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BSOP-with-Boeing-and-FAS-data

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BSOP-with-Boeing-and-FAS-data

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									A1 B1 C1 D1 2 The Black-Scholes Option Pricing Model 3 4 INPUT VARIABLES 5 Stock Price S0 $ 53.18 6 at Valuation Date t0 1/1/1997 7 Exercise Price X $ 53.18 8 Expiration Date tT 1/1/2006 9 Time to expiration (in years) T 9.00 =(+tT-t0)/365.25 10 Annualized volatility sigma 19.000% 11 Risk-free rate of interest k 6.60% 12 Dividend yield q 1.10% 13 COMPUTATIONS 14 d1 1.1534 =(LN(S0/X)+(k-q+sigma^2/2)*T)/(sigma*SQRT(T)) 15 d2 0.5834 =$D$14-(sigma*SQRT(T)) 16 N(d1) 0.8756 =NORMSDIST($D$14) 17 N(d2) 0.7202 =NORMSDIST($D$15) 18 Call Option Value $ 21.03 =S0*EXP(-q*T)*$D$16-X*EXP(-k*T)*$D$17 Note: Boeing reported using a binomial pricing model which could explain the difference in this result from that reported in the annual report

Teresa's columns which can be copied

$ 53.18 1/1/1997 $ 53.18 1/1/2006 9.0000 19.000% 6.60% 1.10% 1.1534 0.5834 0.8756 0.7202 $ 21.03 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

Historical prices provided by CSI, Inc. Boeing Company (BA) Weekly prices (3/25/96 to 3/29/99) DATE HIGH LOW CLOSE VOLUME Return 1996 3/29/1999 35.25 33.5 33.938 10989300 3/22/1999 35.125 34 34.813 16498300 0.025456 =LN(+D7/D6) 3/15/1999 36.563 34 34 20732700 3/8/1999 35.625 33.75 35.125 14492500 3/1/1999 36 33.5 35.563 16108600 2/22/1999 37.5 34.438 35.625 19512900 2/15/1999 36.688 35.25 35.688 10533300 2/8/1999 37.375 35 35.563 13167100 2/1/1999 37.688 33.75 37.25 22182200 1/25/1999 36.438 34.25 34.688 23430700 1/18/1999 34.75 32.563 34.5 17114800 1/11/1999 35.875 32.813 33.688 17302600 1/4/1999 36.75 32.813 35.813 31864700 12/28/1998 33.125 31 32.625 20876600 12/21/1998 32.938 31.563 32.25 18979000 12/14/1998 34.438 31.5 31.75 27230100 12/7/1998 34.938 33 33.125 29369500 11/30/1998 41.25 31.5 32.938 71172600 11/23/1998 44 41.063 41.438 10722700 11/16/1998 43.563 42.063 43.563 16295300 11/9/1998 42.75 41 42.125 16420100 11/2/1998 42.438 37.813 41.875 28132700 10/26/1998 37.875 35.063 37.563 15152000 10/19/1998 37.5 32.563 35.688 22082600 10/12/1998 34.875 31.75 32.25 17990700 10/5/1998 33.5 29.5 32 18849200 9/28/1998 36.25 31.75 32.563 18462700 9/21/1998 34.938 33.688 34.688 19947900 9/14/1998 34.938 33.563 34.438 19904700 9/7/1998 37.75 33.563 34 17751900 8/31/1998 35 29 33.938 40728300 8/24/1998 36.813 33.5 33.938 20712700 8/17/1998 37.938 35.813 36.375 18574500 8/10/1998 39.375 36.313 36.813 26510800 8/3/1998 39.438 36.063 39.25 37568700 7/27/1998 40.25 37.938 38.813 41669100 7/20/1998 50 40 40.313 49921500 7/13/1998 50.125 47.188 50 15299500 7/6/1998 49.438 47.125 47.875 12151100 6/29/1998 49.25 44.125 48.438 16106200 6/22/1998 46.125 42.125 45.688 17096600 6/15/1998 44.563 42.563 42.938 21443100 6/8/1998 46.375 44.25 44.938 18348800 6/1/1998 47.75 45 45.5 18802900 5/25/1998 48.688 45.25 47.75 16316700 5/18/1998 49.375 47.625 48.375 14126700 5/11/1998 50.625 49 49.625 11530000

