Spot Price: $66 Strike price $68 RFR 6% Binomial trees: Additionally, assume that over each of the next two four-month periods, the share price is expected to go up by 11% or down by 10%

a. Use a two-step binomial tree to calculate the value of an eight-month European call option using the no-arbitrage approach. [2.5 marks]

b. Use a two-step binomial tree to calculate the value of an eight-month European put option using the no-arbitrage approach. [2.5 marks]

c. Show whether the put-call-parity holds for the European call and the European put prices you calculated in a. and b. [1 mark]

d. Use a two-step binomial tree to calculate the value of an eight-month European call option using risk-neutral valuation. [1 mark]

e. Use a two-step binomial tree to calculate the value of an eight-month European put option using risk-neutral valuation. [1 mark]

f. Verify whether the no-arbitrage approach and the risk-neutral valuation lead to the same results. [1 mark]

g. Use a two-step binomial tree to calculate the value of an eight-month American put option. [1 mark]

h. Calculate the deltas of the European put and the European call at the different nodes of the binomial three. [1 mark]

Note: When you use no-arbitrage arguments, you need to show in detail how to set up the riskless portfolios at the different nodes of the binomial tree.

Today, a Company’s Price to Earnings ratio (P/E Ratio) is 10.0x. P/E = Price per Share / Earnings per Share. Tomorrow, if new information comes out and becomes public that the product sales will triple, what do you think could be the P/E ratio tomorrow?

You have determined that your firm’s own-price elasticity is -1.5 and that your firm’s cross-price elasticity with a competitor is 0.5. Last month your competitor increased prices by one percent. Today, in response, your manager has proposed also increasing prices by one percent. Your manager’s reasoning that by matching the competitor’s price increase, your firm will increase revenue. Would you support or refute your manager’s argument?

The table below provides information regarding price elasticities, income elasticities and cross-price elasticities of demand.

Answer the following questions by using the information from this table.

a. Which commodities are normal and which are inferior?

b. Which commodities are complements and which are substitutes?

c. Which commodities have elastic and which have inelastic demands?

d. What will happen to the total revenue of bread if its price increases? Why?

e. What will happen to the quantity demanded of coffee if the price of milk increases by 1%?

Suppose that stock price moves up by 5% (u=1.05) and d=1/u. The current stock price is $50. Dividend is zero. Compute the current value of a European call option with the strike price of $51 in 3 months using both replicating portfolio valuation method and the risk neutral valuation method. The risk free rate is APR 5% with continuous compounding (or, 5% per annum)

1. Draw the dynamics of stock price and option price using the one step binomial tree.

2. Draw the dynamics of the replicating portfolio valuation using the one step binomial tree.

3. Present value of debt (B),value of option delta(∆) and risk neutral probability (p).

4. Solve for the option price using replicating portfolio valuation approach and risk-neutral valuation approach, respectively

Determine the linear correlation coefficient between square footage and asking price.

Square Footage, x Selling Price ($000s), y

2209 380.7

3323 396

1105 186.3

1953 334.5

3225 639.7

2741 365.7

3987 608

2147 367

2536 413.6

1632 286.2

1749 265.3

3882   700.2

r= ?

Consider the following information for a non-dividend-paying stock:

Current stock price = 46.20

a) Calculate the maximum profit of a covered call strategy using nearest out-of-the-money options.

b) Calculate the maximum loss of a collar strategy using nearest out-of-the-money options.

c) Calculate the value of a butterfly spread that peaks at LaTeX: S_T=45.00S T = 45.00.

d) Estimate the maximum value of a strategy that pays $1 if the future stock price is between $42.50 and $45.00.

Describe the difference between price-setters and price-takers, giving examples of each. Explain why your examples are price-setters or price-takers.

The following information is for an Apple option (Expires 1/15/2021):

Strike Price: 320.00

Last Price: 187.60

Bid: 183.40

Ask: 185.25

Suppose you buy this option. What is the price that you pay? If the stock price on Jan 15th, 2021 is $325, will you exercise your call? What is the profit on your position?

If the stock price on Jan 15th, 2021 is $315, will you exercise your call? What is your payoff on your position?

XYZ stock price and dividend history are as follows:

An investor buys six shares of XYZ at the beginning of 2015, buys another two shares at the beginning of 2016, sells one share at the beginning of 2017, and sells all seven remaining shares at the beginning of 2018.

a. What are the arithmetic and geometric average time-weighted rates of return for the investor? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

b-1. Prepare a chart of cash flows for the four dates corresponding to the turns of the year for January 1, 2015, to January 1, 2018. (Negative amounts should be indicated by a minus sign.)

b-2. What is the dollar-weighted rate of return? (Hint: If your calculator cannot calculate internal rate of return, you will have to use a spreadsheet or trial and error.)