Question

Compute the probability that the S&P 500 index value is greater than 2,400 in 1 year...

Compute the probability that the S&P 500 index value is greater than 2,400 in 1 year according to the Black Scholes model. Assume that the current level of the index is 2,200, the risk-free rate is 2% per annum, the dividend yield on the index is 1% per annum, and the volatility of the index is 20%.

Business   Finance   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

S is the dividend-adjusted stock price = 2200*e^(-0.01*1) = $2178

r is the risk-free rate = 0.02

Volatility = 0.2

Strike K = 2400

d1= ((ln(2178/2400) + (0.02+(0.2*0.2/2))*1)/(0.2*1)

d1= -0.285

d2 = -0.285 - (0.2*1) = -0.485

N(d2) = 0.3138

Probability that the S&P 500 index value is greater than 2,400 in 1 year according to the Black Scholes model is N(d2) = 0.3138

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Compute the probability that the S&P 500 index value is greater than 2,400 in 1 year...
Compute the probability that the S&P 500 index value is greater than 2,400 in 1 year according to the Black Scholes model. Assume that the current level of the index is 2,200, the risk-free rate is 2% per annum, the dividend yield on the index is 1% per annum, and the volatility of the index is 20%.
The S&P 500 index current level is 3,000. The dividend yield on the index is equal...
The S&P 500 index current level is 3,000. The dividend yield on the index is equal to the risk- free rate of interest. Given a volatility of the index of 25%: a) Computetheprobabilitythattheindexvaluein6monthsisgreaterthan3,300. b) Compute the probability that the index value in 6 months is less than 2700. c) Computetheprobabilitythattheindexvaluein6monthsisbetween2700and3300.
The S&P 500 index current level is 3,000. The dividend yield on the index is equal...
The S&P 500 index current level is 3,000. The dividend yield on the index is equal to the risk- free rate of interest. Given a volatility of the index of 25%: a) Computetheprobabilitythattheindexvaluein6monthsisgreaterthan3,300. b) Compute the probability that the index value in 6 months is less than 2700. c) Compute the probability that the index value in 6 months is between 2700 and 3300.
A stock index level is currently 2,000. Its volatility is 25%. The risk-free rate is 4%...
A stock index level is currently 2,000. Its volatility is 25%. The risk-free rate is 4% per annum (continuously compounded) for all maturities and the dividend yield on the index is 2%. Using the Black-Scholes model: a) Derive the value a 6-month European put option with a strike price of 2020. b) Derive the position in the index that is needed today to hedge a long position in the put option. Assume that the option is written on 250 times...
The value of the S&P500 stock index is 1,000. The risk-free interest rate is 3% per...
The value of the S&P500 stock index is 1,000. The risk-free interest rate is 3% per annum with continuous compounding. The dividend yield on the S&P 500 is 1%, and the volatility of the index is 20% per annum. Find the delta on a 6 months put option with strike price 950. Interpret your result.
An investor owns a $250,000 equity portfolio with a beta of 1.25. The S&P 500 index...
An investor owns a $250,000 equity portfolio with a beta of 1.25. The S&P 500 index is currently 2,000, the risk-free interest rate is 4% per annum, and the dividend yield on the index is 2% per annum. (a) If the index increases to 2,200 over the next six months, what is the expected percentage return on the equity portfolio? (b) Futures contracts (for 100 times the index) are currently priced at 2,100. How could the investor hedge the portfolio...
The value of the S&P500 stock index is 1,000. The risk-free interest rate is 3% per...
The value of the S&P500 stock index is 1,000. The risk-free interest rate is 3% per annum with continuous compounding. The dividend yield on the S&P 500 is 1%, and the volatility of the index is 20% per annum. Find the delta on a 6 months put option with strike price 950. Interpret your result. Please write down the formula, the process and the result
The current level of the S&P 500 index is 2,250. The dividend yield on the S&P...
The current level of the S&P 500 index is 2,250. The dividend yield on the S&P 500 is 3%. The risk-free interest rate is 6% with continuous compounding. The futures price quote for a contract on the S&P 500 due to expire 6 months from now should be __________. A) 2,774.30                       B) 2,784.53                  C) 2,768.63                  D) 2,797.47
On January 1, you sell one April S&P 500 Index futures contract at a futures price...
On January 1, you sell one April S&P 500 Index futures contract at a futures price of 2,300. If the April futures price is 2,400 on February 1, your profit would be __________ if you close your position. (The contract multiplier is 250.) A) $12,500                        B)  -$25,000                 C)  $25,000                   D)  -$12,500 The current level of the S&P 500 index is 2,350. The dividend yield on the S&P 500 is 2%. The risk-free interest rate is 5%with continuous compounding. The futures price quote for a contract on...
The 6-month forward price of the S&P 500 Index is 1400 and the volatility of the...
The 6-month forward price of the S&P 500 Index is 1400 and the volatility of the index is 15%. What is the price of a put option that expires in 6 months if the strike price is 1450, risk free rate is 5% (continuous). The dividend yield on the is 3%.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT