Write and describe the Black-Scholes formulas for pricing European call and put options. The stock price three months from the expiration of an option is R1040, the exercise price of the option is R1000, the risk-free interest rate is 11% per annum, and the volatility is 22% per annum. Calculate the prices of European call and put options.

Write and describe the Black-Scholes formulas for pricing European call and put options. The stock price three months from the expiration of an option is R1040, the exercise price of the option is R1000, the risk-free interest rate is 11% per annum, and the volatility is 22% per annum. Calculate the prices of European call and put options.

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

See similar textbooks

Similar questions

Suppose we have both a European call option and put option with an exercise price of $53 and the underlying stock is currently priced at $50. We are to note also that both options will expiry in six months. Further, market surveys suggest that the price of the stock can either go up by 20% or decrease by 25%. The current risk-free rate of interest is 2% per annum. (a) What is the expected price of the underlying asset at expiry date? (b) What is the value of the call option, using the binomial model? (c) If the put option is selling for $4.80, what should be the price of the call option to avoidarbitrage?
Suppose we have both a European call option and put option with an exercise price of $53 and the underlying stock is currently priced at $50. We are to note also that both options will expiry in six months. Further, market surveys suggest that the price of the stock can either go up by 20% or decrease by 25%. The current risk-free rate of interest is 2% per annum. Required: (a) What is the expected price of the underlying asset at expiry date? (b) What is the value of the call option, using the binomial model? (c) If the put option is selling for $4.80, what should be the price of the call option to avoid arbitrage?
Consider an option on a non-dividend-paying stock when the stock price is $30, the exercise price is $29, the risk-free interest rate is 5% per annum, the volatility is 25% per annum, and the time to maturity is four months. a) What is the price of the option if it is a European put?
Consider a European call option on the S&P 500 that is two months from maturity. The currentvalue of the index is 930, the exercise price is 900, the risk-free interest rate is 8% per annum,and the volatility of the index is 20% per annum. Dividend yields of 0.2% and 0.3% are expectedin the first month and the second month, respectively. Calculate the call price
Consider a 2-year EUROPEAN PUT with a strike price of $65 on a stock whose current stock price is $60. Suppose that there are two time steps, and in each time step the stock price either moves up by 20% or moves down by 20%. Also suppose that risk-free rate is 5% per annum with continuous compounding . What is the value of the European put option?
The stock price is currently $100. Over each of the next two six-month periods, it is expected to go up by 20% or down by 20%. The risk-free interest rate is 5% per annum with continuous compounding. What is the value of a one-year European call option with a strike price of $100? What is the value of a one-year European put option with a strike price of $100? Verify that the European call and European put prices satisfy put-call parity.
Use the Black-Scholes pricing formula to calculate the price today of a European call option with strike £518.23, maturing in 12 months, if the spot price of the underlying is £534.35, its volatility is 25.13% and the risk-free rate is 4%. Give your answer correct to 2 decimal places
A stock price is currently $100. Over each of the next two six-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 8% per annum with continuous compounding. What is the value of a one-year European call option with a strike price of $100? What is the value of a one-year European put option with a strike price of $100? Verify that the European call and European put prices satisfy put–call parity.
Suppose that a stock price is currently 35 dollars, and it is known that four months from now, the price will be either 51 dollars or 29 dollars. Find the value of a European call option on the stock that expires four months from now, and has a strike price of 39 dollars. Assume that no arbitrage opportunities exist and a risk-free interest rate of 10 percent.Answer =dollars.
Consider a 3-month European call option on a non-dividend-paying stock. The current stock price is $20, the risk-free rate is 6% per annum, and the strike price is $20. Assume a risk-neutral world. You calculate the following values using the Black-Scholes-Merton model: d1 = 0.2000 N(d1) = 0.5793 d2 = 0.1000 N(d2) = 0.5398 a) What is the probability that the call option will be exercised? b) What is the expected stock price at the option’s expiration in 3 months? Assume that all values of the stock price less than $20 are counted as zero. c) What is the expected payoff on the option at expiration (in 3 months)? d) Calculate the PV of the expected payoff from part c).
1. Consider an option on a non-dividend paying stock when the stock price is $30, the exercise price is $28, the annual interest rate is 5%, the annual volatility is 25%, and the time to maturity is 6 months. Show the details of your calculations. a) What is the price of the option if it is a European call?
Calculate the price of a three-month European put option on a non-dividend-paying stock with a strike price of $50 when the current stock price is $50, the risk-free interest rate is 10% per annum, and the volatility is 30% per annum.