Fundamentals of Corporate Finance (Special Edition for Rutgers Business School)
11th Edition
ISBN: 9781308509853
Author: Ross, Westerfield, Jordan
Publisher: McGraw Hill
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Chapter 25, Problem 15QP
Black–Scholes [LO2] A stock is currently priced at $47. A call option with an expiration of one year has an exercise price of $50. The risk-free rate is 12 percent per year, compounded continuously, and the standard deviation of the stock’s return is infinitely large. What is the price of the call option?
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H2.
Suppose that a stock price is currently 70 dollars, and it is known that at the end of each of the next two six-month periods, the price will be either 17 percent higher or 17 percent lower than at the beginning of the period. Find the value of an American put option on the stock that expires a year from now, and has a strike price of 76 dollars. Assume that no arbitrage opportunities exist, and a risk-free interest rate of 11 percent.
Answer =
dollars.
Please show proper step by step calculation
Q5. You are considering two investment choices: a. 1 year CD that pays 2% for sure; b. investing in SP500 with 8% expected and 20% stdev. Q5a. If you put 50% in each of the two, what in the mean and stdev for your portfolio return? Q5b. You want to maximize your expected return for the portfolio, as long as the stdev risk is no more than 10% per year. What is the allocation to CD and to stocks? What is the mean return of the portfolio? Q5c. You want to reach 17% mean return per year as a minimum. What is the least amount you need to allocate to stocks? What is the stdev of the portfolio?Q6. In addition to two instruments in Q5, you also can invest in a long term bond with 4% mean return and 10% stdev annually. Stock and bond funds have a correlation of -0.4 (negative 0.4). Q6a. What is the mean return and stdev for a portfolio that is 50% in stock and 50% in bond? Q6b. What is the mean return and stdev for a portfolio that is 25% in stock and 25% in bond and 50% in 1 year CD? Q6c. What…
23.10 What are the prices of a call option and a put option with the following characteristics?
Stock price = $46
Exercise price = $50
Risk-free rate = 6% per year, compounded continuously
Maturity = 3 months
Standard deviation = 54% per year
Chapter 25 Solutions
Fundamentals of Corporate Finance (Special Edition for Rutgers Business School)
Ch. 25.1 - Prob. 25.1ACQCh. 25.1 - Prob. 25.1BCQCh. 25.2 - Prob. 25.2ACQCh. 25.2 - Prob. 25.2BCQCh. 25.3 - Prob. 25.3ACQCh. 25.3 - Prob. 25.3BCQCh. 25.4 - Why do we say that the equity in a leveraged firm...Ch. 25.4 - Prob. 25.4BCQCh. 25.5 - Prob. 25.5ACQCh. 25.5 - Prob. 25.5BCQ
Ch. 25 - Prob. 25.1CTFCh. 25 - Prob. 25.3CTFCh. 25 - Prob. 1CRCTCh. 25 - Prob. 2CRCTCh. 25 - Prob. 3CRCTCh. 25 - Prob. 4CRCTCh. 25 - Prob. 5CRCTCh. 25 - Prob. 6CRCTCh. 25 - Prob. 7CRCTCh. 25 - Prob. 8CRCTCh. 25 - Prob. 9CRCTCh. 25 - Prob. 10CRCTCh. 25 - Prob. 1QPCh. 25 - Prob. 2QPCh. 25 - PutCall Parity [LO1] A stock is currently selling...Ch. 25 - PutCall Parity [LO1] A put option that expires in...Ch. 25 - PutCall Parity [LO1] A put option and a call...Ch. 25 - PutCall Parity [LO1] A put option and call option...Ch. 25 - BlackScholes [LO2] What are the prices of a call...Ch. 25 - Delta [LO2] What are the deltas of a call option...Ch. 25 - BlackScholes and Asset Value [LO4] You own a lot...Ch. 25 - BlackScholes and Asset Value [L04] In the previous...Ch. 25 - Time Value of Options [LO2] You are given the...Ch. 25 - PutCall Parity [LO1] A call option with an...Ch. 25 - BlackScholes [LO2] A call option matures in six...Ch. 25 - BlackScholes [LO2] A call option has an exercise...Ch. 25 - BlackScholes [LO2] A stock is currently priced at...Ch. 25 - Prob. 16QPCh. 25 - Equity as an Option and NPV [LO4] Suppose the firm...Ch. 25 - Equity as an Option [LO4] Frostbite Thermalwear...Ch. 25 - Prob. 19QPCh. 25 - Prob. 20QPCh. 25 - Prob. 21QPCh. 25 - Prob. 22QPCh. 25 - BlackScholes and Dividends [LO2] In addition to...Ch. 25 - PutCall Parity and Dividends [LO1] The putcall...Ch. 25 - Put Delta [LO2] In the chapter, we noted that the...Ch. 25 - BlackScholes Put Pricing Model [LO2] Use the...Ch. 25 - BlackScholes [LO2] A stock is currently priced at...Ch. 25 - Delta [LO2] You purchase one call and sell one put...Ch. 25 - Prob. 1MCh. 25 - Prob. 2MCh. 25 - Prob. 3MCh. 25 - Prob. 4MCh. 25 - Prob. 5MCh. 25 - Prob. 6M
