Consider a put option on a stock that currently sells for £100, but may rise to £120 or fall to £80 after 1 year. The risk free rate of return is 10%, and the exercise price is £90. (a) Calculate the value of the put option using the risk-neutral valuation relationship (RNVR). Explain the reasoning behind your calculations. (b) Calculate the value of the put option by using first principles (No Arbitrage prin- ciples). Explain the reasoning behind your calculations. (c) What is the price of a call option on the same stock with the same exercise price and the same expiration date? Explain the reasoning behind your calculations.

Consider a put option on a stock that currently sells for £100, but may rise to £120 or fall to £80 after 1 year. The risk free rate of return is 10%, and the exercise price is £90. (a) Calculate the value of the put option using the risk-neutral valuation relationship (RNVR). Explain the reasoning behind your calculations. (b) Calculate the value of the put option by using first principles (No Arbitrage prin- ciples). Explain the reasoning behind your calculations. (c) What is the price of a call option on the same stock with the same exercise price and the same expiration date? Explain the reasoning behind your calculations.

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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Consider a put option on a stock that currently sells for £100, but may rise to £120 or fall to £80 after 1 year. The risk free rate of return is 10%, and the exercise price is £90. (a) Calculate the value of the put option using the risk-neutral valuation relationship (RNVR). Explain the reasoning behind your calculations.
Consider a put option on a stock that currently sells for £100, but may rise to £120 or fall to £80 after 1 year. The risk free rate of return is 10%, and the exercise price is £90. (b) Calculate the value of the put option by using first principles (No Arbitrage prin- ciples). Explain the reasoning behind your calculations.
You are interested to value a put option with an exercise price of $100 and one year to expiration. The underlying stock pays no dividends, its current price is $100, and you believe it either increases to $120 or decreases to $80. The risk-free rate of interest is 10%. Calculate the put option's value using the binomial pricing model, presenting your calculations and explanations as follows: a. Draw tree-diagrams to show the possible paths of the share price and put payoffs over one year period. (Note: Show the numbers that are known and use letter(s) for what is unknown in your diagrams.) b. Compute the hedge ratio. c. Find the put option price. Explain your calculations clearly. d. Use put-call parity, find the price of a call option with the same exercise price and the same expiration date.
Suppose you are a seller . At time t = 0 you get £C from the buyer where C is the risk-neutral price of the option. You then have to design a hedging strategy which would allow you to meet your financial obligation in one year’s time. Your portfolio should consist of two investments: you are allowed to buy the underlying shares and to deposit money in the bank. The price of the share evolves according to a geometric Brownian motion. State the formulae you will need to compute the number of shares in the portfolio and the capital deposited in the bank at any time t, 0 ≤ t ≤ 1.
You are evaluating a put option based on the following information: P = Ke-H•N(-d,) – S-N(-d,) Stock price, So Exercise price, k = RM 11 = RM 10 = 0.10 Maturity, T= 90 days = 0.25 Standard deviation, o = 0.5 Interest rate, r Calculate the fair value of the put based on Black-Scholes pricing model. Cumulative normal distribution table is provided at the back.
QUESTIONS: 1) Assuming that the risk-free rate of return is currently 3,2%, the market risk premium is 6% whereas the beta of HelloFresh SH. stock is 1.8, compute the required rate of return using CAPM. 2) Compute the value of each investment based on your required rate of return and interpret the results comparing with the market values. 3) Which investment would you select? Explain why using appropriate financial jargon (language). 4) Assume HelloFresh SH's CFO Mr. Christian Gaertner expects an earnings upturn resulting increase in growth (rate) of 1%. How does this affect your answers to Question 2 and 3? 5) AACSB Critical Thinking Questions: A) Companies pay rating agencies such as Moody's and S&P to rate their bonds, and the costs can be substantial. However, companies are not required to have their bonds rated in the first place; doing so is strictly voluntary. Why do you think they do it? (Textbook page: 198) B) What are the difficulties in using the PE ratio to value stock?…
Assume that K=61, St =65, t = 0.25 (i.e. time to expiry is 3 months), and the risk-free rate is 0.04. The current price of the put option is p = 4. If the price of the call option is 7.17, describe the arbitrage that would be possible, and calculate the profit that would result.
show this on a diagram please. An investor makes the following three investments: (i) the purchase of a stock for £38(ii) the purchase of a put option for £0.50 with a strike price of £35 and (iii) the sale ofa call option (ie. writing a call option) for £0.50 with a strike price of £40 . What is the maximum profit and loss for this position?
You are pricing options with the following characteristics: •Current stock price (St): $35.60 •Exercise price (X): $50 •Time to expiration (T-t): 9 months •Risk-free rate (rf): 3.25% •Volatility (0): 45% (a): What is the Black-Scholes value of call option? In your hand-written solution, provide the calculations of d1,d2, and the final call price. Use Excel or another spreadsheet program to compute the values of N(d1) and N(d2). See the notes for details. (b): Using put-call parity, what is the value of a put option? For this case, assume continuous compounding, which implies that PVt(X)=e-r(T-t).X.
Consider a put option on a stock that currently sells for £100, but may rise to £120 or fall to £80 after 1 year. The risk free rate of return is 10%, and the exercise price is £90. (c) What is the price of a call option on the same stock with the same exercise price and the same expiration date? Explain the reasoning behind your your calculations.
Suppose you construct a strategy based on options on a stock that is currently selling for $100. The strategy is as follows: Buy one call option having an exercise price of $95. Sell two calls having an exercise price of $100. Buy one call option having an exercise price of $105. All of the options are written on the same stock and all have the same expiration date. Compute the payoff (the dollars you receive) from this strategy at the expiration date for each of the following alternative stocks prices: $90, $95, $98, $100, $102, $105, and $110. What additional information would be required to determine whether your strategy had been profitable? What is the name of this strategy?
Which of the following is correct? O A. Common stock valuation usually treats the common stock as a perpetuity. OB. The appropriate measure for risk according to the capital asset pricing model is beta. OC. The present value of a $100 perpetuity discounted at 5% is $2,000. OD. The incremental cost is the cost of making a choice defined in terms of the next best alternative that is foregone. OE. Both B and C.

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