Consider a stock with current price S0 = 29 per share. A european call option on this stock that matures in T = 3 months with strike K = 30 costs PC = 2.9 per share. You are considering two ways to invest 58. Plan A is to buy 58 /29 = 2 shares of the stock and sell them in 3 months. Plan B is to buy 58 / 2.9 = 20 call options on the stock. If ST denotes the stock price per share in 3 months, plan B has higher payoff

Consider a stock with current price S0 = 29 per share. A european call option on this stock that matures in T = 3 months with strike K = 30 costs PC = 2.9 per share. You are considering two ways to invest 58. Plan A is to buy 58 /29 = 2 shares of the stock and sell them in 3 months. Plan B is to buy 58 / 2.9 = 20 call options on the stock. If ST denotes the stock price per share in 3 months, plan B has higher payoff

Intermediate Financial Management (MindTap Course List)

13th Edition

ISBN:9781337395083

Author:Eugene F. Brigham, Phillip R. Daves

Publisher:Eugene F. Brigham, Phillip R. Daves

Chapter5: Financial Options

Section: Chapter Questions

Problem 4MC

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Binomial Model The current price of a stock is 20. In 1 year, the price will be either 26 or 16. The annual risk-free rate is 5%. Find the price of a call option on the stock that has a strike price of 21 and that expires in 1 year. (Hint: Use daily compounding.)
The current price of XYZ stock is $50, and two-month European call options with a strike price of $51 currently sell for $10. As a financial analyst at Merrill Lynch, you are considering two trading strategies regarding stocks and options. Strategy A involves buying 100 shares and Strategy B includes buying 500 call options. Both strategies involve an investment of $5,000.a. How much is the profit (loss) for strategy A if the stock closes at $65?(sample answer: $100.25 or -$100.25) b. How much is the profit (loss) for strategy B if the stock closes at $65? (sample answer: $100.25 or -$100.25) c.How high does the stock price have to rise for strategy B to be more profitable (break-even point)? (sample answer: $100.25)
Suppose that call options on ExxonMobil stock with time to expiration 3 months and strike price $90 are selling at an implied volatility of 30%. ExxonMobil stock currently is $90 per share, and the risk-free rate is 4%.a. If you believe the true volatility of the stock is 32%, would you want to buy or sell call options?b. Now you need to hedge your option position against changes in the stock price. How many shares of stock will you hold for each option contract purchased or sold?
Rebecca is interested in purchasing a European call on a hot new stock, Up, Inc. The call has a strike price of $99.00 and expires in 85 days. The current price of Up stock is $122.83, and the stock has a standard deviation of 35% per year. The risk-free interest rate is 6.95% per year. Up stock pays no dividends. Use a 365-day year. a. Using the Black-Scholes formula, compute the price of the call. b. Use put-call parity to compute the price of the put with the same strike and expiration date. (Note:Make sure to round all intermediate calculations to at least five decimal places.)
Consider a stock priced at $33 with a standard deviation of 0.3. The risk-free rate is 0.05. There are put and call options available at exercise prices of 35 and a time to expiration of six months. The calls are priced at $2.39 and the puts cost $2.05. There are no dividends on the stock and the options are European. Assume that all transactions consist of 100 shares or one contract (100 options). Suppose the investor constructed a covered call. If the transaction is closed out when the option has three months to go and the stock price is at $39, what is the investor's profit?