Moscha's current stock price is $150 per share. In every 6 month period, the price will either go up by 25% or decrease by 20%. Suppose the risk free rate is 12% per year. A. Use one-step binomial tree to value a call option on Moscha that expires in six months with exercise price of $140. B. Replicate the payoff of call option in part A using shares of stocks and borrowing. What is the amount of borrowing?
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- 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.D4) Finance Calculate the price of a 3-month American put option on a non-dividend-paying stock when the stock price is $50, the strike price is $50, the risk-free interest rate is 5% per annum, and the volatility is 25% per annum. Use a binomial tree with a time interval of 1 month.The current price of a non-dividend paying stock is $30. Use a two -step tree to value a European call option on the stock with a strike price of $32 that expires in 6 months. Each step is 3 months, the risk free rate is 8% per annum with continuous compounding. What is the option price when the volatility is 20%? (Hint: Calculate u and d using the CRR approach.) A. $1.48 B. $1.08 C. $1.68 D. $1.28
- Please answer below three requirements: Question- The current price of a non-dividend paying stock is $30. Use a two-step tree to value a put option on the stock with a strike price of $32 that expires in 6 months. Each step is 3 months, and in each step the stock price either moves up by 10% or moves down by 10%. Suppose that the risk free rate is 8% per annum with continuous compounding. 1) What should be the EUROPEAN put option price today? 2) If the option was an AMERICAN put option, what should be the price today? 3) If the volatility was given as 30%, how would the AMERICAN put option price change?HEJO company has the current stock price of $20 today. Use a 1 step binomial tree to estimate the price of a oneyear call on thisstock. Assume the price can increase or decrease by 10% in in the next year with equal likelihood. Risk free rate is 2%, the strike is $21. A. Find the hedge ratio(H), (make sure have the correct sign, this will be written out as a decimal Answer: 0.25 B) Find the call's value or price today Answer: .58 C) Using the above information to price a put using call parity. Answer: 1.17 Please explain without using excel.4. A stock is selling today for $100. The stock has an annual volatility of 45 percent and the annual risk-free interest rate is 12 percent. A 1 year European put option with an exercise price of $90 is available to an investor .a.Use Excel’s data table feature to construct a Two-Way Data Table to demonstrate the impact of the risk free rate of interest and the volatility on the price of this put option: i. Risk Free Rates of 5%, 7%, 9%, 12%, 15% and 18%. ii. Volatility of 35%, 45%, 55%, and 65%. b. How is the put option price impacted by varying the risk free rate of interest? c.How is the put option price impacted by varying the volatility?
- The current price of a non-dividend paying stock is $50. Use a two-step tree to value a European put option on the stock with a strike price of $50 that expires in 12 months. Each step is 6 months, the risk free rate is 5% per annum, and the volatility is 50%. What is the value of the option according to the two-step binomial model. Please enter your answer rounded to two decimal places (and no dollar sign).1. HEJO company has the current stock price of $20 today. Use a 1 step binomial tree to estimate the price of a oneyear call on thisstock. Assume the price can increase or decrease by 10% in in the next year with equal likelihood. Risk free rate is 2%, the strike is $21. A. Find the hedge ratio(H), (make sure have the correct sign, this will be written out as a decimal B) Find the call's value or price today Note: Show the calculation without using excel.Consider a stock with a current price of P $27 Suppose that over the next 6 months the stock price will either go up by a factor of 1.41 or down by a factor of 071. Consider a call option on the stock with a strike price of $25 that expires in 6 months. The nsk-free rate is 6%. (1) Using the binomial model, what are the ending values of the stock price? What are the payoffs of the call option? (2) Suppose you write one call option and buy N shares of stock How many shares must you buy to create a portfolo with a riskless payoff Ge, a hedge portfolio)? What is the payoff of the portfolio? 13)What.is the.present.value of the hedge port- Tolot What &the value of phe calt.option? (4) What s a teplieatirg portfolio What is 2otrage?
- Consider a European call option on a stock with current price $100 and volatility 25%. The stock pays a $1 dividend in 1 month. Assume that the strike price is $100 and the time to expiration is 3 months. The risk free rate is 5%. Calculate the price of the the call option.2) Consider a stock whose current price is $100 and volatility is 20% p.a. The stock is expected to pay a dividend of $2 in one month's time. The risk-free rate is 5% p.a. continuously compounding. (a) Using a two-period binomial tree, what is the value of a 2-month American call whose exercise price is $101? (b) Using a two-period binomial tree, what is the value of a 2-month American put whose exercise price is $101?7) Consider a European call option on a -dividend-paying stock where the stock price is $40, the strıke price is $40, the risk-free rate is 4% per annum, the volatility is 30% per annum, and the time to maturity is six months. A dividend of $1 is expected in 3 months' time a. Calculate u, d̟ and p for a two-step tree b. Value the option using a two-step tree. c. Value the option with 5 time steps using DerivaGem software.