50.1K

Verified Solution

Link Copied!

The following information pertains to the next 3 questions:

Tesla Stock is priced at $732.23 per share. The continuously compounded risk-free rate is 0.10 percent per annum. You observe five actively-traded options on Tesla stock, with characteristics, premiums and sensitivities as follows:

Option Number:	I	II	III	IV	V
Option Type:	Call	Call	Call	Call	Put
Years to Expiration (T):	0.1014	0.1014	0.2548	0.7753	0.7753
Exercise Price (X):	700	800	750	750	750
Option Premium:	76.50	32.85	84.50	165.70	180.60
Delta:	0.6261	0.3655	0.5330	0.6027	-0.3991
Gamma:	0.0025	0.0026	0.0017	0.0009	0.0009
Theta:	-283.1731	-270.9467	-180.8238	-109.2001	-107.1036
Vega:	88.3322	87.6830	146.9481	248.6476	248.9417
Rho:	38.7311	23.8075	77.9206	213.6657	-366.5882
Implied Volatility:	64.93%	62.61%	62.60%	67.93%	67.01%

1. If you expect a large increase in the price of Tesla stock within the next week, which option should you purchase, i.e. which will experience the largest percentage increase in its premium?

A. Option I

B. Option II

C. Option III

D. Option IV

2. Which of the options would experience the greatest rate of time decay over the next few days, in percentage terms, if the stock price, volatility and risk-free rate all remained unchanged?

A. Option I

B. Option II

C. Option IV

D. Option V

3. Which of the following portfolios is hedged against small changes in the price of Tesla stock?

A. Long 0.5330 shares of Tesla stock, Short 1 Option III.

B. Long 1 share of Tesla stock, short 1 Option IV, long 1 option V.

C. Long 0.3991 shares of Tesla stock, Long 1 option V.

D. Portfolios A, B and C above are all hedged against small changes in the price of Tesla stock.

Answer & Explanation Solved by verified expert

See Answer