Homework III

Question 1: Options
Consider the following (incomplete) option price data for U&V Block Inc., recorded at market close on April 5, 1996. The company pays no dividends and all options listed below are European. Assume that the riskless rate is 5% p.a.
                54.75     50   Jul  18   .......   12   4.50
                54.75     55   Jul  72   .......   85   ......
                54.75     60   Jul  52   .......   55   ......
     1. Using a two-period binomial model, show that U&V's stock return
        volatility is about 61%.
     2. Compute all missing option prices in the above table.
     3. Describe the composition of the portfolio that replicates the
        strike 55 call, and show how it evolves across the binomial
        tree. In particular, explain why the hedge ratio increases or
        decreases depending on whether the stock went up or down in
	the first period. 
     4. Repeat part 3 for a put at strike 55. 
     5. Compute the difference between the call and put hedge ratios
	at each stage in the tree (i.e., compute delta for C less
	delta for P without adjusting signs of the latter). It should
	be constant. Explain your answer using put-call parity.
     An Optional Question
     6. A future is a (European-style) contract that simply pays the
        difference between the stock price and an agreed upon strike
	price to its owner at expiry. If the difference is positive,
	the owner receives it; if it is negative, the owner pays the
	difference. Price a strike 55 futures contract using the
	binomial tree set up above. Explain the composition of the
	portfolio that replicates the future at each stage in the
	tree. 
	(Hint: Write out the cashflows from the future at maturity and
	       work backwards, replicating the future using a portfolio
	       of stocks and bonds)

Question 2: The Black-Scholes Model
The following price data are taken from The Wall Street Journal dated April 17, 1996. Assume that the riskless borrowing/lending rate is 5% p.a., that all options are European and that none of the underlying stocks pay dividends.
Bank of New York
	47	50	Jul	108	1.375	....	....
BankAmerica
	74.25	70	Jul	50	6.25	....	....
Netscape
	54.5	55	Jul	96	7.125	....	....

	1. Compute the missing prices. 
	2. Which of the two sectors is more volatile -- high-tech or
	   banking -- on the basis of the prices reported above?
	3. Price July calls and puts at (i) strike 65 for Netscape;
	   (ii) strike 75 for BankAmerica; (iii) strike 55 for Bank of
	   New York. In each case, describe the portfolio that
	   replicates the call or the put. Use the Black-Scholes model
	   for computing the option prices.
	4. Repeat (3), but now using a one period  and  a
	   two-period binomial model. How accurate, in your
	   assessment, are the binomial model prices compared to the
	   Black-Scholes prices?  

You may want to use the option price calculator for solving this problem.
Note Hardcopies of answers to homework 2 are available outside my office (221, 52 HH).