Question
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
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.
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