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- 30 - With reference to the Security Market Line, assume for the current time period the Risk-Free Rate = 3.50% while the Expected Return on the “Market Portfolio” = 9.00% so that the Market Risk Premium = 5.50%. If the supply of the Risk-Free Asset decreases for the next period, while investor demand remains unchanged, the Risk-Free Rate would be expected to: Increase in the second period. Decrease in the second period. Remain Unchanged in the second period. Cannot be determined. None of the above answers is correct.arrow_forward57: A security has a development worth of 100,000; its coupon rate is 4% and its yield is needed to be 8%. What might a purchaser pay for this security if the security is expected a long time from now?arrow_forwardV3. Consider a European call option on Allana Inc. stock. The option matures in 8 months and its strike price is $50. Current stock price per Allana Inc.’s share is $50. Allana Inc. will pay $2 dividend per share in 2 month and $3 per share in 6 months and the risk free rate is 3% per annum with continuous compounding for all maturities. Assume that the standard deviation of Allana Inc.’s stock return is 30% per year. The Black-Scholes value of this call option is ______. $18.31 $15.17 $6.92 $5.24 $2.96arrow_forward
- Question 2. (a) Use the Black-Scholes formula to find the current price of a European call option on a stock paying no income with strike 60 and maturity 18 months from now. Assume the current stock price is 50, the lognormal volatility of the stock is σ = 20%, and the constant continuously compounded interest rate is r = 10%.arrow_forwardH2. Using the Black-Scholes model (BSOPM), compute the standard deviation that is implied by the following call option data as: the time to the option's maturity is 0.25 years, the price of the underlying option asset is RM30, the continuously compounded risk-free interest rate is 0.12. the exercise or striking price is RM30, and the cost or premium of the call is RM1.90.arrow_forwardEagletron’s current stock price is $10. Suppose that over the current year, the stock price will either increase by 100% or decrease by 50%. Also, the risk-free rate is 25% (EAR). a) What is the value today of a one-year at-the-money European put option on Eagletron stock?b) What is the value today of a one-year European put option on Eagletron stock with a strike price of $20?c) Suppose the put options in parts a and b could either be exercised immediately, or in one year. What would their values be in this case?arrow_forward
- 3. Suppose the current stock price is $50 and you believe that, one year from now, the stock will sell for either $60 (up-state) or $30 (down-state). The yield on a 1-year risk-free zero coupon bond is currently 4%. What would be the call option delta (Δ) with an exercise price of $40? (SHOW YOUR WORK)arrow_forward*NoChatGPT answers please 6A) What is the price of a European call option on a non-dividend-paying stock when the stock price is $52, the strike price is $50, the risk-free interest rate is 12% per annum, the volatility is 30% per annum, and the time to maturity is 3 months? 6B) What is the assumption of the Black–Scholes–Merton stock option pricing model about the probability distribution of the stock price in one year? What is the assumption about the probability distribution of the continuously compounded rate of return on the stock during the year?arrow_forward3.a) Discuss the five inputs that are needed for the Black-Scholes estimations and show the relevance of these inputs to investors.b) The current price of Kinston Corporation stock is $10. In each of the next two years, this stock price can either go up by $3.00 or go down by $2.00. Kinston stock pays no dividends. The one year risk-free interest rate is 5% and will remain constant.Using the binomial pricing model, calculate the price of a two-year call option on Kinston stock with a strike price of $9.arrow_forward
- 8- Suppose that you noticed the following prices: C=$12; S-$60; X-$50, for a one year European call option. The simple risk-free interest rate is 10% per year. Is there an arbitrage profit opportunity here? Yes or no? If yes, how would you exploit it? If no, explain why not. PS: In all questions above X denotes the exercise price of the options, C-call premium, P-put premium, and S-stock price.arrow_forward22. What is the price of a perpetuity that has a coupon of $50 per year and a yield to maturity of 2.5%? If the yield to maturity doubles, what will happen to its price?arrow_forwardThe DB stock currently sells for 185 kr. A one-year put option with strike price200 kr has a premium of 30 kr, and the risk free rate is 15%. What is the priceof a one-year call option with strike price 200 kr if we assume there are notransaction costs and the market is free of arbitrage? DO IT FASTarrow_forward
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