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Unformatted text preview: 12-1CHAPTER 12: OPTIONS ON FUTURESEND-OF-CHAPTER QUESTIONS AND PROBLEMS1.The options life is January 31 to March 18, soT = 46/365 = .1260a.Intrinsic Value= Max(0, f - E)= Max(0, 483.10 - 480)= 3.10b.Time Value= Call Price - Intrinsic Value= 6.95 - 3.10= 3.85c.Lower bound= Max[0, (f - E)(1 + r)-T]= Max[0, (483.10 - 480)(1.0284)-.1260]= 3.09d.Intrinsic Value= Max(0, E - f)= Max(0, 480 - 483.10)= 0e.Time Value= Put Price - Intrinsic Value= 5.25 - 0= 5.25f.Lower bound= Max[0, (E - f)(1 + r)-T]= Max[(0, (480 - 483.10)(1.0284)-.1260]= 0(Note: the lower bound applies only to European puts.)g.C= P + (f - E)(1 + r)-T= 5.25 + (483.10 - 480)(1.0284)-.1260= 8.34The actual call price is 6.95, so put-call parity does not hold.2.(f - E)(1 + r)-T= (102 - 100)(1.10)-.25= 1.95C - P = 4 - 1.75 = 2.25C - P is too high so the call is overpriced and/or the put is underpriced (or we could assume the futures isunderpriced). So sell the call, buy the put, and buy the futures. At expiration the payoffs will befTEfT> E Short call-(fT- E)Long putE - fTLong futuresfT- ffT- fE - fE - fThis is equivalent to a risk-free loan, as a lender if E > f or as a borrower if f > E. Here f > E so you are aborrower. The present value should be (E - f)((1 + r)-T= (102 - 100)(1.10)-.25= -1.95. Thus you sell thecall for 4 and buy the put for -1.75 for a net inflow of 2.25. At expiration, you pay back 2.00.3.In Chapters 3 and 4 we covered American call options on the spot and explained that in the absence of12-2dividends they will not be exercised early. They will always sell for at least the lower bound, which ishigher than the intrinsic value, and usually more. However, call options on the futures may be exercisedearly. If the price of the underlying instrument is extremely high, the call will begin to behave like theunderlying instrument. For an option on a futures, this means that the call will behave like the futures,changing almost dollar-for-dollar with the futures price. For an option on the spot, the call will behavelike the spot, changing almost one-for-one with the price of the spot. Exercise of the futures call willrelease funds tied up in the call and provide a position in the futures. Exercise of the call on the spot doesnot, however, release funds, since the investor has to purchase the spot instrument.4.First find the continuously compounded risk-free rate: rc= ln(1.0284) = .0280. Then price the option:The option appears to be underpriced. You could sell -r T1ceN(d ) = 0.5927futures and buy one call,adjusting the hedge ratio through time and earn an arbitrage profit....
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- Fall '08