Consider the one-period binomial model with a single risky asset with current price 33. Its price at time one is believed to either rise to 35 or remain at 33. If the riskfree interest rate is 1.5%, what is the price for a put option with strike price 34 on one unit of the risky asset (rounded to second decimal place)?
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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?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%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?
- 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.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 a one-period binomial model in which the underlying is at 65 Euros, and can go up 30% or down 22% each period. The risk-free rate is 8%. Determine the price of a European put option with exercise price of 70. Assume that the put is selling for 9 Euros. Demonstrate how to execute an arbitrage transaction and calculate the rate of return. Use 10000 puts.
- With all other variables being equal (the same excerise price, underlying asset, implied volatility, interest rate, etc.), an at-the-money option with 30 days to expiration will tpyically have a gamma that is higher than an at-the-moeny option with 180 days to expiration (hint: think of the different shapes of the associated probability distribution and the change in delta) True or False?Assuming a risk-free rate of 8 percent and a market return of 12 percent, would it be wise for investors to acquire an asset with a Beta of 1.5 and a rate of return of 14 percent given the facts above?If the T Bill rate is 1.1% and the market risk premium is 10.8%, what is the CAPM-implied expected return on a portfolio invested 50% in the risk-free asset and 50% in the market?Enter your answer as a percentage rounded to 2 decimal places.
- Suppose that the standard deviation of quarterly changes in the prices of a commodity is $0.65, the standard deviation of quarterly changes in a futures price on the commodity is $0.81, and the coefficient of correlation between the two changes is 0.8. What is the optimal hedge ratio for a three-month contract? What does it mean? Explain what is meant by basis risk when futures contracts are used for hedging.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.)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.