A stock price is currently $100. Over each of the next two 3-month periods, it will go up by 10% or down by 10%. The risk-free interest rate is 6% per annum with semiannual compounding. A (a) What is the value of a 6-month European call option with a strike price of $100? Calculate this directly using a two-period binomial tree and the delta-hedging approach.

A stock price is currently $100. Over each of the next two 3-month periods, it will go up by 10% or down by 10%. The risk-free interest rate is 6% per annum with semiannual compounding. A (a) What is the value of a 6-month European call option with a strike price of $100? Calculate this directly using a two-period binomial tree and the delta-hedging approach.

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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Concept explainers

Treasury Market

On-the-run securities are the most recently issued securities in the market depth and are therefore traded at some premium. The off-the-run securities are the ones issued just before the most recent ones. The on-the-run securities have a lower yield to the investor than the off-the-run securities.

Question

A stock price is currently $100. Over each of the
next two 3-month periods, it will go up
by 10% or down by 10%. The risk-free interest rate
is 6% per annum with semiannual
compounding.
A
(a) What is the value of a 6-month European call
option with a strike price of $100?
Calculate this directly using a two-period binomial
tree and the delta-hedging
approach.

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The current stock price of MRF is ₹ 81000. A European call option on the stock with exercise price of ₹ 75000 will expire in 40days. The annual continuously compounded risk-free interest rate is 10%, standard deviation of the continuously compounded rate of return is 60% p.a. Calculate the value of the Call option. Find the value of the Put option using Put-Call Parity Rule.
The stock price is currently $30. Each month for the next two months it is expected to increase by 8% or reduce by 10%. The risk-free interest rate is 5%. Use a two-step tree to calculate the value of a derivative that pays off [max(30 — St； 0)]2, where St is the stock price in two months? If the derivative is American-style, should it be exercised early?
You Consider a stock with a price of $50 that is expected to increase by 6% or decrease by 8% each month over the next two months. Having a risk-free rate at 3% per year with continuous compounding, calculate the value of a two-month European put option with a strike price of $55. Repeat your calculations for a two-month American put option with a strike price of $55. Show clearly all your calculations and results with the use of the relevant equations and graphs. Discuss your investment decision in each case separately.
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
Use the binomial tree analysis to value a 6-month American put option with a $65 strike price on Crookshanks Corporation. The shares are currently trading for $60. The annualized continuously compounded risk-free rate is 3%. The volatility of the stock is 57%. You will use the Cox Ross Rubenstein method for computing the binomial tree, and use a time step of 2 months.
Suppose the call option of Tesla company has an exercise price of $200 and expires in 90 days. Assume the current price of Tesla stock is $240, with a standard deviation of 40% per year. The risk-free interest rate is 6.18% per year. First, using the Black-Scholes formula, compute the price of the call. And then use put-call parity to compute the price of the put with the same strike and expiration date. Based on put-call parity, what should be the put option price? $ 2.65 $ 1.78 $ 3.69 $ 4.22 None of the above
The price of a European CALL option is $8.00 and a European PUT is $10.00. The expiration date is 1 year and has an exercise price k=$60.00, the share price of the underlying asset is quoted today at $60.00. The risk-free rate is 10% per year. Propose a strategy that generates arbitrage and a profit.
Consider a two-period binomial model in which a non-dividend-paying stock currently trades at £35. Over each of the next two six-month periods, the share price is expected to go up by 12% or down by 9%. The risk-free interest rate is 6% per annum with continuous compounding. Calculate the value of a one-year European put option with a strike price of £36, using a two-period binomial tree method.

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