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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Suppose that call options on ExxonMobil stock with time to expiration 6 months and strike price $87 are selling at an implied volatility of 27%. ExxonMobil stock price is $87 per share, and the risk-free rate is 6%. Required: If you believe the true volatility of the stock is 31%, would you want to buy or sell call options? Now you want to hedge your option position against changes in the stock price. How many shares of stock will you hold for each option contract purchased or sold?
Question 1 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 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 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.
Question 1 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 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 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. note: calculation should be provided with mathematical formulars
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