1997

1998

5/4/1998 4/27/1998 4/20/1998 4/13/1998 4/6/1998 3/30/1998 3/23/1998 3/16/1998 3/9/1998 3/2/1998 2/23/1998 2/16/1998 2/9/1998 2/2/1998 1/26/1998 1/19/1998 1/12/1998 1/5/1998 12/29/1997 12/22/1997 12/15/1997 12/8/1997 12/1/1997 11/24/1997 11/17/1997 11/10/1997 11/3/1997 10/27/1997 10/20/1997 10/13/1997 10/6/1997 9/29/1997 9/22/1997 9/15/1997 9/8/1997 9/1/1997 8/25/1997 8/18/1997 8/11/1997 8/4/1997 7/28/1997 7/21/1997 7/14/1997 7/7/1997 6/30/1997 6/23/1997 6/16/1997 6/9/1997 6/2/1997 5/26/1997 5/19/1997 5/12/1997

52.313 52.375 53.563 54.875 56.25 55.875 52.938 53.438 53.063 54.25 54.75 52.75 50.75 48.875 48.188 45.688 46.25 49.75 49.813 49.188 51.75 52.313 54.625 53.375 50.625 48.125 48.625 49 54.438 55.188 55.25 55 55.125 54.563 55.563 58.188 56.25 57.625 59.25 59.438 59.375 60.5 60.5 56.875 56.438 56.875 58 57.875 55 53.125 51.5 50.813

49.5 48.375 50.375 52.063 54.5 50.25 51.125 50.563 50.188 51.5 49.063 49.938 46.375 46.063 44 42.813 43 45 47.875 47.438 47.375 48.25 51.875 49.25 48.313 45.75 44.563 43 47.75 51 52.063 50.125 52.063 51.375 51.313 55 54.188 54.75 55.375 57.25 57 53.375 55.75 54.938 53.063 53 56.125 54.875 52.25 50.125 48.375 48.875

50.5 51.75 50.688 53.688 55.188 54.938 51.25 53.438 51.813 52.438 54.25 50.125 50.375 46.438 47.625 44.313 43.438 45.125 48.875 47.813 48.563 49 52.375 53.125 50.125 48 45.75 48 48.438 51.875 54.313 52 54.563 52.375 52.938 55.375 54.5 55.625 55.438 58.5 58.5 58.875 56.063 56.5 55.188 53 56.875 57.375 54.938 52.688 50.125 49.375

10038600 17242500 18499600 18127600 17465900 23471600 18830000 18544800 11446900 17231800 22623100 20365400 20805900 17583100 19741000 24771600 28240400 22538900 11141900 6553700 17492000 15882700 18560900 14981600 17965400 19393400 25880700 47244200 71614800 16168600 22150900 29570300 20954400 24730600 23075300 13534300 12587200 12058900 17247800 16041000 13658000 30284300 17584300 12834700 13780000 19773900 12981900 18495200 11660600 14138000 20286800 19735800

5/5/1997 4/28/1997 4/21/1997 4/14/1997 4/7/1997 3/31/1997 3/24/1997 3/17/1997 3/10/1997 3/3/1997 2/24/1997 2/17/1997 2/10/1997 2/3/1997 1/27/1997 1/20/1997 1/13/1997 1/6/1997 12/30/1996 12/23/1996 12/16/1996 12/9/1996 12/2/1996 11/25/1996 11/18/1996 11/11/1996 11/4/1996 10/28/1996 10/21/1996 10/14/1996 10/7/1996 9/30/1996 9/23/1996 9/16/1996 9/9/1996 9/2/1996 8/26/1996 8/19/1996 8/12/1996 8/5/1996 7/29/1996 7/22/1996 7/15/1996 7/8/1996 7/1/1996 6/24/1996 6/17/1996 6/10/1996 6/3/1996 5/27/1996 5/20/1996 5/13/1996

50.813 50.5 51.438 51.125 51.438 50.5 53.625 53.563 54.313 53.313 53.875 55.563 54.938 54.813 55.25 57.25 54 53.75 53.75 52.563 52.688 48.688 49.5 50.188 49.625 47.375 47.5 48.188 49.438 49.625 49.438 49.063 48 47.438 45.75 45.938 46.5 46.063 46.188 46.75 45.875 44.375 44.25 45.375 47.063 45.25 44.625 43.375 43.188 43.375 43.188 41.938

