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Construct a profit profile for the following portfolio options and stocks ** please explain how this is done and show work if possible**

Long 200 share of IBM @ 115

Bell 2 Sept 115 Call @ $5

Buy 2 Sept 115 Put @ $2

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Jamar Ferry
Jamar FerryLv2
28 Sep 2019

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Table 2 gives today’s prices of one-year European put and call options written on a share of stock ABC at different strike prices. Call Price ($) Strike Price ($) Put Price ($) 13.30 100 8.30 10.45 105 10.45 8.30 110 13.30 6.50 115 16.50 Table 2 a) Assuming that the rate of interest is 0% and that the stock does not pay any dividend, use the information in Table 2 to derive the price of a share of stock of ABC today. b) Provide an analysis of the profit at maturity of the following strategies: 1. A bear spread using call options with strike prices of $100 and $110. 2. A strangle using options with strike prices of $100 and $110 where you buy the options today. 3. A butterfly spread using put options with strike prices of $105, $110, and $115 where you buy the $105 and $115 strike puts. In each case provide a table showing the relationship at maturity between profit/loss and the stock price at maturity. Profit is defined as the value of the position at maturity minus its cost today (cost is positive in the case of a debit trade and negative in the case of a credit trade).

Question 1

The following quotes were observed for options on a given stock on November 1 of a given year. These are American options except where indicated.

Calls

Puts

Strike

Nov

Dec

Jan

Nov

Dec

Jan

105

8.40

10

11.50

5.30

1.30

2.00

110

4.40

7.10

8.30

0.90

2.50

3.80

115

1.50

3.90

5.30

2.80

4.80

4.80

The stock price was 113.25. The risk-free rates were 7.30 percent (November), 7.50 percent (December) and 7.62 percent (January). The times to expiration were 0.0384 (November), 0.1342 (December), and 0.211 (January). Assume no dividends.

Answer the following questions. (Refer to chapter 15 teaching note)

(1) What is the intrinsic value of the January 110 call?

(2) What is the intrinsic value of the November 115 call?

(3) What is the intrinsic value of the December 115 put?

(4) What is the intrinsic value of the November 105 put?

(5) What is the time value of the December 115 put?

(6) What is the time value of the November 105 put?

(7) What is the time value of the January 110 call?

(8) What is the time value of the November 115 call?

The following information is given about options on the stock of a certain company.

Current stock price = $114
Exercise price = $115
Continuously compounded risk-free rate = 0.1 percent Time to expiration = 6 months (T = 0.5) in June
The volatility = 0.28

(1) Find the values of N(d1) and N(d2)

(2) What value does the Black-Scholes-Merton model predict for the call?

(3) What is the delta of the call?

(4) If the stock price goes up by $1 to $115, what would be the call price based on the delta?

(5) Suppose that June 115 call has the gamma of .0176. If the stock price goes up by $1 to $115, what would be the delta of the call based on the gamma?

(6) Suppose that the call rho (ρ) is 25.523. If the continuously compounded risk-free rate goes up by 1 percent to 1.1 percent, what would be the expected call price based on the rho?

(7) Suppose that the call vega (ν) is 32.106. If the volatility of the continuously return on the stock increase by 1 percent, what would be the expected call price based on the vega?

(8) Suppose that the theta (θ) is 9.04. If the time to expiration decreases so that the call expires in 3 months (T = .25), what would be the expected call price based on the theta?

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