5. A “cash-or-nothing binary stock option" is a European-style option and pays some fixed amount of cash to the holder at maturity T > 0 if the stock price at time T > 0 is above a certain threshold K (also referred to as the strike price). Suppose a stock price is currently at $50. Assume that over each of the next two 3-month periods the stock price will either go up by 6% or go down by 5%. The risk-free rate is 5% p.a. with continuous compounding. Use a two-step binomial tree model to compute the arbitrage-free price of a cash-or-nothing option written on that stock which pays $1 if the stock price in three months is above K = $50.

5. A “cash-or-nothing binary stock option" is a European-style option and pays some fixed amount of cash to the holder at maturity T > 0 if the stock price at time T > 0 is above a certain threshold K (also referred to as the strike price). Suppose a stock price is currently at $50. Assume that over each of the next two 3-month periods the stock price will either go up by 6% or go down by 5%. The risk-free rate is 5% p.a. with continuous compounding. Use a two-step binomial tree model to compute the arbitrage-free price of a cash-or-nothing option written on that stock which pays $1 if the stock price in three months is above K = $50.

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 is selling today for $110. The stock has an annual volatility of 64 percent and theannual risk-free rate is 7 percent.a. Calculate the fair price for a 1-year European call option with an exercise price of $95.b. Calculate how much the current stock price would need to change for the purchaser ofthe call option to break even in one year.c. Calculate the fair price for a 1 year European put option with an exercise price of $95
In a financial market a stock is traded with a current price of 50. Next period the priceof the stock can either go up with 30 per cent or go down with 25 per cent. Risk-freedebt is available with an interest rate of 8 per cent. Also traded are European optionson the stock with an exercise price of 45 and a time to maturity of 1, i.e. they maturenext period.i) Find prices of Arrow-Debreu securities.ii) Calculate the price of a call option by constructing and pricing areplicating portfolio.
The strike price of a European put option is $30, the current price of the underlying stock is $24, the risk-free nominal rate of return is 6% and every six months the stock can either increase by a factor of 1.6 or decrease by a factor of 0.5. If the probability of the stock decreasing every six months ( nd) is 0.75, calculate the price of the put option if it is priced under the Binomial Method and expires in one year. I
Without using the Black‐Scholes model, compute the price of a European put option on a non‐dividend‐paying stock with the strike price is $70 when the stock price is $73, the risk‐free interest rate is 10% pa, the volatility is 40% pa, and the time to maturity is 6 months?
A stock price is currently $52. Its volatility is 35% p.a. . The risk-free interest rate is 8% p.a. with continuous compounding. What is the value of a 2-year European call option with a strike price of $55, using a 2-step binomial tree? Without doing any calculations, explain what would happen to the value of the option if the stock volatility decreases
Suppose the following for European options: Stock price $94 3-month call options with strike price $97 3-month put option with strike price $98 1-year risk-free rate is 3%. The put option is trading ot $5 and there is an identical call option that is trading for $4. The arbitrage gain that can be made is equal to: O a. $2.00 b. $0.27 Oc. $3.00 O d. $1.27 O e $227
We have a 2-state, 2-period world (i.e. t = 0, 1, 2). The current stock price is 100 and the risk- free rate each period is 2%. Each period the stock can either go up by 10% or down by 10%. A European call option on this stock with an exercise price of 100 expires at the end of the second period. If the stock moves down in period 1, how would you adjust your t = 0 hedge by trading only stock? (closest answer) buy about 0.39 shares of stock sell about 0.62 shares of stock buy about 0.09 shares of stock sell about 0.39 shares of stock sell about 0.09 shares of stock buy about 0.62 shares of stock
(a) The table below gives information about European options with a maturity date of 6 months. Type Of option Strike Price Call 65 Call 58 Put 65 Premium 5 8 4 (i) Devise the payoff profile of the hedging strategy from the above for an investor betting on an increase in the stock price and calculate the payoff if the stock price increases to $66 after 6 months. (8 marks) (ii) Suppose that another investor expects a big stock price movement but is not sure of the direction. She however bets that the downward movement is more likely. Devise the corresponding trading strategy and calculate the payoff if the stock price is $55 after 6 months. (8 marks) (b) By analysing the pay off profiles of a protective put strategy and a straddle, discuss in what ways these strategies shield the investor from potential losses.
When the non-dividend paying stock price is $20, the strike price is $20, the risk-free rate is 5%, the volatility is 20% and the time to maturity is 3 months which of the following is the price of a European put option on the stock? N(.) denotes standard normal distribution values. O 20N(-0.1)-20N(-0.2) 20N(-0.2)-20N(-0.1) O 19.7N(-0.2)-20N(-0.1) O None of these O 19.7N(-0.1)-20N (-0.2)
D6) You use the Black Scholes model to price a Call option on a stock with discrete dividends. The dividends will be given in months 1, 5, and 9, each 3 USD. The current value of the stock is 105 USD, the strike price is 90 USD, the continuously compounded annual risk-free rate is 0.05, the volatility is 0.08, the time to maturity is 12 months. Calculate the price of the option.
5) A certain non-dividend paying stock is trading at $50 and its volatility is o = 25%. The risk-free interest rate is 1.25% per anuum with continuous compounding. a) Use a two-step tree (At = .5) to compute the value of 1-year European put option with strike price of $50? b) What would it be the price if the put were to be American?
A stock currently has a price of 45.00 and pays no dividends. One year from now, there is a 50% (risk-neutral) probability that the price of the stock will be 30.00 and 50% that it will be greater than 40.00. The risk-free rate is 4%. Calculate the price of a one-year European call option with an exercise price of 40.00. Possible Answer A 4.81 B 6.35 9.81 D 10.00 E 1135

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