Question

In each of the following problems, plot and loss diagram(a) for the stock (short or long), b for the option (call or put), and (c) of the result of the strategy that comes combining the stock and the options positions. Be sure to label the axes, and all “Y” -axis and “X” axis intercepts, breakpoints and level of indicators

1. Covered Call Writing Strategy, Where C^E=$10, X=$40, S₀=$30
2. Synthetic Put strategy, where C^E=$8, X=$45, S₀=$25
3. Protective Put Buying Strategy, Where P^E=$12, X=$30, S⁰=$65
4. Synthetic Put strategy, Where P^E=$7, X=$25, S⁰=$50

Answer 1

Covered Call Writing Strategy, Where C = $10, X = $40, S₀= $30

Let's first understand a covered call writing. A covered call writing with instruments is actually the following:

• Buy a stock, S at current price of S₀ = $ 30
• Sell a call option, C on stock S, with strike of X = $ 40. Call premium = C = $ 10

The payoff table is shown below:

S0	30
Exercise Price of Call Option, X	40
Call Premium, C	10
Stock price, ST	Payoff from Long stock = ST - S0	Pay off from short call = C -max(ST - X,0)	Payoff from Portfolio = payoff from long stock + Payoff from short call
0	(30)	10	(20)
5	(25)	10	(15)
10	(20)	10	(10)
15	(15)	10	(5)
20	(10)	10	-
25	(5)	10	5
30	-	10	10
35	5	10	15
40	10	10	20
45	15	5	20
50	20	-	20
55	25	(5)	20
60	30	(10)	20
65	35	(15)	20

And the payoff diagram is:

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Part 2

Synthetic Put strategy, where C =$8, X=$45, S₀=$25

Synthetic Put has been interpreted as Synthetic Long Put. It's created by:

• Short stock,S at S₀ = $ 25
• Long Call Option on the stock, S at exercise price, X = $ 45. Call option premium, C = $ 8

Payoff table is shown below:

S0	25
Exercise Price of Call Option, X	45
Call Premium, C	8
Stock price, ST	Payoff from short stock = S0 - ST	Pay off from Long call = -C + max(ST - X,0)	Payoff from Portfolio = payoff from short stock + Payoff from long call
0	25	(10)	15
5	20	(10)	10
10	15	(10)	5
15	10	(10)	-
20	5	(10)	(5)
25	-	(10)	(10)
30	(5)	(10)	(15)
35	(10)	(10)	(20)
40	(15)	(10)	(25)
45	(20)	(5)	(25)
50	(25)	-	(25)
55	(30)	5	(25)
60	(35)	10	(25)
65	(40)	15	(25)

The payoff diagram is shown below:

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Part 3

Protective Put Buying Strategy, Where P = $12, X = $30, S₀ = $65

The strategy involves:

• Long stock, S at S₀ = $ 65
• Long Put on stock, S for exercise price X = 30. The Put premium, P = $ 12

Payoff table is shown below:

Stock price, ST	Payoff from long stock = ST - S0	Pay off from Long Put = -P + max(X - ST,0)	Payoff from Portfolio = payoff from long stock + Payoff from long Put
30	(35)	(12)	(47)
35	(30)	(12)	(42)
40	(25)	(12)	(37)
45	(20)	(12)	(32)
50	(15)	(12)	(27)
55	(10)	(12)	(22)
60	(5)	(12)	(17)
65	-	(12)	(12)
70	5	(12)	(7)
75	10	(12)	(2)
80	15	(12)	3
85	20	(12)	8
90	25	(12)	13
95	30	(12)	18

And the payoff diagram is as shown below:

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Part 4

Synthetic Put strategy, Where P = $7, X = $25, S₀ = $50

You can't create a synthetic Put Strategy using a Put option. I think this has to read Synthetic Call Strategy.

Please check your question.

Interpret this as Synthetic (Short) Call Strategy. This involves:

• Short a stock, S at S₀ = $ 50
• Short a Put on stock S at exercise of X = $ 25. The Put premium, P = $ 7

The payoff table is shown below:

S0	50
Exercise Price of Put Option, X	25
Put Premium, P	7
	Payoff from short stock = S0 - ST	Pay off from Short Put = P - max(X - ST,0)	Payoff from Portfolio = payoff from short stock + Payoff from short Put
0	50	-18	32
5	45	-13	32
10	40	-8	32
15	35	-3	32
20	30	2	32
25	25	7	32
30	20	7	27
35	15	7	22
40	10	7	17
45	5	7	12
50	0	7	7
55	-5	7	2
60	-10	7	-3
65	-15	7	-8

The payoff diagram is shown below: