1. You are asked to price options on KYC stock. KYC’s stock price can go up by 15 percent every year, or down by 10 percent. Both outcomes are equally likely. KYC does not pay dividend. The risk free rate is 5% (EAR), and the current stock price of KYC is $100.

1. Price a European put option on KYC with maturity of 2 years and a strike price of 100.
2. Given the price of the put option that you calculated in a), specify the ranges of KYC share price at the option’s maturity date for which you will be making a net profit.
3. What is the price of the Call option at the same strike price?
4. Suppose you expect the price of KYC stock to have little variance in the future. How would you design a strategy (using options) to take advantage of this? Show your strategy explicitly. What are the payoffs of your strategy? What is the range in which you will make profits?

You and a friend, along with an eccentric rich probabilist, are observing a Poisson process whose arrival rate is λ = .5 per hour. The probabilist offers to pay you $100 if there is at least one arrival between noon and 2pm, and also offers to pay your friend $100 if there is at least one arrival between 1pm and 3pm.

a. What is the probability that either you or your friend, or both, gets $100?

b. What is the probability that one of you wins $100, but not both?

Consider a Poisson process with arrival rate λ per minute. Given that there were three arrivals in the first 2 minutes, find the probability that there were k arrivals in the first minute; do this for k = 0, 1, 2, and 3.

Given that P(A) = .4, P(A ∩ B) = .1, and P((A ∪ B) c ) = .2, find P(B).

• Ms. Rand is a 65-year-old woman who spends most of her day sitting on her porch and recovering from a recent surgery involving the removal of suspected cancerous lymph glands in the inguinal area. She is now complaining that her shoes are fitting too tightly, and she has developed poorly healing sores on her legs and ankles. A closer examination also shows distention in her varicose veins. Blood tests reveal a low level of proteins in the plasma.

1. Based on the patient's history and the signs and symptoms, identify the fluid imbalance the patient is experiencing, and state the rationale for your answer.

2. Discuss the four general causes of edema and how they apply in the case of this patient.

3. Discuss the swelling, sores, varicose vein distention, and other effects that edema can have on a patient.

Jane owns​100% of Carnate Corporation’s stock and also runs the company as its CEO. Carnate is a C corporation that expects to earn $420,000 before deducting any salary paid to Jane. Jane wants the corporation to pay her $230,000 for current year in pretax dollars. She is considering three different options: (1) a $230,000 dividend. (2) a $115,000 dividend plus a $115,000 salary, or (3) a $230,000 salary.

Any dividends qualify for the preferential capital gains tax rates. Jane​'s husband has no earnings of his own in the current​ year, so her income is the sole source for the family.Jane and her husband file a joint tax return and claim the $24,000 standard deduction.

​* The corresponding amounts if married filing separately are half of the amounts for filing jointly. The preferential rate is zero for taxable income up to

$ 38 comma 600$38,600

if married filing separately.

Calculate the total tax liability​ (corporate and​ individual) for each of the three​options, and determine which option results in the lowest overall tax.

(a)

Estimates of the marginal cost of a drug are $100 for a 100 pill bottle. If the manufacturer charged $75,000 per bottle, what is the elasticity of demand that they believe they faced?

(b)

The marginal cost is $100 / bottle. Suppose another company comes in to the market to compete with the manufacturer, what is the profit maximizing market price of the drug?

6. Perform a make-buy analysis using the following information.

A) Your plant is at 75% capacity, tooling exists and all engineering has been done.

Lot Quantity 100; quoted price for 100 is $2.00 each

Direct Labor per lot $89.55
Direct Mat’l $34.92 per lot  
Variable OH $5.72 per lot
Fixed OH $90.00 per lot
Engineering $500.00 (sunk cost)
Tooling $34.70 (sunk costs)

Buy or Make?

B) PLANT AT 100% of capacity ; quoted price for 100 is $2.00 each (same information, the plant is just at 100% capacity)
Lot Quantity 100
Direct Labor per part $89.55 per lot
Direct Mat’l $34.92 per lot
Variable OH $5.72 per lot
Fixed OH $90.00 per lot
Engineering $500.00 (sunk costs - already done)
Tooling $34.70 (sunk costs - already done)
Buy or make?

A short call option is sold for 1,460 dollars and covers 100 shares of Johnson Incorporated. If the Strike price of the option is 70, what is the break-even share price?

Three different call options on the same stock with the same expiration date have the following strike prices and option prices:

A. Construct a payoff table and draw a profit diagram for an option strategy where you buy 1 $90 call, buy 1 $110 call, and write 2 $100 calls.
B. Calculate the payoffs and profits assuming the spot price is $98 at expiry.
C. What is/are the breakeven price(s), maximum reward, and maximum risk?
D. Describe in what circumstances it might make sense to invest in this package?

6. Describe the payoff for the following options at expiration of the option(s):

a. an owned call option on 50 units of the underlying asset with a strike price of 50.

b. a written put option on 100 units of the underlying asset with a strike price of 40.

c. a written call option on 100 units of the underlying asset with a strike price of 60.

d. a owned put option on 50 units of the underlying asset with a strike price of 50.

            e. a portfolio of options consisting of each of a through d above.

(You may describe the payoffs on these using tables or diagrams. I have a slight preference for diagrams because of the next question.)

For a stock index, S = $100. sigma = 30%, r = 5%, Div = 3%, and T= 3. Let n = 3. Do not use the black scholes model but a binomial model. a. What is the price of a European call option with a strike of $95? b. What is the price of a European put option with a strike of $95? c. Now let S = $95, K = $100, sigma = 30%, r= 3%, and Div = 5%. (You have exchanged values for the stock price and strike price and for the interest rate and dividend yield.) Value both options again. What do you notice? Demonstrate analytically that this is not a coincidence?