Stock index Y is currently priced at $25/unit. The index pays dividends continuously at a rate proportional to its price at a constant rate of 3%. An investor purchases 200 units of the stock index and invests all dividends in the index. The continuously compounded risk-free interest rate is 5%. After four months the investor closes out all positions when the index is priced at $25.90. Calculate the four-month profit.

Stock index Y is currently priced at $25/unit. The index pays dividends continuously at a rate proportional to its price at a constant rate of 3%. An investor purchases 200 units of the stock index and invests all dividends in the index. The continuously compounded risk-free interest rate is 5%. After four months the investor closes out all positions when the index is priced at $25.90. Calculate the four-month profit.

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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A stock trading at $47 has a volatility of 30 percent. The continuously compounded risk-free rate is 6 percent. A dividend of $1.4 is expected in 4 months, and no other dividends are expected during the next 12 months. Price a European call written on this stock with an exercise price of $50 and a time to maturity of one year.
You must show appropriate equations (whenever applicable) and detailed calculations to earn credit. Homework must be typed with one-inch margin on all sides.
The S&R index spot price is 1100 and the continuously compounded interest rate is 5%. You observed a 9-month forward price of 1129.257. (a) What is the implied dividend yield? (b) Suppose you believe the dividend yield will be 3% over the next 9 months. How can you arbitrage?
BUG’s stock price S is $143 today. It pays a dividend of $2 after 2 and a half months. If the continuously compounded interest rate is 1.1 percent per year, then the 2-month forward price on BUG stock is [round to two decimals]
Suppose the stock price is currently $75. For the next six months there is 7.5% probability that the stock will appreciate 8% with 4% annualized drift. The risk-free rate is 1.53% per year with continuous compounding. The dividend yield is 1 p.a.%. Value the following option using binomial tress and 12-time steps. a.) What is the value of a six-month European put option with a strike price of $86. b.) What is the value of a six-month American put option with a strike price of $70. c.) What is the value of a six-month European call option with a strike price of $86. d.) What is the value of a six-month European put option with a strike price of $70. e.) Estimate how high the minimum strike price must be for it to be optimal to exercise the put option immediately.
The common stock of the C.A.L.L. Corporation has been trading in a narrow range around $105 per share for months, and you believe it is going to stay in that range for the next 3 months. The price of a 3-month put option with an exercise price of $105 is $12.86. a. If the risk-free interest rate is 5% per year, what must be the price of a 3-month call option on C.A.L.L. stock at an exercise price of $105 if it is at the money? (The stock pays no dividends.) (Do not round intermediate calculations. Round your answer to 2 decimal places.) Price of a 3-month call option
A Firm has a stock price of 65 and an annual standard deviation of 25%. The risk-free rate is 10% (c.c.). This firm will pay a dividend of $8 in exactly 3 months and no other dividends over the next year. Price an American call written on this stock with an exercise price of $70 and a time to maturity of one year.
The stock market index is trading at 600. Consider a two-stage binomial tree with the length of each stage equal to one month. The volatility of the index is 39.25% and the continuously compounded interest rate is 12% per annum. There is no dividend yield. Calculate the price of a 2-month American put on the index with strike 610.
am. 66.
A stock you are interested in paid a dividend of $1 last year. The anticipated growth rate in What is the price of a $60 strike put? Assume S = $63.75, σ = 0.20, r = 0.055, the stock pays no dividend and the option expires in 50 days? and earnings is 25% for the next 2 years before settling down to a constant 5% growth rate. The discount rate is 12%. Calculate the expected price of
Suppose you can borrow and lend at the annual interest rate of 6% per annum. The IBM stock is trading at $200. It is not going to pay any dividend in one year. Use this information to answer the following three questions. 20. What is the fair forward price of a forward contract which calls for the delivery of 1 share of IBM stock at the end of one year? A. $216 B. $210 C. $214 D. $212 21. If the actual forward price Fa is $214, your arbitrage strategy is to A. buy one share of IBM, borrow $200, and sell the forward B. buy one share of IBM, borrow $212, and buy the forward C. short one share of IBM, lend $200, and buy the forward D. short one share of IBM, borrow $200, and sell the forward 22. At the end of one year, suppose IBM stock price is St, then the cash flow in the spot (stock) market is _, the cash flow in the forward contract is and the arbitrage profit is A. ST, 214- ST, 2 B. -St, ST-214, 2 C. -ST, 214-ST, 2 D. ST, ST-214, 2
The stock price of Heavy Machine (HM) changes only once a month: Either it goes up by 20% or it falls by 16.7%. Its price now is $50. The interest rate is 1% per month. What is the value of a one-month call option with an exercise price of $45?Round to 2 decimal points for each step of the calculation. A. $ 7.20B. $ 7.13C. $ 7.72D. $ 7.80

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