Value of a stock is currently at $40. Volatility of that stock is 30% per year and risk-free interest rate with continuous compounding is at 5% per year. Suppose you are planning to value a 3-month European call option with strike price at $41 using a two-step binomial model. Answer the following using this information. (Binomial Tree Approach to Option Valuation describe how to solve this problem)
What are the values of u, d and q?
u = e^(0.3*(3/12)^(1/2)) = 1.1618
d = 1/u = 1/1.1618 = 0.8607
Value of a stock is currently at $40. Volatility of that stock is 30% per year...
The current price of a non-dividend-paying stock is 30. The volatility of the stock is 0.3 per annum. The risk free rate is 0.05 for all maturities. Using the Cox-Ross-Rubinstein binomial tree model with two time steps to do the valuation, what is the value of a European call option with a strike price of 32 that expires in 6 months?
The spot price of SPY is currently (So= $200) the volatility of SPY is 60% (sigma= 0.060) We are onvested on valuing SPY option at the end of 6 months (T= 6/12= 0.5). The risk free rate with continuous compounding is 4% per amum (r= 0.04) Apply Arbitrage Portfolio approach with one step binomial tree and calculate de value of a six month European call option on SPY with an exercise/strike price of $220 (K=$220)
Problem 12.25. Consider a European call option on a non-dividend-paying stock where the stock price is $40, the strike 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. Calculate u, d, and p for a two step tree b. Value the option using a two step tree. c. Verify that DerivaGem gives the same answer d. Use DerivaGem to value the option with 5,...
The current price of a non-dividend-paying stock is 30. The volatility of the stock is 0.3 per annum. The risk free rate is 0.05 for all maturities. Using the Cox-Ross-Rubinstein binomial tree model with two time steps to do the valuation, what is the value of a European call option with a strike price of 32 that expires in 6 months? (Your answer should be in the unit of dollar (up to the precision of cents), but without the dollar...
A stock is currently priced at $47.00 and pays a dividend yield of 3.7% per annum. The risk-free rate is 5.3% per annum with continuous compounding. In 18 months, the stock price will be either $40.89 or $52.64. Using the binomial tree model, compute the price of a 18 month European call with strike price $48.74.
A stock is currently priced at $51.00 and pays a dividend yield of 4.3% per annum. The risk-free rate is 5.7% per annum with continuous compounding. In 12 months, the stock price will be either $41.31 or $57.12. Using the binomial tree model, compute the price of a 12 month European call with strike price $50.32.
A stock is currently priced at $52.00. The risk free rate is 4.6% per annum with continuous compounding. In 5 months, its price will be $60.84 with probability 0.57 or $44.72 with probability 0.43. Using the binomial tree model, compute the present value of your expected profit if you buy a 5 month European call with strike price $57.00. Recall that profit can be negative.
A stock currently sells for $50. In six months it will either rise to $60 or decline to $45. The continuous compounding risk-free interest rate is 5% per year. Using the binomial approach, find the value of a European call option with an exercise price of $50. Using the binomial approach, find the value of a European put option with an exercise price of $50. Verify the put-call parity using the results of Questions 1 and 2.
Question 1 a. A stock price is currently $30. It is known that at the end of two months it will be either $33 or $27. The risk-free interest rate is 10% per annum with continuous compounding. What is the value of a two-month European put option with a strike price of $31? b. What is meant by the delta of a stock option? A stock price is currently $100. Over each of the next two three-month periods it is...
Question 3 - 20 Points Consider a European call option on a non-dividend-paying stock where the stock price is $33, the strike price is $36, the risk-free rate is 6% per annum, the volatility is 25% per annum and the time to maturity is 6 months. (a) Calculate u and d for a one-step binomial tree. (b) Value the option using a non arbitrage argument. (c) Assume that the option is a put instead of a call. Value the option...