Assume the current spot price of a Bitcoin is $11,270 and the future price on a March 2018 contract is $11,420 per Bitcoin. You enter into 3 long future contracts today (1/29/18), and each contract is for 5 Bitcoins. Your initial margin is $5,000 per contract and your margin call occurs at $3,500 per contract.

Date Price

1/29/18   11,310

1/30/18   11,460

1/31/18   11,600

2/1/18 11,410

2/2/18   11,150

2/5/18   10,900

2/6/18   10,990

2/7/18   10,790

What does your margin account have in it at the end of each day? What does your counterparty’s margin account have in it at the end of each day? The risk-free rate is 2.60% per annum with daily compounding (assume 260 day year). If there is a margin call, note that there is a margin call and record that you deposit the necessary money into the account as a separate transaction instantaneously, i.e. if on 2/2 you needed to put in $1,500 at the end of the day you should show a deposit of $1,500 on 2/2 after the close of the day.

The price of a vacation home is currently $345,866. If the price of vacation homes is increasing at a rate of 3.25% per year, how much would a vacation home cost in 6 years?

what is the price of a European put if the price of the underlying common stock is $20, the exercise price is $20, the risk free rate is 8%, the variance of the price of the underlying stock is 0.36 and the option expires six months from now? use both
a) a two steps binomial tree
b) the black scholes pricing formula

(a) The price elasticity of demand for smoke grinders in response to changes in the price of purpletts is -2. What formula and concept will we use to study the change in quantity demanded of smoke grinders to a change in price of purpletts? What the -2 elasticity of demand tells us about the goods purpletts and smoke grinders? (b) Given the table below, answer the following question. The quantity demanded of which good decreases the most during a recession (when incomes decrease)?

Given the table below ( income elasticity of demand), answer the following question.

Total brand cereal = 0.3, eclipse galsses = -1.5, office chairs = 0, theater tickets = 4, heart shaped pillows = 2

The quantity demanded of which good decreases the most during a recession (when incomes decrease)?

The current price of a stock is $50. In 1 year, the price will be either $65 or $35. The annual risk-free rate is 10%. Find the price of a call option on the stock that has an exercise price of $55 and that expires in 1 year. (Hint: Use daily compounding.)

Income is $3,000, the price of x is $10, and the price of y is $30

1. Using the LaGrangean method, find the utility-maximizing quantities of x and y. (Note:  on this part of the problem only, you MUST write out the Lagrange equation, show all derivatives, and show all other work to receive full credit.)  (20)
2. Suppose that the price of x rises to $20.  Find the substitution and income effects of the change in the price of x.  .

• Be sure to end your answer with something like, “the substitution effect causes you to buy 10 more x and 10 less y, the income effect causes you…. etc.)

3. Carefully graph the results of this problem, being sure to label everything and to show the income and substitution effects on the graph.  (35)
4. Using the income, prices, and the utility that you found in part a. of this problem, graph the ordinary and compensated demand curves for x.  (You found these formulas in the first problem.)

• Be sure to label each axis and all appropriate points on both curves (that is, you should have a point labeled on each curve when the price of x is $10 and when it is $20).  (20)

5. For each of the following, choose “income only”, “substitution only”, or “income and substitution effects.”  (5 each)

1. The ORDINARY demand curves show which effect(s) of a change in price on purchases of X?

___________________________________

2. The COMPENSATED demand curve shows effect(s) of a change in price on purchases of X?

___________________________________

6. For each of the following, choose “ordinary only”, “compensated only”, or “both ordinary and compensated.”  (5 each)

1. A change in utility will shift which demand curve(s)?

___________________________________

2. A change in income will shift which demand curve(s)?

___________________________________

Changes in variables other than the price of a good, such as income or the price of another good lead to a change in demand. This corresponds to a shift of the entire demand curve. Critically analyze the law of demand and identify factors that cause demand to shift to the above situation (through diagram)

The price of a stock is $40. The price of a 1-year European put on the stock with a strike price of $30 is quoted as $7 and the price of a 1-year European call option on the stock with a strike price of $50 is quoted as $5.

(a) Suppose that an investor buys the stock, shorts the call option, and buys the put option. Calculate the profit function and draw a diagram illustrating how the investor's profit or loss varies with the stock price at expiration. Is the graph similar to any of the strategies covered in class? Identify the prices at which you break even with this strategy. What is the most you can win and the most you can lose?

(b) Calculate also the profit function and the profit/loss diagram assuming the investor buys the stock, shorts 2 call options and buys 2 put options.

The current price of a stock is $48. In 1 year, the price will be either $55 or $31. The annual risk-free rate is 6.6%. Find the price of a call option on the stock that has a strike price of $50 and that expires in 1 year. ( Use daily compounding.)     

                   
                     Inputs                      
P0   = ?    u   = ?
X = ?    d   = ?
                      
Cu   = ? Pu   = ?
Cd   = ? Pd   = ?

1. In 1975 the price of a new house was $50,000.

In 2015 the price of a new house is $300,000.

How much has the price of housing increased over the entire 40 years in percentage terms?