A stock has a current price of $67. An option on this stock that expires in six months has an exercise price of $65. Thestock will pay a dividend of $5 in three months. Assume an annualized volatility of 30% and a continuously compoundedrisk - free rate of 5% per annum. Use the Black - Sholes - Merton model to price this option. 1) Suppose the option is aEuropean put. Calculate the value of the put. 2) Suppose this option is an American call. Use Black's approximation tocalculate the value of this call.

An option is an agreement between two parties granting one the opportunity to buy or sell a security…

risk-free rate of 5% per annum. Use the Black - Sholes - Merton model to price this option. 1) Suppose the option is a European put. Calculate the value of the put. 2) Suppose this option is an American call. Use Black's approximation to calculate the value of this call.

risk-free rate of 5% per annum. Use the Black - Sholes - Merton model to price this option. 1) Suppose the option is a European put. Calculate the value of the put. 2) Suppose this option is an American call. Use Black's approximation to calculate the value of this call.

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

A stock has a current price of $67. An option on this stock that expires in six months has an exercise price of $65. The
stock will pay a dividend of $5 in three months. Assume an annualized volatility of 30% and a continuously compounded
risk - free rate of 5% per annum. Use the Black - Sholes - Merton model to price this option. 1) Suppose the option is a
European put. Calculate the value of the put. 2) Suppose this option is an American call. Use Black's approximation to
calculate the value of this call.

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Select all statements which are correct. The value of a European put option is increasing in the strike price. The value of a European call option is increasing in the strike price. The value of a European put option is increasing in the spot price. The value of a European call option is increasing in the spot price.
Consider a two year put options with strike Price sh. 52 on a stick whose current price is sh.50. suppose there is 2 times steps and each step is one year and in each times steps the price move up or down by 20%. Suppose the risk Free rate is 5% . Calculate value of put assuming; A) Europeans options B) American options
We will derive a two-state put option value in this problem. Data: S0 = $180; X = $190; 1 + r = 1.10. The two possibilities for ST are $210 and $110.a. The range of S is $100 while that of P is $80 across the two states. What is the hedge ratio of the put? (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) (The answer for this one is -.80) :)b. Form a portfolio of four shares of stock and five puts. What is the (nonrandom) payoff to this portfolio? (Round your answer to 2 decimal places.) c. What is the present value of the portfolio? (Round your answer to 2 decimal places.) d. Given that the stock currently is selling at $180, calculate the put value. (Do not round intermediate calculations and round your answer to 2 decimal places.)
Given the following data, show the profit from a strategy involving a straddle for the put, call and combined position. The price of a European call and put option are $5 and $6 respectively. Both of the options have a strike price of $30. Explain why a trader might be willing to enter into a straddle. Please show all work. Please use four decimal places for all calculations.
Consider the following portfolio: a newly entered-into long forward contract on an asset and a long position in a European put option on the asset with the same maturity as the forward contract and a strike price that is equal to the forward price of the asset at the time the portfolio is set up. Show that it has the same value as a European call option with the same strike price and maturity as the European put option. Deduce that a European put option has the same value as a European call option with the same strike price and maturity when the strike price for both options is the forward price.
How to solve this problem? plz solve it step by step with formulas, thank u! (which one is the risk-free rate? 1% or 2%) Options on Indexes and Currencies Example Suppose that the current exchange rate of AUD to CAD is 1.2 AUD/CAD and o = 0.4463. Find the price of American put option to sell CAD for AUD at K = $1.1 AUD/CAD before or at half a year from now. Assume that the risk-free rates in Canada and Australia are 2% and 1%, respectively. Find the price of the American call option today by using the two period binomial model.
If the yield curve is upward sloping: Hint: When there is an increase in the demand for an asset, the price of the asset goes up. You expect returns from investing in such ("higher-priced") asset to be lower in the future. Conversely, when there is a decrease in the demand for an asset, the price of the asset goes down. You expect returns from investing in such ("lower-priced") asset to be higher in the future. O investors expect the short-term interest rates to fall in the future. investors often shift their investment holdings away from long-term securities. investors often short sell short-term securities. investors often shift their investment holdings away from short-term securities.
Which one of the following statements is true? Multiple Choice O O O O A call with a strike price of $25 and a stock price of $23 has positive intrinsic value. A European style option is more valuable than an American style option. An American style out-of-the-money call option can have a positive value. A $40 put option has more intrinsic value than a $50 put option on the same underlying asset. The time value of an option is equal to the intrinsic value minus the option premium.
Consider a call and a put options with the same strike price and time to expiry. Given that the strike price is exactly equals to the forward price, then: A. Put and call have same premium B. The premium of the put is equal to the forward price C. The premium of the put is equal to the premium of the call plus the present value of the strike D. The premium of the call is equal to the forward price
find a formula for the price of European call option. if R=0 and S=(0)=X=1. Compute the price for U=0.01 and D=-0.19
Which of the following statements about European option contracts is TRUE? a. Typically American options are cheaper than otherwise similar European options due to the uncertainty regarding the date of exercise. b. One can synthesise a long forward position in the underlying by being long a call and short a put c. A long call position and a short put position both involve buying the underlying and so are equivalent d. The price of an option can be obtained by computing the true probabilities of each state of nature, working out the expected option payoff across those states and then discounting back to the present.
What does WRF = -0.50 mean? Group of answer choices The investor can borrow money at the risk-free rate. The investor can lend money at the current market rate. The investor can borrow money at the current market rate. The investor can borrow money at the prime rate of interest. The investor can lend money at the prime rate of interest.

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