Question

1. Lavender Berhad’s stock is currently selling at RM30. The call stock option with an exercise price of RM25 has 180 days to expiration. The annual risk-free interest rate is 8%. The variance has been estimated to be 40% per annum.

Assume: 365 days in a year

From the above information you are required to answer the questions below:

1. determine the value of this call option based on Black-Scholes model.

2. determine the corresponding value of put option.                                     

2. =When you are making a call option, you opt to have these situations, discuss:

1. “on the money”                                                                                        

2. “out of the money”                                                                                   

P/S : PLEASE PROVIDE FULL CALCULATION

Answer 1

Particulars	Values
Stock Price or Spot Price	$ 30.00
Strike Price or Exercise Price	$ 25.00
SD	0.4
variance (SD^2)	0.16
Risk free Rate	8.00%
Time period in Years (180/365)	0.4932

Step1:
Ln (S / X )
S - Stock Price
X - Exercise Price
= Ln ( 1.2 )
= 0.1823

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
= { [ 0.1823 + [ [ ( 0.16 / 2 ) + 0.08 ] * 0.4932 ] } / [ 0.4 * SQRT ( 0.4932 ) ]
= { [ 0.1823 + [ [ 0.08 + 0.08 ] * 0.4932 ] } / [ 0.4 * ( 0.7022 ) ]
= { 0.1823 + [ 0.16 * 0.4932 ] } / [ 0.2809 ]
= { 0.1823 + 0.0789 } / [ 0.2809 ]
= 0.2612 / 0.2809
= 0.9299

Step3 :
d2 = d1 - [ SD * SQRT ( T ) ]
= 0.9299 - [ 0.4 * SQRT ( 0.4932 ) ]
= 0.9299 - [ 0.4 * 0.7022 ]
= 0.9299 - 0.2809
= 0.649

Step 4 :
NT( d1) = 0.3212

Step 5:
NT (d2) = 0.2389

Step 6 :
N(d1) = 0.5 + NT(d1)
= 0.5 + 0.3212
= 0.8212

Step7:
N(d2) = 0.5 + NT(d2)
= 0.5 + 0.2389
= 0.7389

Step 8:

e-rt :
= e^-0.08*0.4932
= e^-0.0395
= 0.9613

Step 9:
Value of Call = [ S * N( d1 ) ] - [ X * e^-rt * N ( d2 ) ]
= [ $ 30 * 0.8212 ] - [ $ 25 * 0.9613 * 0.7389 ]
= [ $ 24.6363 ] - [ $ 17.7579 ]
= $ 6.88

Value of the Call: $ 6.88

Step 10:
N(-d1) = 1 - N(d1)
= 1 - 0.8212
=0.1788

Step 11:
N(-d2) = 1 - N(d2)
= 1 - 0.7389
= 0.2611

Step 12:
Value of Put = [ X * e^-rt * N(-d2) ] - [ S * N(-d1) ]
= [ $ 25 * e^-0.08 * 0.4932 * 0.2611 ] - [ $ 30 * 0.1788 ]
= [ $ 25 * 0.9613 * 0.2611 ] - [ $ 30 * 0.1788 ]
= [ $ 6.27 ] - [ $ 5.36 ]
= $ 0.91

The value of the Put = $ 0.91

Check:
Vc + PV of Strike Price
= $ 6.88 + $ 24.0325
= $ 30.91

Stock Price + Vp
= $ 30 + $ 0.91
= $ 30.91

Vc + PV of strike Price = Stock Price + Vp

Holder of call option will have right to buy underlying asset at the agreed price ( Strike Price). As he is receiving right, he needs to pay premium to writer of call option.
He will exercise the right, when expected spot price > Strike Price. Then writer of option has to sell at the strike Price.

When the expected spot price or Future Spot > Strike price it is called on the money

Here if future spot price is greater than RM 25 then it will called on the money

When the expected spot price or Future Spot < Strike price it is called out of the money

Here if future spot price is less than RM 25 then it is called out of the money

if the future spot price is equal to RM 25 then it is called at the money

Please let me know if you have any queries