Exam 13: Market-Making and Delta-Hedging

Assume S = $33.00,σ = 0.32,r = 0.06,div = 0.01,on a $35 strike call.Given delta = 0.3854 and gamma = 0.0847,what is the delta-gamma approximation for the call price on a $0.50 stock price increase? Assume 68 days until expiration.

What is the total dollar cost to create a delta hedge position against a 200 short call position? Assume calls are priced at $4.16,the delta is 0.7644,and stock price is $73.00.

What are the two methods by which insurance companies hedge their risk of extreme losses?

Assume S = $56.00,σ = 0.45,r = 0.05,div = 0.0,on a $55 strike call and 45 days until expiration.Given delta = 0.6253,gamma = 0.0735,and theta = -0.0253,what is the approximate change in call price over 1 day,all else being the same?

Assume S = $62.50,σ = 0.20,r = 0.03,div = 0.0,on a $60 strike call and 81 days until expiration.Given a delta = 0.7092,gamma = 0.0582,and theta = -0.0158,what is the PREDICTED call price,using the delta,gamma,theta approach,after 1 day,assuming a $0.50 rise in the stock price?

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 pays a 1.0% continuous dividend,r = 0.05,σ = 0.28,and the stock price is $62.00.What is the profit or loss per share if on a long call position,with 73 days until expiration,the price immediately rises to $63.00?

What actions are required to both delta-hedge and gamma-hedge a written option position?

Discuss the three methods used to reduce the risk of extreme price moves.Ask the class to also elaborate on why simple delta hedging is inadequate to the task.

Assume S = $33.00,σ = 0.32,r = 0.06,div = 0.01.You short 100 $35 strike calls at 68 days until expiration.Under a delta hedge position,what is your overnight profit/loss if the stock rises to $34.50?

Which of the following is NOT a source of cash while maintaining a delta neutral hedge?

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

The equation used by Black and Scholes to characterize the behavior of an option,expressed with Greeks,holds true for American options as well as European options with one exception.What is the exception?

Describe the true relationship between option prices and delta.Use calls as an example.

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.

Since delta of an option changes over the same time period that a stock price is changing,what is the delta used to calculate the approximate change in the option price?

Assume that a $50 strike call 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 call position if the option expires in 60 days and the price rises to $50.00 after 5 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 = $45,σ = 0.25,r = 0.05,div = 0.0,on a 45 strike call and 55 days until expiration.Given delta = 0.5502 and gamma = 0.0876,what is the delta-gamma approximation for the call price on a $0.90 stock price decline?