48.375 47.188 49.188 48.875 49.813 47 50.5 51.125 51.125 50.063 50.563 53.188 52.625 52.625 52.063 52.5 52.625 51.5 51.625 51.438 50.063 47 47.188 49.063 46.063 45.5 45.125 45.5 47.063 48.438 48.438 47.188 46.813 45.375 44.875 44.813 45.188 44.688 45 44.625 43.25 41.25 39.938 43.563 44 43.563 41.313 41.5 41.313 41.875 40.813 39

48.938 50.25 51 49.813 50.188 49 50.875 52.875 51.5 53.188 50.875 53.938 53.875 54.75 53.563 54.938 53.063 52.563 53.188 52.188 52.688 48.375 47.813 49.688 49.313 45.875 46.938 45.938 47.063 49.125 48.938 48.938 47.438 47.438 45.5 45.125 45.25 45.188 45.875 45.5 45.813 44.188 43.625 44.133 44.938 43.563 44.563 41.688 42.938 42.625 41.938 41.5

23110200 44924800 9743800 13080000 12503600 19478000 11054200 14529200 14875200 17355800 16547200 9436600 10418800 11398400 19360000 19934600 11068200 15115600 10355600 5173200 32199800 13607600 10111600 7150400 14853400 12059400 14359800 14482400 9562400 9803000 8286200 8300800 8173800 11229200 12318000 10843000 9479600 9229200 8699400 7823000 10502400 11126000 14621200 11753200 9717600 12214200 13921400 7739000 10701000 7707000 9516400 15107400

0.01182 -0.01898 0.009535 -0.0854 -0.01169 0.038466 -0.00758 -0.07227 0.022907 -0.02153 0.024194 0.042881 -0.00381 0 -0.03113 0 -0.04171 -0.00828 0.002766 -0.00137 0.015089 -0.00821 0.006856 -0.03611 -0.01282 0.011577 0.018076 -0.03108 0.022696 -0.06669 0.029544 -0.00732 -0.01625 -0.0105

0.01182 -0.01898 0.009535 -0.0854 -0.01169 0.038466 -0.00758 -0.07227 0.022907 -0.02153 0.024194 0.042881 -0.00381 0 -0.03113 0 -0.04171 -0.00828 0.002766 -0.00137 0.015089 -0.00821 0.006856 -0.03611 -0.01282 0.011577 0.018076 -0.03108 0.022696 -0.06669 0.029544 -0.00732 -0.01625 -0.0105

5/6/1996 4/29/1996 4/22/1996 4/15/1996 4/8/1996 4/1/1996 3/25/1996

39.75 41.063 41.375 41 42.125 43.563 44.563

37.063 38.063 39.938 39.688 38.438 42.25 43.188

39.688 39 40.375 40.563 40.75 42.688 43.313

17643000 14149600 8642600 11826400 23062000 11105600 9993600

-0.04464 -0.01749 0.034649 0.004646 0.0046 0.046462 0.014535 Std Dev Volatility

No. of weeks in sample Note: In the 1997 annual report, Boeing reported using volatility of 19%, dividend yield rate of 1.1%, and 6.6% risk-free interest rate to estimate fair values of the options granted in 1997. The fair value was computed using a binomial model which gave a reported value of $20.67.

-0.04464 -0.01749 0.034649 0.004646 0.0046 0.046462 0.014535 0.029788 0.214808 41

A1 B1 2 Calculating the Implied Volatility 3 4 INPUT VARIABLES 5 Stock Price 6 at Valuation Date 7 Exercise Price 8 Expiration Date 9 Time to expiration (in years) 10 Implied Annualized Volatility 11 Risk-free rate of interest 12 Dividend yield 13 COMPUTATIONS 14 15 16 17 18 Theoretical B&S Call Option Value 19 Actual Price of this Call Option

C1

D1

using the Black-Scholes Option Pricing Model
S0 t0 X tT T sigma k q d1 d2 N(d1) N(d2) 94.00 6/30/1998 80.00 11/22/1998 0.397260274 0.5885 0.0535 0.00% 0.6775 0.3066 0.7510 0.6204 22.00 22.00

Black-Scholes Option Pricing Model

35976 36121 NOTE: Use GOAL SEEK to calculate Implied Volatility (D10) by setting the theoretical price (D18) to the actual price (in D19) =(LN(S0/X)+(k-q+d10^2/2)*T)/(d10*SQRT(T)) =$D$14-(d10*SQRT(T)) =NORMSDIST($D$14) =NORMSDIST($D$15) =S0*EXP(-q*T)*$D$16-X*EXP(-k*T)*$D$17 (Actual quote, say, from the Wall Street Journal)


								
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