Financial Derivatives

Question 1
Long put option
The purchase or buying of a put option allows an investor to benefit from a decrease in the price of the underlying asset, while also limiting the amount of loss he/she may sustain. The purchaser of a put option will pay a premium to have the right, but not the obligation, to sell a specific number of shares at an agreed upon strike price. If the price rises dramatically, the purchaser of the put option can choose to do nothing and just lose the premium that he/she invested. This is indicated from the diagram below
Payoff diagram of Long Put Option





Price of stock
P ………………………….

From the diagram above, the purchaser of the put option will pay a premium (P) in order to get the right but not obligation to sell the stock at an agreed upon price. The potential loss will be limited to the premium paid. This is because when there is an increase in the price of the stock, the investor will not exercise the option and limit the losses to the premium paid (P). The gains arise when there is a decrease in the price of the stock. In this case, the investor will exercise the option and gain. In that case the put is in-the-money. As indicated in the portion or line above the stock price from the diagram.

Short Put Option
The writer of a put option has an obligation to buy the stock from the put buyer at the agreed upon or exercise price. The writer or seller will receive a premium and have an obligation to buy the stock at an agreed price from the buyer. If price of the stock goes up and the put is not exercised, the writer or seller gains by keeping the premium. If the stock price falls, the writer will be obligated or forced to buy the stock at a price greater than its value. The payoff diagram of a short put option is indicated below:
Payoff diagram of a Short Put Option

P …………………

Price of Stock at expiration


From the diagram above, the gain of the writer is limited to the premium (P) received for the put option. This is because when the price goes up the purchaser of the option will not exercise it, the writer or seller will nevertheless keep the premium (P). However, when the price of the stock falls, the writer of the put option is obliged to buy the stock from the buyer of the put option making him lose. That is the line below the price of stock in the diagram

Question 2
The forward rate should have be about GBP 1 = GHS 0.6453
Since the market forward rate is GBP 1 = GHS 0.66, there will be mispricing, this will bring arbitrageur into action.
The arbitrageur will buy the pounds with the cedis or borrow cedis and convert it to pounds at a rate of GBP 1 = GHS 0.62 and simultaneously enter into a forward contract to sell the pounds at the rate of GBP 1 = GHS 0.66 at the end of the two years. At the contract expiration date, the arbitrageur will have GBP 1 which is delivered on the forward contract and for which GHS 0.66 is received. This means that for every GHS 0.62 invested by an arbitrageur, GHS 0.66 will be received in two years. At the end of the two years, if the cedis were borrowed, he will pay the GHS 0.62 borrowed per pound from the GHS 0.66 received from each pound. The returns of the arbitrageur will be as follows;
(0.66 /0.62)2 -1 =0.133 or 13% which greater than the risk free rate of the Ghanaian cedis of 7%.














REFERENCES:
Don M.C and Robert B. (2013), An Introduction to Derivatives and Risk Management. Canada
Johnson K.E (2009), Options Spread Strategies: Trading Up, Down and Sideways Markets. New York: Bloomberg Financials
Silvka R.K (1980), Risk and Returns for Options Investment. Financial Analyst Journal: 67-73



Group Assignment – Derivative and Risk managementPage 4