Let us understand this better with an illustration of a real life example where the stock price actually moves up and let us see the impact on the value of the call option.

Input Data

Input Data

Stock Price now (P)

120.00

Stock Price now (P)

125.00

Exercise Price of Option (EX)

125.00

Exercise Price of Option (EX)

125.00

Number of periods to Exercise in years (t)

0.08333

Number of periods to Exercise in years (t)

0.08333

Compounded Risk-Free Interest Rate (rf)

5.00%

Compounded Risk-Free Interest Rate (rf)

5.00%

Standard Deviation (annualized s)

30.00%

Standard Deviation (annualized s)

30.00%

Output Data

Output Data

Present Value of Exercise Price (PV(EX))

124.4803

Present Value of Exercise Price (PV(EX))

124.4803

s*t^.5

0.0866

s*t^.5

0.0866

d1

-0.3800

d1

0.0914

d2

-0.4666

d2

0.0048

Delta N(d1) Normal Cumulative Density Function

0.3520

Delta N(d1) Normal Cumulative Density Function

0.5364

Bank Loan N(d2)*PV(EX)

39.8844

Bank Loan N(d2)*PV(EX)

62.4791

Value of Call

2.3542

Value of Call

4.5732

(Note - Period is reduced to yearly decimals

In the above instance we have assumed that all the factors remain constant but only the stock price goes up from Rs.120 to Rs.125. You will see that the value of the call option also goes up. That is because a call option is a right to buy the stock at the strike price, which is Rs.125 in this case. As the stock price keeps going up it becomes more and more in the money and hence the call becomes more valuable. What happens to the option value as the price goes up further. Will the option value grow at a faster rate or a slower rate? Let us simulate another situation with an additional Rs.5 increase in the stock price. What happens? Check our workings below:

Input Data

Input Data

Stock Price now (P)

120.00

Stock Price now (P)

130.00

Exercise Price of Option (EX)

125.00

Exercise Price of Option (EX)

125.00

Number of periods to Exercise in years (t)

0.08333

Number of periods to Exercise in years (t)

0.08333

Compounded Risk-Free Interest Rate (rf)

5.00%

Compounded Risk-Free Interest Rate (rf)

5.00%

Standard Deviation (annualized s)

30.00%

Standard Deviation (annualized s)

30.00%

Output Data

Output Data

Present Value of Exercise Price (PV(EX))

124.4803

Present Value of Exercise Price (PV(EX))

124.4803

s*t^.5

0.0866

s*t^.5

0.0866

d1

-0.3800

d1

0.5443

d2

-0.4666

d2

0.4577

Delta N(d1) Normal Cumulative Density Function

0.3520

Delta N(d1) Normal Cumulative Density Function

0.7069

Bank Loan N(d2)*PV(EX)

39.8844

Bank Loan N(d2)*PV(EX)

84.2001

Value of Call

2.3542

Value of Call

7.6944

(Note - Period is reduced to yearly decimals

When the stock price goes up by another Rs.5 to Rs.130, then the value of the call option goes up further to Rs.7.6944. But you will also notice that the percentage rise is much lower in the second round than the first round. That is because, the option value has two components viz. the time value and the intrinsic value. As the stock price crosses Rs.125, it acquires intrinsic value also, apart from time value. Thus the impact of time value on the total option valuation keeps going down consistently. This trend will continue as you keep going further up.