Please correct answer and don't used hand raiting and don't used Ai solution 1.Calculate the call price given the following parameters. The stock price is now $30. The stockhas an annualized volatility of 40%. The risk-free rate is 10%. The option has an exercise priceof $35 and will expire in 3 months. show all work2. A stock is currently trading at $40. In one year, the stock will either be $55 or $30. The riskfree rate is 8% per year. What's the price of a put option with a strike of 40? Show all work

1. BLACK-SCHOLES OPTION PRICING MODELThe Black-Scholes model is based on several key assumptions:-…

Answered: 1.Calculate the call price given the…

EBK CONTEMPORARY FINANCIAL MANAGEMENT

14th Edition

ISBN:9781337514835

Author:MOYER

Publisher:MOYER

Chapter20: Financing With Derivatives

Section20.A: The Black-scholes Option Pricing Model

Problem 1P

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Suppose that a Stock has a current price of $40 and that in 6-months it may go up by 20% or down by 15%. Assuming the annual risk-free rate is 3%, compounded semi-annually, answer the following: a) Calculate the value of a $35 Call with two 6-month periods (i.e. 12-months) to expiry using the Risk Neutral Approach. b) Calculate the value of a $35 Put using Put-Call Parity. c) Without performing any calculations, explain in 1-2 sentences what you would expect to happen to the value of the Call and Put if the Exercise Price decreased. d) Do this question in the blank space below - i.e. DO NOT answer this sub-part (d) in Excel. Only your solution written below will be marked: Suppose the market price of a 12-month Call with an exercise price of $35 is $6.00. The Put price is as you calculated in (b) above. Using a payoff table, illustrate an arbitrage opportunity as a result of the mispricing of the Call. Show your workings to 3 decimal places. (If you need more space, please use the back…
The price of a stock is currently $37. Over the next half year, the price is anticipated to rise to $42 or decline to $36. The upside has a 60% probability of occurring. The risk-free interest rate is 5% p.a.. What is the price of a six month call option with an exercise price of $38?
Consider the three calls from the previous problem expiring in T = 1 year. Suppose that the premium of the three options are $7, $3, $1 for A, B, and C, respectively, today (time 0). Suppose the price on the stock today is $14. Suppose the risk-free rate is constant at 5%. Graph the profit function for the butterfly strategy at time T taking into consideration the time value of the initial cost. By how much would the asset have to change over the year for your butterfly portfolio to be a loss?
Consider a stock currently priced at $40. Assume that in each period of one month, the stock could either appreciate or depreciate by 10% . The risk - free rate is 2% per annum. What would be the value of a 2 - month ATM Asian put?
Suppose Carol's stock price is currently $20. If the standard deviation of the continuously compounded returns (σ) on a stock is 60 percent per year. The annual risk-free rate is 12%, compounded every 6 months. A. Using one-step binomial tree, what is the current value of a six-month call option with an exercise price of $25?B. Using two-step binomial tree, what is the current value of a one-year put option with an exercise price of $25?
The following information is given: Time to expiration 1 year. Standard deviation 40% per year. Exercise price $72. Stock price $72. Risk free rate 4% a year. Use the Black–Scholes formula to find the value of the calloption. What is the value of the put option with the same exercise price and time to expiration? What is the value of the call option if time to expiration is 3 years? What is the value of the call option if the standard deviation is 20%? What is the value of the call option if the exercise price is $90? What is the value of the call option if the current stock price is $50? What is the value of the call option if the risk-free rate is 8%?
A stock price is currently $10. Over each of the next two three - month periods it is expected to go up by 10 percent or down by 10 percent. The risk - free interest rate is 6.184 percent per annum,the interest rate is a simple interest rate(use continuous compounding to get proper rf). The strike price is $10. Calculate the call option price and the put option price.
Suppose the stock price is 40 and we need to price a call option with a strike of 50 maturing in 4 months. The stock is not expected to pay dividends. The continuously-compounded riskfree rate is 3%/year, the mean return on the stock is 7%/year, and the standard deviation of the stock return is 40%/year.
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?
Consider the futures contract written on the S&P 500 index and maturing in one year. The interest rate is 3%, and the future value of dividends expected to be paid over the next year is $35. The current index level is 2,000. Assume that you can short sell the S&P index.a. Suppose the expected rate of return on the market is 8%. What is the expected level of the index in one year?b. What is the theoretical no-arbitrage price for a 1-year futures contract on the S&P 500 stock index?c. Suppose the actual futures price is 2,012. Is there an arbitrage opportunity here? If so, how would you exploit it?
The current price of a stock is $14 . In 6 months, the price will be either $20 or $12 . The annual risk-free rate is 7% . Find the price of a call option on the stock that has a strike price of $13 and that expires in 6 months. (Hint: Use daily compounding.) Assume a 365-day year. Do not round intermediate calculations. Round your answer to the nearest cent.
Suppose Carol's stock price is currently $20. If the standard deviation of the continuously compounded returns (σ) on a stock is 60 percent per year. The monthly risk-free rate is 1 percent. Using one-step binomial tree, what is the current value of a six-month call option with an exercise price of $15?

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