Pricing a European Call Option
Value of u
Value of d
Value of p
Pricing a European Call Option Data Current stock price: $50 Risk-free interest rate: 1% per annum,...
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?
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...
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...
. The spot price per share is $115 and the risk free rate is 5% per annum on a continuously compounded basis. The annual volatility is 20% and the stock does not pay any dividend. All options have a one-year maturity. In answering the questions below use a binomial tree with three steps. Each step should be one-third of a year. Show your work. 1.Using the binomial tree, compute the price at time 0 of a one-year European call option...
The spot price per share is $115 and the risk free rate is 5% per annum on a continuously compounded basis. The annual volatility is 20% and the stock does not pay any dividend. All options have a one-year maturity. In answering the questions below use a binomial tree with three steps. Each step should be one-third of a year. 1)Using the binomial tree, compute the price at time 0 of a one-year European put option on 100 shares of...
Find the fair value of an European call option and an American put option using the incoherent and coherent binomial option tree if the underlying asset pays dividend of 4 PLN in one and half month. The initial stock price is 60 PLN, the strike price of 58 PLN is expiring at the end of the third month, the continuously compounded risk-free interest rate is 10% per annum, and the stock volatility is 20%.
5. Consider a European call option on the stock of XYZ, with a strike price of $25 and two months to expiration. The stock pays continuous dividends at the annual yield rate of 5%. The annual continuously compounded risk free interst rate is 11%. The stock currently trades for $23 per share. Suppose that in two months, the stock will trade for either S18 per share or $29 per share. Use the one-period binomial option pricing model to find today's...
Use the BSM model to calculate the price of a 13-month European call option with a strike price of $40 on a stock that is currently $48 and is expected to pay a $5 dividend in 6 months. The risk-free interest rate is 4% (annualized, continuously compounded), and the volatility of the stock’s returns is 55% per annum. (Reminder: your answer can have N(.) terms in it.)
The volatility of a stock is 0.3 per annum. In a Cox-Ross-Rubinstein binomial tree in which one step represents a time interval of 3 months, what are the proportional up-movement and down-movement factors, u and d, respectively? a. u=1.16, d=0.86 b. u=1.30, d=0.70 c. u=1.24, d=0.81 d. u=1.35, d=0.74