In: Finance

The price of a stock is $40. The price of a one-year put with strike price $30 is $0.70 and a call with the same time to maturity and a strike of $50 costs $0.50. Both options are European.

(a) An investor buys one share, shorts one call and buys one put. Draw and comment upon the payoff of this portfolio at maturity as a function of the underlying price.

(b) How would your answer to (a) change if the investor buys one share, shorts two calls and buys two puts instead.

(a)

Stock price | Long stock payoff | Payoff short call strike $50 | Payoff long put strike $30 | Combined position |

20 | -20 | 0.5 | 9.3 | -10.2 |

21 | -19 | 0.5 | 8.3 | -10.2 |

22 | -18 | 0.5 | 7.3 | -10.2 |

23 | -17 | 0.5 | 6.3 | -10.2 |

24 | -16 | 0.5 | 5.3 | -10.2 |

25 | -15 | 0.5 | 4.3 | -10.2 |

26 | -14 | 0.5 | 3.3 | -10.2 |

27 | -13 | 0.5 | 2.3 | -10.2 |

28 | -12 | 0.5 | 1.3 | -10.2 |

29 | -11 | 0.5 | 0.3 | -10.2 |

30 | -10 | 0.5 | -0.7 | -10.2 |

31 | -9 | 0.5 | -0.7 | -9.2 |

32 | -8 | 0.5 | -0.7 | -8.2 |

33 | -7 | 0.5 | -0.7 | -7.2 |

34 | -6 | 0.5 | -0.7 | -6.2 |

35 | -5 | 0.5 | -0.7 | -5.2 |

36 | -4 | 0.5 | -0.7 | -4.2 |

37 | -3 | 0.5 | -0.7 | -3.2 |

38 | -2 | 0.5 | -0.7 | -2.2 |

39 | -1 | 0.5 | -0.7 | -1.2 |

40 | 0 | 0.5 | -0.7 | -0.2 |

41 | 1 | 0.5 | -0.7 | 0.8 |

42 | 2 | 0.5 | -0.7 | 1.8 |

43 | 3 | 0.5 | -0.7 | 2.8 |

44 | 4 | 0.5 | -0.7 | 3.8 |

45 | 5 | 0.5 | -0.7 | 4.8 |

46 | 6 | 0.5 | -0.7 | 5.8 |

47 | 7 | 0.5 | -0.7 | 6.8 |

48 | 8 | 0.5 | -0.7 | 7.8 |

49 | 9 | 0.5 | -0.7 | 8.8 |

50 | 10 | 0.5 | -0.7 | 9.8 |

51 | 11 | -0.5 | -0.7 | 9.8 |

52 | 12 | -1.5 | -0.7 | 9.8 |

53 | 13 | -2.5 | -0.7 | 9.8 |

54 | 14 | -3.5 | -0.7 | 9.8 |

55 | 15 | -4.5 | -0.7 | 9.8 |

56 | 16 | -5.5 | -0.7 | 9.8 |

57 | 17 | -6.5 | -0.7 | 9.8 |

58 | 18 | -7.5 | -0.7 | 9.8 |

59 | 19 | -8.5 | -0.7 | 9.8 |

60 | 20 | -9.5 | -0.7 | 9.8 |

Here, from the combined position payoff, we observe that when the stock price at maturity is lesser than 40, the investor faces a loss and if the stock price at maturity is greater than 40, the investor has a profit. The maximum loss of the investor is -10.2 when the stock price is less than $30 and the maximum profit is 9.8 when the stock price crosses $20. Hence, both the upper as well as the lower limit of the investor position is capped.

Inshort, this payoff replicates a bull call spread.

b)

Stock price | Long stock payoff | Payoff 2 short call strike $50 | Payoff 2 long put strike $30 | Combined position |

