Practice Final
Short and Medium Questions (5 short questions, 2 medium questions: 50 minutes) Each short multiple-choice question is worth 1 point
1. You own a long forward position with Ft,T = 100. At settlement, the price of the underlying asset is 50. What is your payoff at settlement? (For a question similar to this, you will have a box on Canvas you type the answer into)
2. You sell a European put option with strike $240. On the expiration date the price of the underlying stock is $220. What is your cash flow at expiration? (You will have to input the answer into a box into Canvas)
3. You short a European call option with strike K1 and buy a European call option with strike K2 > K1 on the same underlying asset with the same expiration at T. If ST < K1, do you make an overall profit?
(a) Yes, you make a profit
(b) No, you make a loss
(c) There is not enough information to answer this question
4. How can you create a synthetic long position in a stock so that you pay St today and get a payoff of ST at time T? Assume markets do not allow any arbitrage.
(a) Buy forward on stock and lend St at continuously compounded interest rate r
(b) Short forward on stock and lend St at continuously compounded interest rate r
(c) Buy a call on the stock with strike K which expires at T, short a put on the stock with strike K which expires at T, and borrow e-r(T-t)K.
(d) Short a call on the stock with strike K which expires at T, buy a put on the stock with strike K which expires at T, and borrow e-r(T-t)K.
5. Company A makes payments to its bank every six months of LIBOR + .5%. It enters a swap with Company B spanning the lifetime of its loan. According to the swap, Company B will pay Company A a floating rate of LIBOR + .2% and Company A will pay Company B a fixed rate of 5% every six months on the same day as Company A’s payments are due on its loan to the bank. In total, does Company A have a fixed or a floating liability?
(a) Fixed Liability
(b) Floating Liability
Medium Questions
Each medium question is worth 2 points
1. You buy a European put with maturity at T with strike K = $200. You also buy the underlying asset. ST is the price of the underlying asset at maturity. What is the cash flow of your portfolio at time T (not accounting for any costs of purchasing the portfolio) if a) ST = 180, and if b) ST = 210? (You will have two boxes in Canvas you have to input the final solution into).
2. A company expects to buy 10,000 barrels of oil to sell in 6 months. How can the company use forward contracts to create a perfect hedge if each forward contract is written on 1,000 oil barrels and matures in 6 months? Assume the forward price for each barrel of oil today for delivery in 6 months is $82, the spot price of a barrel of oil today is $79 dollars and the spot price of a barrel of oil in 6 months is $86 dollars. What net price does the company pay for each barrel of oil in 6 months (account for both the purchase and the forward position)? (You will have to fill in multiple blanks.)
The company can [] [long/short] [] [enter the number] forward contracts. They pay a net price of [] [enter the number] for each barrel of oil in 6 months.
Long Questions (50 minutes)
Each long question is worth 4 points
1. A stock is selling for $100. Each year it will either increase or decrease in value by 20% (u = 1.2, d = 0.8). The continuously compounded riskless rate is such that er = 1.10. In the binomial pricing, one period corresponds to one year.
An exotic put option on this stock matures in two years (T=2 years). The option can only be exercised at maturity. Upon maturity, the strike price of the option is calculated as the maximum price of the stock over the lifetime of the option which starts at t = 0 and ends at t = 2 (Smax). The payoff is therefore max{Smax - ST , 0}.
Below is a binomial tree showing the evolution of the stock price.
Calculate the option payoffs at all nodes at t = 2, i.e. calculate fuu , fud , fdu and fdd? [You will have to input 4 numerical values in Canvas]
2. The current price of a share of Apple is $160. Consider a European put and a European call on a share of Apple sharing the common strike price of $150 and the common maturity of 8 months. The price of the put is $25 and the price of the call is $45. The present value of the strike price $150 today is $145. Are there any arbitrage opportunities (you will have to input yes/no)? If there is an arbitrage opportunity, please construct a portfolio such that you have a strictly positive cash flow today and a cash flow of 0 in 8 months (You will have to input long/short/NA for the call, put and stock and input borrow/lend/NA for the PV(K)). What is your cash inflow today (You will have to input a number)?