Question 2(a) Use the Black-Scholes formula to find the current price of a European call option ona stock paying no income with strike 60 and maturity 18 months from now. Assume the20%, and the constantcurrent stock price is 50, the lognormal volatility of the stock is a =continuously compounded interest rate is r 10%(b) Repeat part (a) for a European put with strike 60 and maturity 18 months fromnow

Calculation of Price of European Call and Put Option:The price of European call option is $4.18 and…

Answered: Question 2 (a) Use the Black-Scholes…

Intermediate Financial Management (MindTap Course List)

13th Edition

ISBN:9781337395083

Author:Eugene F. Brigham, Phillip R. Daves

Publisher:Eugene F. Brigham, Phillip R. Daves

Chapter5: Financial Options

Section: Chapter Questions

Problem 5P

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Put–Call Parity The current price of a stock is $33, and the annual risk-free rate is 6%. A call option with a strike price of $32 and with 1 year until expiration has a current value of $6.56. What is the value of a put option written on the stock with the same exercise price and expiration date as the call option?
Question 2. (a) Use the Black-Scholes formula to find the current price of a European call option on a stock paying no income with strike 60 and maturity 18 months from now. Assume the current stock price is 50, the lognormal volatility of the stock is σ = 20%, and the constant continuously compounded interest rate is r = 10%.
only answer b) Question 2. (a) Use the Black-Scholes formula to find the current price of a European call option on a stock paying no income with strike 60 and maturity 18 months from now. Assume the current stock price is 50, the lognormal volatility of the stock is σ = 20%, and the constant continuously compounded interest rate is r = 10%. (b) Repeat part (a) for a European put with strike 60 and maturity 18 months from now
QUESTION: 2. What is the fair value for a six-month European call option with a strike price of $135 over a stock which is trading at $138.15 and has a volatility of 42.5% when the risk free rate is 1.85% using the two step binomial tree? a) What is the delta of this option? b) What is the probability of an up movement in this stock? c) What is the probability of a down movement in this stock? d) What is the proportional move up for this stock e) What is the proportional move down for this stock f) What would be the value of the put option with the same strike price?
*NoChatGPT answers please 6A) What is the price of a European call option on a non-dividend-paying stock when the stock price is $52, the strike price is $50, the risk-free interest rate is 12% per annum, the volatility is 30% per annum, and the time to maturity is 3 months? 6B) What is the assumption of the Black–Scholes–Merton stock option pricing model about the probability distribution of the stock price in one year? What is the assumption about the probability distribution of the continuously compounded rate of return on the stock during the year?
Exercise 1.A stock is worth $50 on december, 1st 2021. This price increases by 4% ou decreases by 4% every 2 months. The flat continuous rate of interest is 5% and the continuous rate of dividend is 2%.a) What is the premium of an American call on this stock with a maturity of 6 months and a strike price of $48?b) What is the premium of a European put on the stock? Maturity and strike price remain unchanged.c) In option pricing theory, what does ‘risk neutral’ probability mean? What is the probability the European put gets exercised?
Question 4. A stock that pays no dividends has price today of 100. In one year’s time the stock is worth 110 with probability 0.75 and 85 with probability 0.25. The one-year annually compounded interest rate is 5%. a) Calculate the forward price of the stock for a forward contract with maturity one year. b) Calculate the price of a one-year European put option with strike 100. c) Suppose you observe that the put option in part (b) has a market price of 4. Determine an arbitrage portfolio and calculate how much profit is generated at time T = 1 by this portfolio.
A. Consider a stock worth K12.50 that can go up or down by 15% per period. Assume aperiod process of one. The risk-free rate is 10%. Find the value of the call optiontoday, with the strike price of K11.50. B. What is the price of a European put option on a non-dividend paying stock when thestock price is K69, the strike price is K70, the risk-free rate is 5% per annum, thevolatility is 35% per annum, and the time to maturity is 6 months?
The current price of a non - dividend paying stock is $38.52. Use a two-step tree to value a European call option on the stock with a strike price $32.3 that expires in 12 months. The risk free rate is 9.9% per annum, and the volatility is 28.1%. What is the option price?
a) What is a lower bound for the price of a three-month European put option on a non-dividend-paying stock when the current stock price is $566, the strike price is $523, and the (continuously compounded) risk-free rate is 6% per annum? b) Describe how an investor can create a short calendar spread position using call options. Draw a figure to describe the value of position when the short maturity option expires.
Consider a 3-month European call option on a non-dividend-paying stock. The current stock price is $20, the risk-free rate is 6% per annum, and the strike price is $20. Assume a risk-neutral world. You calculate the following values using the Black-Scholes-Merton model: d1 = 0.2000 N(d1) = 0.5793 d2 = 0.1000 N(d2) = 0.5398 a) What is the probability that the call option will be exercised? b) What is the expected stock price at the option’s expiration in 3 months? Assume that all values of the stock price less than $20 are counted as zero. c) What is the expected payoff on the option at expiration (in 3 months)? d) Calculate the PV of the expected payoff from part c).
The price of a European call option on a stock with a strike price of $50.9 is $5.6. The stock price is $40.1, the continuously compounded risk-free rate (all maturities) is 5.2% and the time to maturity is one year. A dividend of $0.6 is expected in six months. What is the price of a one-year European put option on the stock with a strike price equal to the call's strike price? Please state the formula and steps, thanks

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