0 | -40 | 1 | 58.6 | 19.6 |

1 | -39 | 1 | 56.6 | 18.6 |

2 | -38 | 1 | 54.6 | 17.6 |

3 | -37 | 1 | 52.6 | 16.6 |

4 | -36 | 1 | 50.6 | 15.6 |

5 | -35 | 1 | 48.6 | 14.6 |

6 | -34 | 1 | 46.6 | 13.6 |

7 | -33 | 1 | 44.6 | 12.6 |

8 | -32 | 1 | 42.6 | 11.6 |

9 | -31 | 1 | 40.6 | 10.6 |

10 | -30 | 1 | 38.6 | 9.6 |

11 | -29 | 1 | 36.6 | 8.6 |

12 | -28 | 1 | 34.6 | 7.6 |

13 | -27 | 1 | 32.6 | 6.6 |

14 | -26 | 1 | 30.6 | 5.6 |

15 | -25 | 1 | 28.6 | 4.6 |

16 | -24 | 1 | 26.6 | 3.6 |

17 | -23 | 1 | 24.6 | 2.6 |

18 | -22 | 1 | 22.6 | 1.6 |

19 | -21 | 1 | 20.6 | 0.6 |

20 | -20 | 1 | 18.6 | -0.4 |

21 | -19 | 1 | 16.6 | -1.4 |

22 | -18 | 1 | 14.6 | -2.4 |

23 | -17 | 1 | 12.6 | -3.4 |

24 | -16 | 1 | 10.6 | -4.4 |

25 | -15 | 1 | 8.6 | -5.4 |

26 | -14 | 1 | 6.6 | -6.4 |

27 | -13 | 1 | 4.6 | -7.4 |

28 | -12 | 1 | 2.6 | -8.4 |

29 | -11 | 1 | 0.6 | -9.4 |

30 | -10 | 1 | -1.4 | -10.4 |

31 | -9 | 1 | -1.4 | -9.4 |

32 | -8 | 1 | -1.4 | -8.4 |

33 | -7 | 1 | -1.4 | -7.4 |

34 | -6 | 1 | -1.4 | -6.4 |

35 | -5 | 1 | -1.4 | -5.4 |

36 | -4 | 1 | -1.4 | -4.4 |

37 | -3 | 1 | -1.4 | -3.4 |

38 | -2 | 1 | -1.4 | -2.4 |

39 | -1 | 1 | -1.4 | -1.4 |

40 | 0 | 1 | -1.4 | -0.4 |

41 | 1 | 1 | -1.4 | 0.6 |

42 | 2 | 1 | -1.4 | 1.6 |

43 | 3 | 1 | -1.4 | 2.6 |

44 | 4 | 1 | -1.4 | 3.6 |

45 | 5 | 1 | -1.4 | 4.6 |

46 | 6 | 1 | -1.4 | 5.6 |

47 | 7 | 1 | -1.4 | 6.6 |

48 | 8 | 1 | -1.4 | 7.6 |

49 | 9 | 1 | -1.4 | 8.6 |

50 | 10 | 1 | -1.4 | 9.6 |

51 | 11 | -1 | -1.4 | 8.6 |

52 | 12 | -3 | -1.4 | 7.6 |

53 | 13 | -5 | -1.4 | 6.6 |

54 | 14 | -7 | -1.4 | 5.6 |

55 | 15 | -9 | -1.4 | 4.6 |

56 | 16 | -11 | -1.4 | 3.6 |

57 | 17 | -13 | -1.4 | 2.6 |

58 | 18 | -15 | -1.4 | 1.6 |

59 | 19 | -17 | -1.4 | 0.6 |

60 | 20 | -19 | -1.4 | -0.4 |

Here, we observe that payoff is asymetrical and the maximum profit occours when the stock price at maturity is $50. However, the downside is unlimited as if the stock price ends below $60, the payoff is negative. Higher the stock goes above $60, more negative the payoff is and higher the losses for the investor.

The price of a stock is $40. The
price of a one-year European put option on the stock with a strike
price of $30 is quoted as $7 and the price of a one-year European
call option on the stock with a strike price of $50 is quoted as
$5. Suppose that an investor buys 100 shares, shorts 100 call
options, and buys 100 put options.
Construct a payoff and profit/loss table

The current price of a stock is $40. The price of a one-year
European put option on the stock with a strike price of $30 is
quoted at $2 and the price of a one-year European call option on
the stock with a strike price of $50 is quoted at $3.
(2 points) Investor D wants to own the shares but wants to
reduce his initial investment cost. So he buys the stock and shorts
the call option on 100...

.2. The price of a stock is $40. The price of a one-year
European put option on the stock with a strike price of $30 is
quoted as $7 and the price of a one-year European call option on
the stock with a strike price of $50 is quoted as $5. Suppose that
an investor buys 100 shares, shorts 100 call options, and buys 100
put options.
Draw a diagram illustrating how the investor’s profit or loss
varies with the...

5. The price of a stock is $40. The price of a one-year European
put option on the stock with a strike price of $30 is quoted as $7
and the price of a one-year European call option on the stock with
a strike price of $50 is quoted as $5. Suppose that an investor
buys 100 shares, shorts 100 call options, and buys 100 put options.
a. Construct a payoff and profit/loss table b. Draw a diagram
illustrating how...

Consider a stock that does not pay dividend. A one-year European
put option with strike $40 is trading at $2.40 and a one-year
European put option with strike $50 is trading at $12.30. The
risk-free interest rate is 5% per annum with continuous
compounding. Construct an arbitrage strategy.

The price of a stock is $40. The price of a 1-year European put
on the stock with a strike price of $30 is quoted as $7 and the
price of a 1-year European call option on the stock with a strike
price of $50 is quoted as $5.
(a) Suppose that an investor buys the stock, shorts the call
option, and buys the put option. Calculate the profit function and
draw a diagram illustrating how the investor's profit or...

ABC stock is trading at 40. The trader has already sold one put
with the strike price of 40 at 4 with expiry date 1 month from now.
The trader reviews the market and short sells one share. You are
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Assume the interest rate is flat at 0% pa for all periods. Also
assume that 1 put is on one share
a. Compute the net profit at...

Problem 3 – Naked Put
A put with the strike price of $40 was sold short at $4.20 when the
price of the underlying stock was $38.00 per share. Draw the
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$0.90 with a strike price of $50. He also sells a one-year call for
$1.05 with a strike price of $70.
What is the total cost of acquiring this position?
What is the maximum payoff for this position?
What is the maximum profit for this position?
What is the minimum payoff for this position?
What is the minimum profit for this position?
Draw the payoff and profit graphs...

An investor purchases a stock for $60 and a one-year put
for $0.70 with a strike price of $55. He also sells a one-year call
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position?
What is the maximum payoff for this
position?
What is the maximum profit for this
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What is the minimum payoff for this
position?
What is the minimum profit for this
position?
Draw the payoff and profit graphs...

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