Exam 11: The Black-Scholes Formula

Given the following data, what is the approximate implied volatility? Assume S = $38.50, K = $40, r = .06, Call price = $1.60 the stock pays no dividend and the option expires in 45 days.

Assume that a $50 strike put pays a 2.0% continuous dividend, r = 0.07, σ = 0.25, and the stock price is $48.00. What is the profit or loss, per share, for a short put position if the option expires in 60 days and the price rises to $50.00 after 5 days?

Assume S = $33.00, σ = 0.32, r = 0.06, div = 0.01. You short 100 $35 strike puts at 68 days until expiration. Under a delta hedge position, what is your overnight profit/loss if the stock rises to $34.50? Assume no cost to short stock.

Which Greek is also called the time decay?

What is net dollar gain or cost required to create a short put delta hedge against a 100 short put position? Assume puts are priced at $1.98, the delta is 0.489, the stock price is $34.50, and no cost to short stock.

Assume that a $60 strike call has a 2.0% continuous dividend, r = 0.05, and the stock price is $61.00. What is the theta of the option as the expiration time declines from 60 to 50 days?

What is the difference between a standard bull spread and a calendar bull spread?

Assume that a $55 strike call has a 1.5% continuous dividend, r = 0.05 and the stock price is $50.00. If the option has 45 days until expiration, what is the vega given a shift in volatility from 33.0% to 34.0%?

What is the price of a $25 strike call? Assume S = $23.50, σ = 0.24, r = 0.055, the stock pays a 2.5% continuous dividend and the option expires in 45 days?

Suppose a $60 strike call has 45 days until expiration and pays a 1.5% continuous dividend. Assume S = $58.50, σ = 0.25, and r = 0.06. What is the option elasticity given an immediate price increase of $1.50?

Given the following data, what is the approximate implied volatility? Assume S = $41, K = $40, r = .08, Call price = $2.70 the stock pays no dividend and the option expires in 90 days.

Assume that a $75 strike call has a 1.0% continuous dividend, 90 days until expiration and stock price of $72.00. What is the rho of the option as the interest rate changes from 6.0% to 5.0%?

Suppose the 120-day futures price on gold is $115.00 per ounce and the volatility is 20.0%. Assume interest rates are 3.5%. What is the price of a $110 strike call futures option that expires in 120 days?

What is the delta on a $25 strike put? Assume S = $24.00, σ = 0.35, r = 0.06, the stock pays a 2.0% continuous dividend and the option expires in 40 days?

Which Greek is also called time decay and why?

Suppose the spot exchange rate is $1.22 per British pound and the strike on a dollar denominated pound put is $1.20. Assume r = 0.04, r_f = 0.05, σ = 0.20 and the option expires in 270 days. What is the put option price?

Assume that an investor is currently holding a reverse straddle position (i.e. a short put and short call), which is currently a profitable investment. All else being equal, what would this investor like to happen to vega?

As the date of expiration approaches, what change in theta might counteract or slowdown the drop in the option price?

What prevents a market-maker from readjusting her delta hedge on a continual basis?

What is the price of a $30 strike put? Assume S = $28.50, σ = 0.32, r = 0.04, the stock pays a 1.0% continuous dividend and the option expires in 110 days?