Question

In: Finance

1. Please use binomial option pricing model to derive the value of a one-year put option....

1. Please use binomial option pricing model to derive the value of a one-year put option. The current share price is ?0 = 100 and exercise price ? = 110. The T-bill rate is ? = 10% per year and annual standard deviation is 20%.

2. Use the Black-Scholes formula to find the value of the same option in the previous problem and compare the difference between these two types of methods.

Solutions

Expert Solution

1) Up-move factor U = = e^(0.2*(1^0.5)) = 1.2214

Down-move factor D = 1/U = 0.8187

Probability of up-move = = (e^(0.1*1)-0.8187)/(1.2214-0.8187)

Probability of up-move =0.71137

Probability of down -move = = 1-0.71137 = 0.28863

Stock price in case of upmove = 1.2214*100 = $122.14

Stock price in case of down-move = 0.8187*100 = $81.87

Payoff in case of upmove = 0

Payoff in case of down-move = 110-81.87 = $28.13

Put option value = 0.71137*0 + 0.28863*28.13

Put option value = $8.11916

2)

Put opttion value using a Black-Scholes model is given by

d1 = (ln(100/110) + (0.1+ (0.2*0.2/2))*1)/(0.2*(1^0.5)) = 0.123449

d2 = 0.123449 - (0.2*(1^0.5) = -0.07655

p = 110*e^(-0.1*1)*N(0.07655) - 100*N(-0.123449)

N(0.07655) = 0.530509232

N(-0.123449) = 0.450875779

p = 110*e^(-0.1*1)*0.530509232- 100*0.450875779

p = $7.715

Difference between these two types of methods.

Put option price using Binomial model = $8.11916

Put option price using Black-Scholes model = $7.715

Difference = 8.11916-7.715 = $0.40416


Related Solutions

(1) Please use binomial option pricing model to derive the value of a one-year put option....
(1) Please use binomial option pricing model to derive the value of a one-year put option. The current share price is ?0 = 100 and exercise price ? = 110. The T-bill rate is ? = 10% per year and annual standard deviation is 20%. (2) Use the Black-Scholes formula to find the value of the same option in the previous problem and compare the difference between these two types of methods.
Use the binomial option pricing model to find the value of a call option on £10,000...
Use the binomial option pricing model to find the value of a call option on £10,000 with a strike price of €12,500. The current exchange rate is €1.50/£1.00 and in the next period the exchange rate can increase to €2.40/£ or decrease to €0.9375/€1.00 (i.e. u = 1.6 and d = 1/u = 0.625). The current interest rates are i€ = 3% and are i£ = 4%. Choose the answer closest to yours. €3,373 €3,275 €3,243 €2,500
In the Binomial Option Pricing Model, compare the price of an American Put and a European...
In the Binomial Option Pricing Model, compare the price of an American Put and a European put price using the same 5 step tree with 3 months to maturity and a sigma of 23%. Let the starting futures price be 72, the strike be 75 and let r = 5%.
Use the binomial option pricing model to find the implied premium of a CALL option on...
Use the binomial option pricing model to find the implied premium of a CALL option on Wendy’s. Wendy’s stock is currently trading at $20.66. Have the model price at 10 day intervals for 3 nodes: 10 days, 20 days, and 30 days. The strike price is $18. The risk free rate is 2.5% and the volatility(standard deviation) of the stock is .40. Show the entire binomial tree.
Use the binomial options pricing model to find the price of a call option with a...
Use the binomial options pricing model to find the price of a call option with a strike price of $40 and one year to expiration. The current stock price is $40 and has equal probabilities for a price of $70 or $30 at expiration in one year. The one year continuous risk-free interest rate is 6%. A.) What is the hedge ratio for the call option? B.) What is the price of the call option?
Please discuss the Black & Scholes model and the binomial model approach to option pricing. What...
Please discuss the Black & Scholes model and the binomial model approach to option pricing. What are the advantages and disadvantages of these two approaches? Determine the price of a call and put option assuming that the exercise price is $105, the value of the stock is $101, risk-free rate is 2.05%, standard deviation of returns on the stock is 28%, and the option has 6 months remaining to maturity. What is the price sensitivity of the call and put...
Use the Black-Scholes option pricing model to price a one-year at the money call option on...
Use the Black-Scholes option pricing model to price a one-year at the money call option on a stock that is trading at $50 per share, Rf is 5%, annual volatility is 25%. REMEMBER TO USE THE NORMAL PROBABILITY DOCUMENT posted on moodle. You are not allowed to use Excel, you can only use your financial calculator. Show all your work, including intermediate steps. Simply writing the final answer will not get credit, even if the answer is correct. a) What...
Discuss differences between the binomial option pricing model and the risk-neutral method of option pricing.
Discuss differences between the binomial option pricing model and the risk-neutral method of option pricing.
discuss the differences between the binomial option pricing model and the risk-neutral method of option pricing.
discuss the differences between the binomial option pricing model and the risk-neutral method of option pricing.
What is the objective of a hedge portfolio in the Binomial Option Pricing Model?
What is the objective of a hedge portfolio in the Binomial Option Pricing Model?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT