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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Transcribed Image Text: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.
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 quarterly
compounding 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 these
information to estimate the call price.
a) Discuss the five inputs that are needed for the Black-Scholes estimations and shows
its 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 pays
no 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 on
Kinston stock with a strike price of $9.
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