A. What is the price of a call option with a strike of $80 and a maturity of 2.5 years? Theunderlying asset is currently trading at $75. The risk-free rate is 6% and the volatility of theunderlying asset is 64%B. What is the price of a put option with an identical strike price?C. Calculate the delta, theta, and vega of the call option. Express theta per month and vergaper 1% increase in volatility.D. After 5 months the price has gone up by $10 and the volatility by 10%. Using delta, theta, andvega that you have calculated, what is the total change in value of the option?

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Answered: A. What is the price of a call option…

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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A non-dividend paying asset is current priced at $25 and the risk-free interest rate is 8% per annum. Today, you enter into a six-month futures contract to buy a unit of this asset. Three months from now the underlying price has fallen to $20 (but note that the interest rate has not moved). Which of the answers below is closest to the fall in the futures price? Use discrete discounting. a. $4.50 b. $6.50 c. $7.50 d. $5.50
Calculate the Modified Duration of the following securities: 10 % semi-annual coupon maturating in 5 years trading at a yield of 8 % 6 % annual coupon maturating in 9 years trading at a yield of 8 % Also, please explain what is convexity as it applies to one of the above securities
Calculate the implied volatility on a security given the following information: a call option on the security has a premium of 3.5p, the security itself is trading at 50p, the call has an exercise price of 51p and has 120 days to maturity, and the riskless interest rate is 12 per cent. Calculate the implied volatility on a security given the following information: a call option on the security has a premium of 3.5p, the security itself is trading at 50p, the call has an exercise price of 51p and has 120 days to maturity, and the riskless interest rate is 12 per cent.
5. Suppose the one-year futures price on a stock-index portfolio is 1218, the stock index currently is 1200, the one-year risk-free interest rate is 3%, and the ybar-end dividend that will be paid on a $1,200 investment in the index portfolio is $15. a. By how much is the contract mispriced? b. Formulate a zero-net-investment arbitrage portfolio and show that you can lock in riskless profits equal to the futures mispricing. Assume a zero bid-ask spread in security and futures transactions. Now assume that if you short sell the stocks in the index portfolio, the proceeds are kept with the broker, and you do not receive any interest income of the funds. Is there still an arbitrage opportunity (assuming that you don't already own the shares in the index)? d. Given the short sale rules, what is the no-arbitrage band for the stock-futures price relationship? Specifically, how high and how low can the futures price be without giving rise to arbitrage opportunities. C.
What is a fair price of a 26-year semi-annual coupon bond, with a coupon rate of 6.88%, a face value of $1000, and a yield-to-maturity of 7.7%? (Answer to nearest $0.01)
6.Assume we have the following information: Spot price : 1146.00 Actual futures price : 1192.50 Theoretical futures price : 1160.00 Maturity : 3 months a. Is the futures fairly priced? Suppose an arbitrageur wish to take advantage of this opportunity. He has RM10,000,000.00 which he can fund at the current risk-free rate of 5%. b. What should he do? c. How many contracts should be shorted or bought? d. Assume that the arbitrageur maintains this position until contract expiry at which time futures and cash prices have converged to 1165. How much profit would he makes?
You have been provided with the following options. a. A 10-year, R1000 face value, 10 percent coupon bond with semiannual interest payments. b. A 10-year, R1000 face value, 10 percent coupon bond with annual interest payments. C.A 10-year, R1000 face value, zero coupon bond. d. A 10-year R100 annuity. ) Determine which one poses the highest price risk
6(b) Suppose that a futures price is currently £30. The risk-free interest rate is 5% per annumcontinuously compounded. A three-month American call futures option with a strike priceof £28 is worth £4. Calculate bounds for the price of a three-month American put futuresoption with a strike price of £28.
A portfolio of derivatives on an asset is worth $10,000, the asset price is $ 250 and the risk - free interest rate is 4%. The theta and gamma of the portfolio is zero. What is the delta?
a) Assume the yield to maturity on a 10 year Australian government bond is 2% and the market risk premium is 5%. what is the expected rate of return on a share with market average systematic risk? provide workings and explain beta value used it is b) explain what happens to the risk of a portfolio as the number of assets in the portfolio is increased?
5

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A. What is the price of a call option with a strike of $80 and a maturity of 2.5 years? The underlying asset is currently trading at $75. The risk-free rate is 6% and the volatility of the underlying asset is 64%