Question

A company current stock price at RM16.00, the exercise price at RM17.00. If government bond yield is 10%, and the company’s share prices volatile at 35% in annualised form. The company does not pay any dividend. Using the Black-Scholes option pricing model, calculate:

(i) the fair value for a RM17.00 call option with 90 days to maturity.
(ii) the fair value for a RM17.00 put option with 90 days to maturity.

Answer 1

Particulars	Values
Stock Price or Spot Price	16.00
Strike Price or Exercise Price	17.00
SD	0.35
variance (SD^2)	0.1225
Risk free Rate	10.00%
Time period in Years (90/365)	0.2466

Step1:
Ln (S / X )
S - Stock Price
X - Exercise Price
= Ln ( 0.9412 )
= -0.0606

Step2:
d1 ={ [ Ln (S/X) + [ [ ( SD^2 / 2 ) + rf ] * t ] } / [ SD * SQRT ( T ) ]
S - Stock Price
X - Exercise Price
Rf - Risk free Rate per anum
T - Time in Years
= { [ -0.0606 + [ [ ( 0.1225 / 2 ) + 0.1 ] * 0.2466 ] } / [ 0.35 * SQRT ( 0.2466 ) ]
= { [ -0.0606 + [ [ 0.0613 + 0.1 ] * 0.2466 ] } / [ 0.35 * ( 0.4966 ) ]
= { -0.0606 + [ 0.1613 * 0.2466 ] } / [ 0.1738 ]
= { -0.0606 + 0.0398 } / [ 0.1738 ]
= -0.0208 / 0.1738
= -0.1197

Step3 :
d2 = d1 - [ SD * SQRT ( T ) ]
= -0.1197 - [ 0.35 * SQRT ( 0.2466 ) ]
= -0.1197 - [ 0.35 * 0.4966 ]
= -0.1197 - 0.1738
= -0.2935

Step 4 :
NT( d1) = -0.0438
-0.0438

Step 5:
NT (d2) = -0.1141
-0.11409

Step 6 :
N(d1) = 0.5 + NT(d1)
= 0.5 + -0.0438
= 0.4562

Step 7:
N(d2) = 0.5 + NT(d2)
= 0.5 + -0.1141
= 0.3859

Step 8:
e-rt :
= e^-0.1*0.2466
= e^-0.0247
= 0.9756

Step 9:
Value of Call = [ S * N( d1 ) ] - [ X * e^-rt * N ( d2 ) ]
= [ 16 * 0.4562 ] - [ 17 * 0.9756 * 0.3859 ]
= [ 7.2992 ] - [ 6.4004 ]
= 0.9

Step 10:
N(-d1) = 1 - N(d1)
= 1 - 0.4562
=0.5438

Step 11:
N(-d2) = 1 - N(d2)
= 1 - 0.3859
= 0.6141

Step 12:
Value of Put = [ X * e^-rt * N(-d2) ] - [ S * N(-d1) ]
= [ 17 * e^-0.1 * 0.2466 * 0.6141 ] - [ 16 * 0.5438 ]
= [ 17 * 0.9756 * 0.6141 ] - [ 16 * 0.5438 ]
= [ 10.19 ] - [ 8.7 ]
= 1.48

Check:
Vc + PV of Strike Price
= 0.9 + 16.5852
= 17.48

Stock Price + Vp
= 16 + 1.48
= 17.48

Vc + PV of strike Price = Stock Price + Vp

Value of the call is 0.9 & Value of the put is 1.48