A 1 2 3 4 5 6 7 8 SXrTSigmad1B C D E F G H I Black-Scholes option pricing formula505010.00%125%0.5250Current stock priceExercise priceRisk-free rate of interestTime to maturity of option (in years)Stock volatility<-- (LN(S/X)+(r+0.5*sigma^2)*T)/(sigma*SQRT(T))9 d210 11 N(d1)0.2750<-- d1 - sigma*SQRT(T)0.7002<-- Uses formula NormSDist(d1)<-- Uses formula NormSDist(d2)<-- S*N(d1)-X*exp(-r*T)*N(d2)<-- call price - S + X*Exp(-r*T): by Put-Call parity12 N(d2)0.608313 14 Call price7.4915 Put price2.7316 17 18 StockB-S19 PriceValue20 21 3610.224622 388.722023 407.361524 426.149625 445.087026 464.169127 483.387228 502.729829 522.183530 541.734531 561.369232 581.074533 600.838934 620.651835 640.504336 660.388637 680.298538 39 40 41 42 StockB-S Call43 PriceValue44 45 200.00108346 230.00832247 260.03981448 290.1354949 320.358386IntrinsicValue141210864200000000001614121086420Intrinsic Put Value versus Black-ScholValueB-S ValueIntrinsic ValueValue ($)354555Stock price S ($)6575When the stock price is low, the B-S value is less than theintrinsic value. If we could exercise early, the option wouldhave increased value. Hence: Early exercise may be valuablefor puts.IntrinsicValue00000252015Intrinsic Call Value versus Black-Scholes ValueB-S Call ValueIntrinsic ValueA 50 51 52 53 54 55 56 57 58 59 60 61 353841444750535659626568B 0.7836161.4801762.4949293.8451325.5199677.4878999.70582812.1272814.7081517.4099520.2010423.05661C 000000369121518D 1510E F Intrinsic ValueG H I 50020406080J 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Scholes 19 20 21 22 23 24 25 26 27 28 29 7530 31 32 33 34 less than the35 36 uldercise may be valuable37 38 39 40 41 42 43 44 s 45 46 47 48 49 J 50 51 52 53 54 55 56 57 58 59 60 61