InvestorQ : How does a decrease in the stock price impact the value of the call option on a particular stock?
Priyanka Jain made post

How does a decrease in the stock price impact the value of the call option on a particular stock?

Answer
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Mary Joseph answered.
1 year ago


Let us understand this better with an illustration of a real life example where the stock price actually moves down 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)

115.00

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

-0.8714

d2

-0.4666

d2

-0.9580

Delta N(d1) Normal Cumulative Density Function

0.3520

Delta N(d1) Normal Cumulative Density Function

0.1918

Bank Loan N(d2)*PV(EX)

39.8844

Bank Loan N(d2)*PV(EX)

21.0412

Value of Call

2.3542

Value of Call

1.0123

(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 down from Rs.120 to Rs.115. You will see that the value of the call option also goes down. 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 down it becomes more and more out of the money and hence the call becomes less valuable. What happens to the option value as the price goes down further. Will the option value fall at a faster rate or a slower rate? Let us simulate another situation with another Rs.5 reduction in the stock price. What happens? Check our workings below:

Input Data

Input Data

Stock Price now (P)

120.00

Stock Price now (P)

110.00

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

-1.3847

d2

-0.4666

d2

-1.4713

Delta N(d1) Normal Cumulative Density Function

0.3520

Delta N(d1) Normal Cumulative Density Function

0.0831

Bank Loan N(d2)*PV(EX)

39.8844

Bank Loan N(d2)*PV(EX)

8.7892

Value of Call

2.3542

Value of Call

0.3490

(Note - Period is reduced to yearly decimals

Now what do we see in this case? When the stock price goes down by another Rs.5 to Rs.110, then the value of the call option goes down further to Rs.0.3490. But you will also notice that the percentage rise is much higher 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 falls below Rs.120, it only has time value and that trend towards zero very quickly as prospects of a bounce become remote. Thus the impact of time value on the total option valuation keeps going up consistently. This trend will continue as you keep going further down.