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QUESTION 1a) Suppose you own 10,000 shares that are worth £50 each . i) Evaluate how...

QUESTION 1a) Suppose you own 10,000 shares that are worth £50 each

. i) Evaluate how put options can be used to provide you with insurance against a decline in the value of your holding over the next four months. ii) Construct a payoff diagram to illustrate your answer.

(b) Suppose that zero interest rates with continuous compounding are as follows:

Maturity (years) rate per annum %
1 2.0
2 3.0
3 3.7
4 4.2
5 4.5

Calculate forward interest rates for the second, third, fourth, and fifth years.

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Answer:

1)

a)

A put option is an option that gives the holder the right to sell the share at pre determined strike price in the case the stock value declines

Hence to provide an insurance against falling stock price, we will need to buy equivalent worth of put options

Put options to be bought - 10000 * 50 = 500000

After buying four months, if share price declines, portfolio value remains unchanged and if stock rises, then put option would expire without being exercised

b)

Forward rates can be calculated by using the formula given below:

Here,

Forward rate is .

Zero rates are .

Time to maturity is.

or the second year, , , , and :

Therefore,

For the third year, , , , and .

Therefore,

The forward rate for the third year is per annum

For the fourth year, , , , and .

Therefore,

The forward rate for the fourth year is per annum.

For the fifth year,, , , and .

Therefore,

The forward rate for the fifth year is per annum.

Conclusion: The forward rates for given zero rates are mention in the table below:

Maturity (years)

Zero Rate (% per annum)

Forward rates (% per annum)

1

2.0

2

3.0

4.0

3

3.7

5.1

4

4.2

5.7

5

4.5

5.7

jeff jeffy answered 1 year ago
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