Calculate the volatility and the current price of oil futures implied by the call 1600 August and the call 1700 August of Figure 19.8 by using the Black-Scholes formula with \(T=.25\).

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OIL CRUDE OIL (NYM) 1,000 BBLS.; $ PER BBL. Strike Calls-Settle Puts-Settle Price Jun Jly Aug Jun Jly Aug 0.04 0.21 0.42 Jun July na 0.10 0.36 0.59 Aug na 0.60 0.82 Sept na Dec Jun Dec 1600 1.33 1.21 1.29 1650 0.86 0.86 0.97 1700 0.51 0.58 0.70 0.22 1750 0.25 0.40 0.50 0.46 0.90 1800 0.11 0.25 0.34 0.82 1.25 1850 0.04 0.16 0.24 Est vol 3,794 Wed 18,173 calls 8,785 puts Op int Wed 211,586 calls 170,881 puts FIGURE 19.8 Quotes of oil future options and oil futures. Volatility can be estimated option prices. Risk-neutral probabilities can be determined directly from futures market prices. METALS AND PETROLEUM Lifetime Open High Low Settle Chg High Low CRUDE OIL, Light Sweet (NYM) 1,000 bbls.; $ per bbl. 16.84 17.30 16.78 17.29.43 21.35 14.02 17.02 16.60 17.00 +.35 20.78 14.15 Open Interest 124,032 73,360 16.90 16.56 16.88 +.30 20.78 14.35 34,123 16.81 16.57 16.83 +27 20.78 14.50 28,809 16.57 16.80 16.55 16.80 +23 21.25 14.93 16.90 16.87 16.87 16.96 +.18 21.21 15.73 17.18.16 20.80 16.50 28,690 17,396 10,793 Jan 17.40 17.58 17.40 17.43 + .14 20.26 17.22 14,698 Dec ...... 17.73.13 20.40 17.53 19,072