Question

Q3. Suppose you write 30 put option contracts with a strike of $100 and expiring in 3 months. The put options are trading at $4.80. What is your net gain/loss if the underlying stock price at maturity is $110? What is the break-even price when your profit from this investment is zero?

Q4. A strangle is created by buying a put option, and buying a call on the same stock with higher strike price and same expiration. A put with an exercise price of $100 sells for $6.95 and a call with a strike of $110 sells for $8.60. Draw a graph showing payoff and profit for a strangle using these options.

Answer 1

Q3: Put option gives right to sell a stock at the strike price.

On maturity, the stock price is $110.

Investor has the right to sell at $100. Since the stock is worth $110 on maturity, there is no point in selling at less than market price of $100 by exercising the put option.

Hence, the investor would not exercise the option and it will go worthless.

The loss would be the price at which the options were purchased.

Total loss = 30 * 4.80 = $144

To break even, the investor should recoup this loss of $4.80 from each option contract. This means he should profit $4.80 from each put option contract. This implies he should exercise at a price where he will make a profit of $4.80 from each.

Hence, the stock price at maturity should be equal to = Strike price - price of put option premium

Break even price = $100 -$ 4.80 = $95.2

If the stock price is $95.2, then the investor can sell the stock at $100 by exercising put option right and make a profit of $4.80 and thereby eliminating the loss.

Q4: Strangle pay-off

The profit.loss table is constructed below using following relationships./formulas:

Put profit / loss = Max ((Strike price - Expiry price), 0 ) - Option premium

Call profit / loss = Max (Expiry price - Strike price), 0) - Option premium

Stock Price	Put profit/Loss	Call Profit/Loss	Total Payoff
70	23.05	-8.6	14.45
75	18.05	-8.6	9.45
80	13.05	-8.6	4.45
85	8.05	-8.6	-0.55
90	3.05	-8.6	-5.55
95	-1.95	-8.6	-10.55
100	-6.95	-8.6	-15.55
105	-6.95	-8.6	-15.55
110	-6.95	-8.6	-15.55
115	-6.95	-3.6	-10.55
120	-6.95	1.4	-5.55
125	-6.95	6.4	-0.55
130	-6.95	11.4	4.45
135	-6.95	16.4	9.45
140	-6.95	21.4	14.45
145	-6.95	26.4	19.45
150	-6.95	31.4	24.45
155	-6.95	36.4	29.45
160	-6.95	41.4	34.45

The graph is plotted using excel and given below: