options.
A call option give the buyer the right but not the obligation to buy a given quantity of the
underlying asset, at a given price known as 'exercise price' or 'strike price' on or before a given
future date called the 'maturity date' or 'expiry date'. A call option gives the buyer the right to
buy a fixed number of shares/commodities in a particular security at the exercise price up to the
date of expiration of the contract. The seller of an option is known as 'writer.' Unlike the buyer,
the writer has no choice regarding the fulfilment of the obligations under the contract. If the
buyer wants to exercise his right, the writer must comply. For this asymmetry of privilege, the
buyer must pay the writer the option price, which is known as 'premium.'

Example: An investor buys one European Call option on one share of Reliance Petroleum
at a premium of ` 2 per share on July 31. The strike price is ` 60 and the contract matures on
September 30. The pay-off table shows the pay-offs for the investor on the basis of fluctuating
spot prices at any time. It may be clear from the following graph that even in the worst-case
scenario, the investor would only lose a maximum of ` 2 per share, which he/she had paid for
the premium. The upside to it has an unlimited profit opportunity.
On the other hand, the seller of the call option has a pay-off chart completely reverse of the call
options buyer. The maximum loss that he can have is unlimited, though the buyer would make
a profit of ` 2 per share on the premium payment.

LOVELY PROFESSIONAL UNIVERSITY 67