InvestorQ : How does an increase in the stock price impact the value of the put option on a particular stock and why is that so?
Mary Joseph made post

How does an increase in the stock price impact the value of the put option on a particular stock and why is that so?

Answer
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swati Bakhda answered.
1 year ago


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 put option.

Input Data

Input Data

Stock Price now (P)

120

Stock Price now (P)

125

Exercise Price of Option (EX)

125

Exercise Price of Option (EX)

125

Number of periods to Exercise in years (t)

0.08333333

Number of periods to Exercise in years (t)

0.083333333

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^0.5

0.0866

s*t^0.5

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 Put

6.8345

Value of Put

4.0535

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 put option also goes down. That is because a put option is a right to sell the stock at the strike price, which is Rs.125 in this case. As the stock price keeps going higher it becomes more and more out of the money and hence the put otion becomes less valuable. What happens to the option value as the price goes up further. Will the option value fall at a faster rate or a slower rate? Let us simulate another situation with another Rs.5 increase in the stock price. What happens? Check our workings below:

Input Data

Input Data

Stock Price now (P)

120

Stock Price now (P)

130

Exercise Price of Option (EX)

125

Exercise Price of Option (EX)

125

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^0.5

0.0866

s*t^0.5

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 Put

6.8345

Value of Put

2.1747

Now what do we see in this case? When the stock price goes up by another Rs.5 to Rs.130, then the value of the put option goes down further to Rs.2.1747. 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 goes above Rs.125, it only has time value and that trend towards zero very quickly as prospects of a fall in price 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 up in the stock price.