Question

On 14 August British Biotech traded options were quoted on NYSE Liffe as follows:

Calls for british biotech: 160(option) 30 1/2(September) 40(Dec.) 53(March)

Puts for british biotech: 7 1/2(september) 16 1/2(december) 23 1/2(march)

Calls for 177 1/2: 189(option) 20 1/2(September) 31(Dec.) 45 1/2(March)

Puts for 177 1/2: 16(september) 27(december) 34 1/2(march)

Assume: No transaction costs.

Required

(a) Imagine you write a December 180 put on 14 August. Draw a graph showing your profit

and loss at share prices ranging from 100p to 250p.

(b) Draw a graph showing the buyer’s profit and loss at the same share price range.

(c) Compare your answers for (a) and (b) and comment (100 words max).

Answer 1

Part (a)

Write a Dec 180 Put

Put Premium, P = 27, Strike Price, K = 180, If S is the asset price at expiration then Profit & Loss

= P - max (K - S, 0) = 27 - max (180 - S, 0)

Profit (Loss) Matrix will be:

Share Price, S (P)	Profit / (Loss) (P) = 27 - max (180 - S, 0)
100	-53
110	-43
120	-33
130	-23
140	-13
150	-3
160	7
170	17
180	27
190	27
200	27
210	27
220	27
230	27
240	27
250	27

And the diagram is:

Part (b)

Buyer's profit / (Loss) will be the mirror image,

Profit / Loss = max (K - S, 0) - P = max (180 - S, 0) - 27

The matrix is:

Share Price, S (P)	Profit / (Loss) (P) = max (180 - S, 0) - 27
100	53
110	43
120	33
130	23
140	13
150	3
160	-7
170	-17
180	-27
190	-27
200	-27
210	-27
220	-27
230	-27
240	-27
250	-27

And the payoff diagram is:

Part (c)

Part (a) Writing the option: Upside is limited to the put premium of 27 pounds, while the downside is unlimited. If stock prices do fall, this can lead to enormous loss to the writer.

Part (a): Buying the option: The profit / (Loss) matrix is the mirror image. While upside is unlimited, the downside is limited to 27 pounds which the premium paid to buy the option. This can work wonders in a situation when stock price is expected to fall.

The break even price in both the cases is 153 pounds, in which case profit to either party is zero.