Use a 2-step binomial tree to value a put option. All of the steps in your calculation should be shown including the calculation of P and the calculation of each of the option nodes U, D, UU, UD & DD. • Assume that at each node the stock moves up 20% or down 20%.

Use a 2-step binomial tree to value a put option. All of the steps in your calculation should be shown including the calculation of P and the calculation of each of the option nodes U, D, UU, UD & DD. • Assume that at each node the stock moves up 20% or down 20%.

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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Question

Please answer question attached below.

Use a 2-step binomial tree to value a put option.
All of the steps in your calculation should be shown including the
calculation of P and the calculation of each of the option nodes U, D, UU,
UD & DD.
Assume that at each node the stock moves up 20% or down 20%.
The option expires in 2 years. The interest rate is 5% continuously
compounded.
The spot price is 100 and the option strike price is 104.
• Early Exercise is not possible with this option.

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1) Draw the binomial tree listing only the option prices at each node. Assume the following data on a 6-month call option, using 3-month intervals as the time period. K = $40, S = $37.90, r = 5.0%, σ = 0.35 2) Draw the binomial tree listing only the stock prices at each node. Assume the following data on a 6-month call option, using 3-month intervals as the time period. K = $70, S = $68.50, r = 6.0%, σ = 0.32 3) Draw the binomial tree listing only the option prices at each node. Assume the following data on a 6-month put option, using 3-month intervals as the time period. K = $40.00, S = $37.90, r = 5.0%, σ = 0.35 4) Using a binomial tree explanation, explain the situation in which an American option would alter the pricing of an option.
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.
Suppose that a call option with a strike price of $48 expires in one year and has a current market price of $5.17. The market price of the underlying stock is $46.25, and the risk-free rate is 1%. Use put-call parity to calculate the price of a put option on the same underlying stock with a strike of $48 and an expiration of one year. The price of a put option on the same underlying stock with a strike of $48 and an expiration of one year is $. (Round to the nearest cent.)
Please answer the five questions below. You may attach a spreadsheet or enter the answers in this box 1. A one year call option has a strike price of 50, expires in 6 months, and has a price of $4.74. if the risk free rate is 3%, and the current stock price is $45, what should the corresponding put be worth?
Give typing answer with explanation and conclusion A call option has a strike price of $11, and a time to expiration of 0.8 in years. If the stock is trading for $20, N(d1) = 0.5, N(d2) = 0.12, and the risk free rate is 5.40%, what is the value of the call option?
Consider a put option written on an underlying security that has a current value of $100 and has a volatility of 25% (i.e. .25). The put has a strike price of $100 and expires in 1 year. The risk-free rate is 3% (.03). If the time to expiration is changed from 1 to 2 to 3 years, what happens to the value of vega (the change in the put value given a percentage point change in the volatility – say from 25% to 26%)? (Note: vega is defined in note N16 on page 8; see ). What is the comparison of the change in vega (given a change from 1 to 2 to 3 years to expiration) if the strike price is $105 (relative to if the strike is $100)?
Suppose a stock is currently (time t = 0) worth 100. Further, suppose the one year annually compounded interest rate is 2%, and the two year annually compounded rate is 3%. Find the following:a) The forward price for a forward contract on the stock with maturity year T1 = 1. b) The forward price for a forward contract on the stock with maturity year T2 = 2.c) The forward price for a forward contract with maturity T1 = 1 on a ZCB with maturity T2 = 2.d) The forward price for a forward contract with maturity T1 = 1 on a forward contract on the stock with maturity T2 = 2 and delivery price K = 101.
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.
Give typing answer with explanation and conclusion to all parts Consider a put option whose underlying asset is a stock index with 6 months to expiration and a strike price of $1000. Suppose the risk-free interest rate for the six months is 2% and that the option’s premium is $74.20. (a) Find the future premium value in six months. (b) What is the buyer’s profit is the index spot price is $1100? (c) What is the buyer’s profit is the index spot price is $900
Consider a put option whose underlying asset is a stock index with 6 months to expiration and a strike price of $1000. Suppose the risk-free interest rate for the six months is 2% and that the option’s premium is $74.20. (a) Find the future premium value in six months. (b) What is the buyer’s profit is the index spot price is $1100? (c) What is the buyer’s profit is the index spot price is $900 Only typed answer
Using the binomial call option model to find the current value of a call option with a $25 exercise price on a stock currently priced at $26. Assume the option expires at the end of two periods, the riskless interest rate is ½ percent per period. What are the hedge ratios?
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.

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