Here, the S0 = 200; X = 190; r = 3%, t = 5/12 = 0.42. q = 0%, C = 40. Using this information, implied volatility is determined by applying Black-Scholes' option pricing model.
using these equations in excel, when sigma = 50%, C = 31.51 & when sigma = 100%, C = 55.47. Therefore, sigma should be between 50% & 100%. Similarly checking, we can find that 60%<sigma<70%. Iterating this process further, C = 40 when sigma = 67.59%.
Consider continuous-time model and five-month European call option on a non- dividend stock which a stock...
4) A nine-month European call option is written on a stock that provides a continuous dividend yield of 4%; the strike price is $110, the risk-free rate is 2% and the stock's volatility is 30%. Assume that the stock is currently selling for $115. What is the price of the call?
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...
Consider a European put option on a non-dividend-paying stock. The current stock price is $69, the strike price is $70, the risk-free interest rate is 5% per annum, the volatility is 35% per annum and the time to maturity is 6 months. a. Use the Black-Scholes model to calculate the put price. b. Calculate the corresponding call option using the put-call parity relation. Use the Option Calculator Spreadsheet to verify your result.
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.)
(b) A 6-month European call option on a non-dividend paying stock is cur- rently selling for $3. The stock price is $50, the strike price is $55, and the risk-free interest rate is 6% per annum continuously compounded. The price for 6-months European put option with same strike, underlying and maturity is 82. What opportunities are there for an arbitrageur? Describe the strategy and compute the gain.
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,...
5) A three-month European put option is written on a stock that provides a continuous dividend yield of 2%; the strike price is $95, the risk-free rate is 2% and the stock's volatility is 40%. Assume that the stock is currently selling for $90. What is the price of the put?
What is the price of a European put option on a non-dividend-paying stock when the stock price is $69, the strike price is $70, the risk-free interest rate is 5% per annum, the volatility is 35% per annum, and the time to maturity is six months?
A European call option on a non-dividend payment stock with a strike price of$18 and an expiration date in one year costs $3. The stock price is $20 and the risk free rate is 10% per annum. Can you design an arbitrage scheme to exploit this situation?
A six-month European call option on a non-dividend-paying stock is currently selling for $6. The stock price is$64, the strike price is S60. The risk-free interest rate is 12% per annum for all maturities. what opportunities are there for an arbitrageur? (2 points) 1. a. What should be the minimum price of the call option? Does an arbitrage opportunity exist? b. How would you form an arbitrage? What is the arbitrage profit at Time 0? Complete the following table. c....