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What is gamma risk? Suppose you were managing an optionportfolio and had gamma risk. How would you get rid of gamma riskwithout incurring any other significant risk, at least for smallmarket moves?

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Elin Hessel
Elin HesselLv2
28 Sep 2019

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Q2. A calendar spread is a combination of two options with different time to expiration. Calendar spread is also known as a time spread.

IV is $2/day. Underling is currently priced at $100. Assume normal distribution and zero interest rate.

You decided to long a 2 week ATM CALL option (DTE=1) and short a 1 week ATM CALL option (DTE=5).

Q2a. What is your net cost of the calendar spread when initially bought?

Q2b. What should be the cost of your calendar spread at $1/day or $4/day volatility?

Q2c. What is the delta/theta/gamma of the calendar spread when initially bought?

Q2d. What is the value of the calendar (aka how much you can sell the spread for) if underlying trades at $100 one day later, BASED on theta/gamma/delta?

Q2e. What is the value of the calendar (aka how much you can sell the spread for) if underlying trades at $99 one day later, BASED on theta/gamma/delta??

Q2f. What is the value of the calendar (aka how much you can sell the spread for) if underlying trades at $101 one day later, BASED on theta/gamma/delta?

Q2g. What is the value of the calendar (aka how much you can sell the spread for) if underlying trades at $102 one day later, BASED on theta/gamma/delta?

Q2h. What is the value of the calendar (aka how much you can sell the spread for) if underlying trades at $98 one day later, BASED on theta/gamma/delta??

Q2i. What is the value of the calendar (aka how much you can sell the spread for) if underlying trades at $104 one day later, BASED on theta/gamma/delta?

Q2j. What is the value of the calendar (aka how much you can sell the spread for) if underlying trades at $96 one day later, BASED on theta/gamma/delta?

Q2k. What is the breakeven size of underlying movement for your calendar spread?

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?

HI:

I had asked these questions previously, but recieved the wrong answers to them. Can someone else look at these.

Your company has approximately $500,000 to invest in a project and has narrowed their selection down to the following three projects. The hurdle rate (WACC) used by the company is 15%. For purposes of payback analysis, assume that the payouts on each project flow evenly in the year of the payout. Project Alpha requires a $480,000 investment and will pay $240,000 at the end of each of the first four years, and then the project will be scrapped. Project Beta requires a $420,000 investment, and will pay $125,000 out in each of the ten years, and then will be scrapped. Project Gamma requires a $470,000 investment, but takes seven years to begin generating profits. It will generate $450,000 per year in years 7 through 9, and $950,000 in year 10. After year 10, this project will also be scrapped.

State dollar answers to the nearest whole dollar. For percentage answers, drop the % sign and round to one decimal place.

Question 10

What is the MIRR of Gamma?

Question 13 3 pts

In what month is payback achieved for Gamma? (i.e. 3 yrs and 2 months would be in month 38)

Question 14 3 pts

In what month is discounted payback achieved for Alpha? (i.e. 3 yrs and 2 months would be in month 38)

Question 15 3 pts

In what month is discounted payback achieved for Beta? (i.e. 3 yrs and 2 months would be in month 38)

Question 16 3 pts

In what month is discounted payback achieved for Gamma? (i.e. 3 yrs and 2 months would be in month 38)

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