InvestorQ : How does the volatility impact the value of the put option and what is the impact if the volatility is decreased. How does the put option get impacted? # How does the volatility impact the value of the put option and what is the impact if the volatility is decreased. How does the put option get impacted? Answer 1 year ago

The volatility is important because it determines the time value of the option. Higher the volatility in the price of the stock, higher is the time value of the option. That is because there is greater probability of the option prices moving in your favour when there is more volatility in the stock price. The same rule applies to put option also because put and call options are based on the probability of the prices moving in your favour and that means volatility should work in favour of options price. Let us see this example in practical terms.

 Input Data Input Data Stock Price now (P) 120 Stock Price now (P) 120 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) 25.00% 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 0.0722 d1 -0.3800 d1 -0.4718 d2 -0.4666 d2 -0.5440 Delta N(d1) Normal Cumulative Density Function 0.3520 Delta N(d1) Normal Cumulative Density Function 0.3185 Bank Loan N(d2)*PV(EX) 39.8844 Bank Loan N(d2)*PV(EX) 36.5004 Value of Put 6.8345 Value of Put 6.2029

In the above illustration, we have kept all the other parameters the same but we have reduced the volatility. Effectively, we have reduced the volatility from 30% to 25%. The impact of this is decrease in the value of the put option. Volatility is directly related to the time value. As the volatility is reduced the time value of the put option also reduces and thus the total value of the put option also reduces. We all know that the value of the put option is the sum total of the intrinsic value of the option and the time value of the option. Interestingly, a reduction in the volatility represented by the standard deviation impacts the calls and puts in a similar manner. The volatility and the time to expiry are the only two factors that impact calls and puts in the same direction.

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