The current stock price of Alcoa is $115, and the stock does not pay dividends. The...

The current stock price of Alcoa is $115, and the stock does not pay dividends. The instantaneous risk-free rate of return is 6%. The instantaneous standard deviation of Alcoa's stock is 35%. You want to purchase a put option on this stock with an exercise price of $120 and an expiration date 30 days from now. According to the Black-Scholes OPM, you should hold __________ shares of stock per 100 put options to hedge your risk.

Solutions

Expert Solution

Input Data
Stock Price now (P)		115
Exercise Price of Option (EX)		120
Number of periods to Exercise in years (t)		0.082191781
Compounded Risk-Free Interest Rate (rf)		6.00%
Standard Deviation (annualized s)		35.00%


Output Data
Present Value of Exercise Price (PV(EX))		119.4097
s*t^.5		0.1003
d1		-0.3248
d2		-0.4252
Delta N(d1) Normal Cumulative Density Function		0.3727
Bank Loan N(d2)*PV(EX)		40.0448

Shares to hold= [Number of option-(N(d1)X100)]

=100-0.3727*100 = 62.73

Therore shares to hold =63

jeff jeffy answered 1 year ago

Next > < Previous

Related Solutions

The current stock price of Johnson & Johnson is $178, and the stock does not pay dividends. The instantaneous risk-

The current stock price of Johnson & Johnson is $178, and the stock does not pay dividends. The instantaneous risk-free rate of return is 6%. The instantaneous standard deviation of J&J's stock is 30%. You want to purchase a put option on this stock with an exercise price of $171 and an expiration date 60 days from now. Assume 365 days in a year. With this information, you calculate the probability that a random draw from a standard normal distribution...

The current stock price is $65 and it will pay $3 dividends in 1 month and...

The current stock price is $65 and it will pay $3 dividends in 1 month and 4 months. A European at-the-money put option with 5 months to maturity is traded for $6.A European at-the-money call option with 5 months to maturity is $5. The spot rate for 1, 4, 5 months are 13%,11% and9.5%(c.c). 1.Is there an arbitrage opportunity? If yes describe the investment strategy that pays off today and has for sure zero cash flows at any time in...

The current stock price of Johnson & Johnson is $46, and the stock does not pay...

The current stock price of Johnson & Johnson is $46, and the stock does not pay dividends. The instantaneous risk-free rate of return is 6%. The instantaneous standard deviation of J&J's stock is 40%. You want to purchase a put option on this stock with an exercise price of $37 and an expiration date 45 days from now. Using Black-Scholes, the put option should be worth ______ today. .06 .13 9.05 9.41

The current stock price of Johnson & Johnson is $62, and the stock does not pay...

The current stock price of Johnson & Johnson is $62, and the stock does not pay dividends. The instantaneous risk-free rate of return is 3%. The instantaneous standard deviation of J&J's stock is 35%. You want to purchase a put option on this stock with an exercise price of $53 and an expiration date 72 days from now. Using Black-Scholes, the put option should be worth ______ today.

A trader observes that a) A put on stock X which does not pay dividends with strike price

A trader observes that a) A put on stock X which does not pay dividends with strike price$20 and exercisable in one year trades at $3 and b) A call on the same stock with the same strikeprice and also exercisable in one year trades at $25. If the stock trades today at $30/share and therisk-free rate is 10%, design a profitable arbitrage strategy for the trader.

Judgment Case 18–5 Treasury stock; stock split; cash dividends; Alcoa LO18–5 through LO18–8 Alcoa is the...

Judgment Case 18–5 Treasury stock; stock split; cash dividends; Alcoa LO18–5 through LO18–8 Alcoa is the world’s leading producer of primary aluminum, fabricated aluminum, and alumina. The following is a press release from the company: ALCOA ANNOUNCES 33% INCREASE IN BASE DIVIDEND, 2-FOR-I STOCK SPLIT PITTSBURGH—Alcoa today announced that its Board of Directors approved a base quarterly dividend increase of 33.3%. Real World Financials Alcoa’s announcement indicated that the new quarterly dividend would be $0.25 per share. It also stated...

The current price of a stock is $102.00. If dividends are expected to be $10 per...

The current price of a stock is $102.00. If dividends are expected to be $10 per share for the next 5 years, and the required return is 12%, then what should price of the stock be in 5 years when you plan to sell it? If the dividend and required return is expected to increase by $5 five years from now, does the current stock price also increase by $5? Why or why not?

The current price of a stock is ?$68.36. If dividends are expected to be ?$1.00 per...

The current price of a stock is ?$68.36. If dividends are expected to be ?$1.00 per share for the next six ?years, and the required return is 6%, then what should the price of the stock be in 6 years when you plan to sell? it? The price 5 years from now will be ?$____ . ?(Round your response to the nearest? dollar.)

The current price of a stock is $55.68. If dividends are expected to be $0.80 per...

The current price of a stock is $55.68. If dividends are expected to be $0.80 per share for the next five years, and the required return is 6%, then what should the price of the stock be in 5 years when you plan to sell it? If the dividend and required return remain the same, and the stock price is expected to increase by $1 five years from now, does the current stock price also increase by $1? Why or...

The current price of a stock is $65.88. If dividends are expected to be $1 per...

The current price of a stock is $65.88. If dividends are expected to be $1 per share for the next five years, and the required return is 10%, what should the price of the stock be in five years when you plan to sell it? If the dividend and required return remain the same, and the stock price is expected to increase by $1 five years from now, does the current stock price also increase by $1? Why or why...

Subjects