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?

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

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.

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