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| A call option with a strike price of $50 on a stock selling at $55 costs $6.50. What are the call options intrinsic and time values? |
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Definition
| 1. The intrinsic value = 55 – 50 = 5.00. The time value = 6.50 – 5.00 = 1.50 |
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Term
| A put option on a stock with a current price of$33 has an excercise price of $35. The price of the corresponding call option is $2.25. According to put-call parity, if the effective annual risk-free rate of interest is 4% and there are three months until expiration, what should the stock price be? |
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Definition
| 2. Put = 2.25 – 33 + 35 / e.04x.25 = 3.90 |
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| A call option on Jupiter Motors stock with an excercise price of $75 and one-year expiration is selling at $3. A put option on Jupiter stock with an excercise price of $75 and one-year expiration is selling at $2.50. If the risk-free rate is 8% and Jupiter pays no dividends, what should the stock price be? |
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Definition
| 3. 2.50 = 3.00 – S + 75 / e.08 x1 , solving for S = 69.73 |
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Term
| We showed in the text that the value of a call option increases with the volatility of the stock. Is this also true of put option values? Use the put-call parity relationship as well as a numerical example to prove your answer |
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Definition
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Term
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Definition
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Term
Find the Black-Scholes value of a put option on the stock in the previous problem with the same excercise price expiration as the call option
book 537 |
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Definition
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Term
| All else being equal, is a put option on a high beta stock worth more than one on a low beta stock? The firms have identical firm-specific risk |
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Definition
| 15. Holding firm-specific risk constant, higher beta implies higher total stock volatility. Therefore, the value of the put option increases as beta increases. |
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Term
| All else being equal, is a call option with a lot firm-specific risk worth more than one on a stock with little firm-specific risk? The betas of the stocks are equal. |
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Definition
| 16. Holding beta constant, the stock with high firm-specific risk has higher total volatility. Therefore, the option on the stock with a lot of firm-specific risk is worth more. |
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Term
| All else equal will a call option with a higher exercise price have a higher or lower hedge ratio than one with a low exercise price? |
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Definition
| 17. The call option with a high exercise price has a lower hedge ratio. The call option is less in the money. Both d1 and N(d1) are lower when X is higher. |
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Term
| Should the rate of return of a call option on a long-term Treasury bond be more or less sensitive to changes in interest rates than the rate of return of the underlying bond? |
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Definition
| 18. The call option is more sensitive to changes in interest rates. The option elasticity exceeds 1.0. In other words, the option is effectively a levered investment and is more sensitive to interest rate changes. |
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Term
| If the stock price falls and the call price rises, then what has happened to the call option's implied volatility? |
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Definition
| 19. The call option’s implied volatility has increased. If this were not the case, then the call price would have fallen. |
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Term
| If the time to expiration falls and the put price rises, then what has happened to the put option volatility? |
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Definition
| 20. The put option’s implied volatility has increased. If this were not the case, then the put price would have fallen. |
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Term
| According to the Black-Scholes formula, what will be the value of the hedge ratio of a all option as the stock price becomes infinitely large? explain |
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Definition
| 21. As the stock price becomes infinitely large, the hedge ratio of the call option [N(d1)] approaches one. As S increases, the probability of exercise approaches 1.0 [i.e., N(d1) approaches 1.0]. |
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Term
| According to the Black-Scholes formula, what will be the value of the hedge ratioof a put option for a very small exercise price? |
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Definition
| 22. The hedge ratio of a put option with a very small exercise price is zero. As X decreases, exercise of the put becomes less and less likely, so the probability of exercise approaches zero. The put's hedge ratio [N(d1) –1] approaches zero as N(d1) approaches 1.0. |
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