Implied Volatility

InputsOption Type: 1=Call, 0=Put 1 1 1 1 1 0 0 0

$1,403 $1,403 $1,403 $1,403 $1,403 $1,403 $1,403 $1,403Riskfree Rate - Annual (R) 5.34% 5.34% 5.34% 5.34% 5.34% 5.34% 5.34% 5.34%Exercise Price (E) $1,350 $1,375 $1,400 $1,425 $1,450 $1,350 $1,375 $1,400Time To Maturity - Yrs (T) 0.1028 0.1028 0.1028 0.1028 0.1028 0.1028 0.1028 0.1028Dividend yield (d) 1.18% 1.18% 1.18% 1.18% 1.18% 1.18% 1.18% 1.18%Observed Option Price $81.00 $66.25 $46.00 $31.00 $19.25 $18.00 $23.63 $30.50

Outputsd1 0.556 0.329 0.125 -0.129 -0.419 0.612 0.389 0.136d2 0.472 0.244 0.051 -0.198 -0.482 0.537 0.320 0.073N(d1) 0.711 0.629 0.550 0.448 0.338 0.730 0.651 0.554N(d2) 0.682 0.596 0.520 0.422 0.315 0.704 0.625 0.529

$81.00 $66.25 $46.00 $31.00 $19.25 $76.86 $57.62 $39.63

-d1 -0.556 -0.329 -0.125 0.129 0.419 -0.612 -0.389 -0.136-d2 -0.472 -0.244 -0.051 0.198 0.482 -0.537 -0.320 -0.073N(-d1) 0.289 0.371 0.450 0.552 0.662 0.270 0.349 0.446N(-d2) 0.318 0.404 0.480 0.578 0.685 0.296 0.375 0.471

$22.14 $32.25 $36.87 $46.73 $59.84 $18.00 $23.62 $30.50

SolverDiffer (observed - model) 6.1E-05 -2E-05 -4E-05 -8E-05 4.6E-05 4.6E-05 2E-05 -5E-05Implied Volatility from Calls 26.03% 26.73% 23.11% 21.28% 19.78%Implied Volatility from Puts 23.30% 21.60% 19.52%

BLACK SCHOLES OPTION PRICING

Stock Price Now (Ps)

Model Call Price (Vc)

Model Put Price (Pp)

$1,325 $1,350 $1,375 $1,400 $1,425 $1,450 $1,47515%

18%

21%

24%

27%

30%

"Scowl" Pattern of Implied Volatilities

Exercise Price

Imp

lied

Vo

lati

lity

(C

alls

,Pu

ts)

0 0

$1,403 $1,4035.34% 5.34%$1,425 $1,4500.1028 0.10281.18% 1.18%$41.50 $55.00

-0.161 -0.504-0.219 -0.5580.436 0.3070.413 0.288

$25.77 $14.41

0.161 0.5040.219 0.5580.564 0.6930.587 0.712

$41.50 $55.00

-6E-05 4E-05

18.33% 16.78%

$1,325 $1,350 $1,375 $1,400 $1,425 $1,450 $1,47515%

18%

21%

24%

27%

30%

"Scowl" Pattern of Implied Volatilities

Exercise Price

Imp

lied

Vo

lati

lity

(C

alls

,Pu

ts)