InvestorQ : How does the volatility impact the value of the call option and what is the impact if the volatility of the price increases. How does the call option get impacted?
Aditi Sharma made post

How does the volatility impact the value of the call option and what is the impact if the volatility of the price increases. How does the call option get impacted?

Answer
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shrinidhi Rajan answered.
1 year ago


The time to expiry is important because it determines the time value of the option. Higher the time to expiry, 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 time left for expiry. Let us see this example in practical terms when volatility is increased by 20%.

Input Data

Input Data

Stock Price now (P)

120.00

Stock Price now (P)

120.00

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)

36.00%

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

0.1039

d1

-0.3800

d1

-0.3008

d2

-0.4666

d2

-0.4047

Delta N(d1) Normal Cumulative Density Function

0.3520

Delta N(d1) Normal Cumulative Density Function

0.3818

Bank Loan N(d2)*PV(EX)

39.8844

Bank Loan N(d2)*PV(EX)

42.6790

Value of Call

2.3542

Value of Call

3.1371

In the above illustration, we have kept all the other parameters the same but we have increased the volatility by 20%. Effectively, we have increased the volatility from 30% to 36%. The impact of this is an increase in the value of the call option. Volatility is directly related to the time value as greater the volatility means more chances of being profitable within the same period of time. As the volatility is increased the time value of the call option also increases and thus the total value of the call option also increases. We all know that the value of the call option is the sum total of the intrinsic value of the option and the time value of the option.

But what would happen if we increased the volatility by another 20%. This would effectively take the volatility higher from 36% to 43.2%. Obviously the value of call will increase further but will it be more than the first 20% move or the less than the first move. Let us look at the table below:

Input Data

Input Data

Stock Price now (P)

120.00

Stock Price now (P)

120.00

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)

43.20%

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

0.1247

d1

-0.3800

d1

-0.2316

d2

-0.4666

d2

-0.3563

Delta N(d1) Normal Cumulative Density Function

0.3520

Delta N(d1) Normal Cumulative Density Function

0.4084

Bank Loan N(d2)*PV(EX)

39.8844

Bank Loan N(d2)*PV(EX)

44.9142

Value of Call

2.3542

Value of Call

4.0978

(Note - Period is reduced to yearly decimals

While the value of the call goes up further with the higher volatility, the subsequent 20% increase in volatility has a lesser impact on the call value as the elasticity of time value of the call option tends to saturate after a point of time.