What is the new call value predicted by the theta

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Reference no: EM133583630

Homework

Task

In this homework, you will solve problems about Options Trading using the "Greek" parameters.

Question I. Suppose a stock is currently trading at 100. An at-the-money call with a maturity of three months has the following price and greeks:

C = 5.598
= 0.565
= 0.032
= -12.385
V = 19.685
ρ = 12.71

1. If the stock price moves to S = 101, what is the predicted new option price (using the delta alone)?

2. If the stock price moves to S = 101, what is the predicted new call delta?

3. Repeat these questions assuming the stock price moves to 98 instead.

4. If the stock price registers a large jump increase to 120, what is the new call value predicted by the delta alone? By the delta and gamma combined?

5. Go back to the original parameters. If the time to maturity falls by 0.01, what is the new call value predicted by the theta?

6. Repeat the last question if the time to maturity falls by 0.05.

7. Go back to the original parameters. If the volatility increases by 1%, what is the predicted new value of the call? What if volatility fell by 2%?

(h) Go back to the original parameters. If interest rates should rise by 50 basis points, what is the new call value predicted by the rho?

Question II. A stock is currently trading at 55. You hold a portfolio of the following instruments:

1. Long 200 shares of stock.
2. Long 200 puts with a strike of 50 and maturity of three months.
3. Short 200 calls with a strike of 60 and maturity of three months.

You are given the following information:

Instrument. Price Delta Gamma Vega Theta Rho
Call with K = 50 6.321. 0.823 0.038 7.152 -5.522. 9.730
Put with K = 50 0.700 -0.177. 0.038 7.152 -3.053 -2.615
Call with K = 55 3.079. 0.565 0.057 10.827. -6.812 6.993
Put with K = 55 2.396 -0.435 0.057 10.827 -4.096 -6.586
Call with K = 60 1.210 0.297. 0.050 9.515 -5.513 3.779
Put with K = 60 5.465 -0.703. 0.050 9.515 -2.551 -11.035

1. What is the current value of your portfolio?

2. What is the delta of your portfolio? The gamma? The vega? The theta? The rho?

3. Suppose you want to make your portfolio gamma neutral. What is the cost of achieving this using the 55-strike call? What is the theta of your new position?

4. What is the cost if you used the 55-strike put? What is the theta of the new position?

Question III. Using the same information as in Question II, calculate the following quantities:

1. The delta and gamma of a covered call portfolio with K = 55 (i.e., a portfolio where you are long the stock and short a call with a strike of 55).

2. The delta and gamma of a protective put portfolio with K = 50 (long the stock and long a put with a strike of 50).

3. The delta and gamma of a bull spread using calls with strikes of 55 and 60 (long a 55-strike call, short a 60-strike call).

4. The delta and gamma of a butterfly spread using calls with strikes of 50, 55, and 60 (long a 50-strike call, long a 60-strike call, and short two 55-strike calls).

5. The delta and gamma of a collar with strikes 50 and 60 (long position in the stock, long a 50-strike put, short a 60-strike call).

Question IV. You hold two types of calls and two types of puts on a given stock. The deltas and gammas of the respective types are (+0.40, +0.03), (+0.55, +0.036), (-0.63, +0.028), and (-0.40, +0.032). You have a long position in 1,000 of the first type of call, a short position in 500 of the second type of call, a long position in 1,000 of the first type of put, and a short position in 500 of the second type of put.

1. What is the aggregate delta of your portfolio? The aggregate gamma?

2. Suppose you decide to gamma hedge your portfolio using only the first type of call. What is the resulting delta of the new portfolio? What position in the underlying is now required to create a delta-neutral gamma-neutral portfolio?

Reference no: EM133583630

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