nsider a one-period binomial model in which the underlying is at 65 and can go up 30% and down 22%. The risk-free rate is 8%. The price of the call option with exercise prices of 70 would be: a. 84.50 b. 0.5769 c. 0 d. 7.75
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- Consider a one-period binomial model in which the underlying is at 65 and can go up 30% and down 22%. The risk-free rate is 8%. The price of the call option with exercise prices of 70 would be:
|
a. 84.50 |
b. 0.5769 |
c. 0 |
d. 7.75 |
- Refer to Problem #1. Suppose that the call is selling for 9 in the market and assume that we would execute an arbitrage transaction, the
rate of return on a 10,000 call option would be:
|
a. 16.20% |
b. 18.19% |
c. 15.17% |
d. 16.78% |
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- In a binomial model, a call option and a put option are both written on the same stock. The exercise price of the call option is 30 and the exercise price of the put option is 40. The call option’s payoffs are 0 and 5 and the put option’s payoffs are 20 and 5. The price of the call is 2.25 and the price of the put is 12.25. a. What is the riskless interest rate? Assume that the basic period is one year. b. What is the price of the stock today?The prices of a certain security follow a geometric Brownian motion with parameters mu=.12 and sigma=.24. If the security's price is presently 40, what is the probability that a call option, having four months until its expiration time and with a strike price of K=42, will be exercised? (A security whose price at the time of expiration of a call option is above the strike price is said to finish in the money.) If the interest rate is 8%, what is the risk-neutral valuation of the call option?A call option with an exercise price of $10 and 3 months to maturity has a price offer of $0.75. The stock price is $10.90 and the risk-free rate is 5%. Is this a boundary violation? If so, calculate the arbitrage profit available.
- The prices of a certain security follow a geometric Brownian motion with parameters mu=.12 and sigma=.24. If the security's price is presently 40, what is the probability that a call option, having four months until its expiration time and with a strike price of K=42, will be exercised? (A security whose price at the time of expiration of a call option is above the strike price is said to finish in the money).Consider an American put option with time to expiry 15 months, and a strike of 74. The current price of the underlying is 71. Divide the time to expiry into three 5-months intervals. Assume that in each 5-months interval, the price can either rise by 5, or fall by 5, with unknown probability. The risk-free (continuously compounding) rate is 0.042. Using a binomial tree, identify the circumstances under which early exercise would be rational for the holder of this option. Draw the binomial tree and show the necessary calculation and briefly explain the answer.We will derive a two-state put option value in this problem. Data: S0 = 100; X = 110; 1 + r = 1.10. The two possibilities for ST are 130 and 80.a. Show that the range of S is 50, whereas that of P is 30 across the two states. What is the hedge ratio of the put?b. Form a portfolio of three shares of stock and five puts. What is the (nonrandom) payoff to this portfolio?c. What is the present value of the portfolio?d. Given that the stock currently is selling at 100, solve for the value of the put.
- Suppose the current stock price of JuJube Inc is ¥100, the risk-free interest rate is 5%, the standard deviation is 25%, the time to maturity is 4 months, the strike price is ¥85, and the price of a call option is ¥25.20. Using the put-call parity relationship, the put option price is closest to A. ¥25.20 B. ¥16.40 C. ¥5.20 D. ¥8.80 E. None of the aboveAssume the Black-Scholes framework. Let S be a stock such that S(0) = 21, the dividend rate is δ = 0.02, the risk free rate is r = 0.05, and the volatility is σ = 0.2. (a) Calculate the expected payoff of a 6 month call with strike price 17. (b) Calculate the cost of such a call. (c) Calculate the cost of a 6 month put with strike price 17. (d) Calculate the price of a derivative that pays |S(0.5) − 17| in six monthsAssume that using the Security Market Line (SML) the required rate of return (RA) on stock A is foundto be half of the required return (RB) on stock B. The risk-free rate (Rf) is one-fourth of the requiredreturn on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A (A) to beta of B(B). d) Assume that the short-term risk-free rate is 3%, the market index S&P500 is expected to payreturns of 15% with the standard deviation equal to 20%. Asset A pays on average 5%, has standarddeviation equal to 20% and is NOT correlated with the S&P500. Asset B pays on average 8%, also hasstandard deviation equal to 20% and has correlation of 0.5 with the S&P500. Determine whetherasset A and B are overvalued or undervalued, and explain why. (Hint: Beta of asset i (??) =???????, where ??,?? are standard deviations of asset i and marketportfolio, ??? is the correlation between asset i and the market portfolio)Question 2. Foreign exchange marketsStatoil, the national…
- Assume that using the Security Market Line (SML) the required rate of return (RA) on stock A is foundto be half of the required return (RB) on stock B. The risk-free rate (Rf) is one-fourth of the requiredreturn on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A (A) to beta of B(B). d) Assume that the short-term risk-free rate is 3%, the market index S&P500 is expected to payreturns of 15% with the standard deviation equal to 20%. Asset A pays on average 5%, has standarddeviation equal to 20% and is NOT correlated with the S&P500. Asset B pays on average 8%, also hasstandard deviation equal to 20% and has correlation of 0.5 with the S&P500. Determine whetherasset A and B are overvalued or undervalued, and explain why. (Hint: Beta of asset i (??) = ???????, where ??,?? are standard deviations of asset i and marketportfolio, ??? is the correlation between asset i and the market portfolio)A futures price is currently 41 and has a volatility of 30%. The risk-free rate is 5%. The strike price on a 9-month put is 40. A three-period binomial lattice is used. Calculate the risk-neutral probability p*.The Treasury bill rate is 4.9%, and the expected return on the market portfolio is 11.1%. Use the capital asset pricing model. What is the risk premium on the market? (Enter your answer as a percent rounded to 1 decimal place.) What is the required return on an investment with a beta of 1.2? (Enter your answer as a percent rounded to 2 decimal places.) If an investment with a beta of 0.46 offers an expected return of 8.7%, does it have a positive NPV? If the market expects a return of 12.2% from stock X, what is its beta? (Round your answer to 2 decimal places.)
