A bank has just sold a call option on 500,000 shares of a stock. The strike price is 40; thestock price is 40; the risk-free rate is 5%; the volatility is 30%; and the time to maturity is3 months.a) What position should the company take in the stock for delta neutrality?b) Suppose that the bank does set up a delta neutral position as soon as the option has beensold and the stock price jumps to 42 within the first hour of trading. What trade isnecessary to maintain delta neutrality? Explain whether the bank has gained or lostmoney in this situation. (You do not need to calculate the exact amount gained or lost.)c) Repeat part b) on the assumption that the stock jumps to 38 instead of 42.a) Give an example of how a swap might be used by a portfolio manager.b) Explain the nature of the credit risks to a financial institution in a swap agreement.The quoted futures price corresponds to a forward rate of 8% per annum with quarterlycompounding and actual/360. The parameters for Black's model are therefore: F, = 0.08,K = 0.08, R= 0.075, o, = 0.15, t, = 0.75, and P(0,t)= e0075«1 = 0.9277. Use theseinformation to estimate the call price.a) Discuss the five inputs that are needed for the Black-Scholes estimations and showsits relevance to investors.b) Thecurrent price of Kinston Corporation stock is $10. In each of thenext two years,this stock price can either go up by $3.00 or go down by $2.00. Kinston stock paysno dividends. The one year risk-free interest rate is 5% and will remain constant.Using the binomial pricing model, calculate the price of a two-year call option onKinston stock with a strike price of $9.

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A bank has just sold a call option on 500,000 shares of a stock. The strike price is 40; the stock price is 40; the risk-free rate is 5%; the volatility is 30%; and the time to maturity is 3 mon ths. a) What position should the company take in the stock for delta neutrality? b) Suppose that the bank does set up a delta neutral position as soon as the option has been sold and the stock price jumps to 42 within the first hour of trading. What trade is necessary to maintain delta neutrality? Explain whether the bank has gained or lost money in this situation. (You do not need to calculate the exact amount gained or lost.) c) Repeat part b) on the assumption that the stock jumps to 38 instead of 42.

A bank has just sold a call option on 500,000 shares of a stock. The strike price is 40; the stock price is 40; the risk-free rate is 5%; the volatility is 30%; and the time to maturity is 3 mon ths. a) What position should the company take in the stock for delta neutrality? b) Suppose that the bank does set up a delta neutral position as soon as the option has been sold and the stock price jumps to 42 within the first hour of trading. What trade is necessary to maintain delta neutrality? Explain whether the bank has gained or lost money in this situation. (You do not need to calculate the exact amount gained or lost.) c) Repeat part b) on the assumption that the stock jumps to 38 instead of 42.

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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Q4, all parts
2B) You have $600,000 to invest in the stock market. Suppose you invested one-third of your wealth in stock Q and the rest in stock L. These stocks have the following characteristics: Stock Q has an expected return of 10% and a standard deviation of 7%. Stock L has an expected return of 18% and a standard deviation of 11%. Determine the expected return and standard deviation on a portfolio of stocks Q and L, when the two stocks are uncorrelated and when they are negatively perfectly correlated. Interpret and compare your answers in these two cases.
a) Draw the payoff patterns of i) a long call position ii) a long put position. b) A stock is currently trading at $155. The volatility of the stock price is 20% per annum and the risk-free rate is 8% per annum. What is the Black-Sholes price of a one-year call option with a strike price equal to $160? Assume that the stock will pay no dividends.
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