Assignment
1- Put Call Parity: Suppose that WYZ stock is currently valued at $53 and that call and put options on WYZ stock with an exercise price of $50 sell for $6.74 and $2.51, respectively. Assume that both options can only be exercised in exactly six months. Find the implied rate of return (EAR) on a six-month T-bill.
2- Put Call Parity: following the previous problem, assuming that the actual T-bill rate is 6.25% (instead of the one found in problem 1) and ignoring transaction costs, construct a financial arbitrage position (long some portfolio and short some other portfolio) that produces a profit at no risk. Show the initial investment (cash flows) and the cash flows at maturity.
3- Put Call Parity: back to the first problem, assume further that the WYZ stock pays a dividend of $1 just before the expiration of a call and a put option. The theoretical price differential (c - p) should be: ____________
4- Options versus Stocks (Leverage): You strongly believe that the price of Breener Inc. stock will rise substantially from its current level of $137, and you are considering buying shares in the company. You currently have $13,700 to invest. As an alternative to purchasing the stock itself, you are also considering buying call options on Breener stock that expire in three months and have an exercise price of $140. These call options cost $10 each.
a. Compare and contrast the size of the potential payoff and the risk involved in each of these alternatives.
b. Calculate the three-month rate of return on both strategies assuming that at the option expiration date Breener's stock price has (1) increased to $155 or (2) decreased to $135.
c. At what stock price level will the person who sells you the Breener call option break even? Can you determine the maximum loss that the call option seller may suffer, assuming that he does already own Breener stock?
5- Payoffs and No-Arbitrage Pricing: As an option trader, you are constantly looking for opportunities to make an arbitrage transaction (i.e., a trade in which you do not need to commit your own capital or take any risk but can still make a profit). Suppose you observe the following prices for options on DRKC Co. stock: $3.18 for a call with an exercise price of $60, and $3.38 for a put with an exercise price of $60. Both options expire in exactly six months, and the price of a six-month T-bill is $97.00 (for face value of $100).
a. Using the put-call-spot parity condition, demonstrate graphically how you could synthetically recreate the payoff structure of a share of DRKC stock in six months using a combination of puts, calls, and T -bills transacted today.
b. Given the current market prices for the two options and the T -bill, calculate the noarbitrage price of a share of DRKC stock.
c. If the actual market price of DRKC stock is $60, demonstrate the arbitrage transaction you could create to take advantage of the discrepancy. Be specific as to the positions you would need to take in each security and the dollar amount of your profit.
6- Main Option Strategies: You are currently managing a stock portfolio worth $55 million (1 million shares) and you are concerned that, over the next four months, equity values will be flat and may even fall. Consequently, you are considering two different strategies for hedging against possible stock declines: 1) buying a protective put, and 2) selling a covered called (i.e. selling a call option based on the same underlying stock position you hold). An over-the-counter derivatives dealer has expressed interest in your business and has quoted the following bid and offer prices (in millions) for the at-the-money call and put options that expire in four months and match the characteristics of your portfolio:
|
|
Bid
|
Ask
|
|
Call
|
$2.553
|
$2.573
|
|
Put
|
$1.297
|
$1.317
|
a. For each of the following expiration date values for the unhedged equity position, calculate the terminal values (net of initial expense) for the protective put strategy.
35, 40, 45, 50, 55, 60, 65, 70, 75
b. Draw a graph of the protective put net profit structure in Part a) and demonstrate how this position could have been constructed by using call options and T-bills, assuming a risk free rate of 7 percent.
c. For each of these same expiration date stock values, calculate the terminal net profit values for a covered call strategy.
d. Draw a graph of the covered call net profit structure in Part c) and demonstrate how this position could have been constructed by using put options and T-bills, again assuming risk free rate of 7%.