Question

The other alternative is to purchase a PUT contract on euro

denominated bonds.

Calculate the net profit or loss per unit on a put option contract with

a strike price of €1,008 with a premium of €4.00 for the following

maturity prices:

€985, €1,000, €1,015 and €1,020

f. Explain how the option contract in part e protects against interest

rate rises and how this form of protection differs from the futures

contract.

Answer 1

A put option is an option contract giving the owner the right, but not the obligation, to sell a specified amount of an underlying security at a specified price within a specified time.

For a put option, payoff is given by the mathematical representation below:

In our question, Strike price = €1,008; Option premium = €4

(i) Maturity price of €985

Net payoff = Max(0, 1008 - 985) - 4 = 19 (PROFIT)

(ii) Maturity price of €1,000

Net payoff = Max(0, 1008 - 1000) - 4 = 4 (PROFIT)

(iii) Maturity price of €1,015

Net payoff = Max(0, 1008 - 1015) - 4 = -4 (LOSS)

(iv) Maturity price of €1,020

Net payoff = Max(0, 1008 - 1020) - 4 = -4 (LOSS)

Now, you see the benefit of having a put option, loss is caped and you (theoretically) have unlimited profit. (Note: theoretically, since the maturity price cannot be less than 0. So, the maximum profit per put option is Strike Price - Premium Paid).

f.

The put option can be a part of the bond holder's strategy to cap the losses from fall in bond prices. Bond prices fall when the interest rate rises (inverse relation between bond prices and interest rates). Hence, put option can help hedge the bond owner against increase in interest rates.

Hedging via futures contract produced symetric gains and losses when the interest rates move in any direction. Basically, it will need both the counterparties involved to honour the contract, and may lead to unlimited gains or losses.

However, hedging via options gives flexibility to cap losses, while maintaining the potential for unlimited gains. It is a right and not an obligation (like in case of futures contract) for the holder to buy or sell the asses in case of any adverse interest rate movements. Like in the above question, profit was unlimited for the put option holder, but loss was capped.