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3-1 CHAPTER 3: PRINCIPLES OF OPTION PRICING END-OF-CHAPTER QUESTIONS AND PROBLEMS 1. The average of the bid and ask discounts is 8.22. Discount = 8.22(68/360) = 1.5527 Price = 100 - 1.5527 = 98.4473 Yield = (100/98.4473) (365/68) - 1 = .0876 Note that even though the T-bill matured in 67 days, we must use 68 days since that is the option's time to expiration. 2. This would create an arbitrage opportunity. The call would be purchased and immediately exercised. For example, suppose S = 44, E = 40, and the call price is $3. Then an investor would buy the call and immediately exercise it. This would cost $3 for the call and $40 for the stock. Then the stock would be immediately sold for $44, netting a risk-free profit of $1. In other words, the investor could obtain a $44 stock for $43. Since everyone would do this, it would drive the price of the call up to at least $4. If the call were European, however, immediate exercise would not be possible (unless, of course, it was the expiration day), so the European call could technically sell for less than the intrinsic value of the American call. We saw, though, that the European call has a lower bound of the stock price minus the present value of the exercise price (assuming no dividends). Since this is greater than the intrinsic value, the European call would sell for more than the intrinsic value. Then at expiration, it would sell for the intrinsic value. 3. European call: We know that its price cannot exceed S but must exceed Max(0, S-E(1+r) -T ). With an infinite time to expiration, the present value of E is zero so the lower bound is S and, since the upper bound is S, the call price must be S. American call: We know that its price cannot exceed S but it must be at least as valuable as a European call. Thus its value must also be S. Note that if exercised early it would be worth only S-E so it will never be exercised early. 4. Ordinarily the option with the longer time to expiration would sell for more. If both options were deep out-of- the-money, however, they could both sell for essentially nothing. The market would be expecting that both the shorter- and longer-lived options will expire out-of-the-money. 5. If both options were deep out-of-the-money, they might have prices of zero. As in the previous question, the two options are expected to expire out-of-the-money. 6. The call is underpriced, so buy the call, sell short the stock, and buy risk-free bonds with face value of E. The cash received from the stock is greater than the cost of the call and bonds. Thus, there is a positive cash flow up front. The payoffs from the portfolio at expiration are as follows: If S T < E, -S T (from the stock) E (from the bonds) the total, E - S T , is positive If S T E, S T - E (from the call)
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3-2 - S T (from the stock) E (from the bonds) the total is zero.
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This note was uploaded on 03/09/2011 for the course FINA 4210 taught by Professor Staff during the Fall '08 term at North Texas.

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