Question

Consider the following information for a non-dividend-paying stock:

Current stock price = 46.20

Call Price	Exercise Price	Put Price
7.03	40	0.83
5.24	42.5	1.54
3.76	45	2.56
2.61	47.5	3.9

a) Calculate the maximum profit of a covered call strategy using nearest out-of-the-money options.

b) Calculate the maximum loss of a collar strategy using nearest out-of-the-money options.

c) Calculate the value of a butterfly spread that peaks at LaTeX: S_T=45.00S T = 45.00.

d) Estimate the maximum value of a strategy that pays $1 if the future stock price is between $42.50 and $45.00.

Answer 1

a)

The maximum profit of a covered call strategy using nearest out-of-the-money options is :

Nearest OTM call option is of Exercise price 47.5 .

Max Profit of a covered call = (Exercise price - Current stock price) + Premium recieved.

= (47.5 - 46.2) + 2.61 = 3.91

b)

The maximum loss of a collar strategy using nearest out-of-the-money options is :

Max loss of a collar strategy = (Current stock price - Nearest OTM Put Exercise Price) + (Net premium)

= (46.2 - 45 ) + (2.56 - 2.61) = 1.2 - 0.05 = 1.15

c)

As its not mentioned whether to value Long call, Long put or Short call, Short put butterfly spread. Let's go with Long call butterfly spread.

The value of a butterfly spread that peaks at 45 will be by going :-

Long on In-The-Money Call option i.e. Long call at 42.5 (Paying Premium)

Short twice on At-The-Money Call option i.e. Short call at 45. (Receiving Premium)

Long on Out-The-Money Call option i.e. Long call at 47.5 (Paying Premium)

C^-= Short Call Premium.

C⁺ = Long Call Premium.

Value = C^- @ 42.5 + (2 x C⁺ @ 45) + C^- @ 47.5

= 5.24 + (2 x -3.76) + 2.61

= 0.33

Whether Stock price at maturity go Higher than 47.5 or Lower than 42.5, profit will remain same at 0.33.

d)

We can use Bull Call Strategy if investor believe price will not go beyond 45 at expiration. This strategy implies buying one option and writing another with Higher exercise price.

So, we can go short on Call option at exercise price of 45 giving C^- = 3.76 and go Long on Call option at exercise price of 42.5 paying C⁺ = -5.24.

If price stays between 42.5 & 45, maximum profit remain same at 1.02 (Approx to 1).

Suppose price at expiration is 44 then,

Profit = (St - Sx⁺) + (Sx^- - St ) + (Net Premium)

where,

St = Stock Price

Sx^- = Short postion Exercise Price

Sx⁺ = Long postion Exercise Price

Therefore,

Profit = (44 - 42.5) + (45 - 44) + ( 3.76 - 5.24)

= 1.5 + 1 - 1.48

= 1.02