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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4. Which of the below represents the value of an American option in each state? max(Payoff if exercised, Value if held) Payoff if exercised Risk-neutral probability min(Payoff if exercised, Value if held)
Consider a European call on Amazon Stock (AMZN) that expires in one period. The current stock price is $100, the strike price is $120, and the risk-free rate is 5%. Assume AMZN stock will either go up to $140 or down to $80. Construct a replicating portfolio using shares of AMZN stock and a position in a risk-free asset ... what is the value of the call option? Call Option Price = $4.84 Call Option Price = $2.95 Call Option Price = $7.93 Call Option Price = $12.04
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.)
Using put-call parity, if the price of an At-the-Money Call option maturing in 1 day is $3.14, what is the price of an of an At-the-Money Put option maturing in 1 day (give an approximation)? A. $0.95 B. $2.86 C. $3.14 D.$3.26
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.
An investor buys a 6-month European call option with an exercise price of $35 for $6, and sells a 6-month European call option with an exercise price of $40 for $4. a) What kind of a spread does this strategy create? Answer in terms of “Bull Spread” versus “Bear Spread”. b) Calculate both the total payoff and profit on this strategy at the expiration of the options. Please use a Table (as in the class notes) to identify the payoff and profit.
Given the following information, predict the European call option's new price after the risk free rate changes. Initial call option price = $3 Initial risk free rate = 9.9% Rho = 9 New risk free rate = 9.5% (required precision 0.01 +/- 0.01) Greeks Reference Guide: Delta = ∂π/∂S Theta = ∂π/∂t Gamma = (∂2π)/(∂S2) Vega = ∂π/∂σ Rho = ∂π/∂r Recall that rho is defined as the partial derivative of the option's price with respect to the risk free rate. (i.e. rho = ∂π / ∂r).
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.
use binomial option pricing model for this question. suppose the current spot rate for USD/CHF is 0.7. you need to find the one-year call option price of USD/CHF with the exercise price of 0.68 USD/CHF. Assume that our future states will be either 0.7739 U&SD/CHF or 0.6332 USD/CHF. 1) What are the payoffs of a call option (for both states) 2) what is the hedge ratio of the call option?
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.

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