InvestorQ : What happens to the value of the call and put options under Black & Scholes when the volatility of the stock goes up or moves up?
Arya Nanda made post

What happens to the value of the call and put options under Black & Scholes when the volatility of the stock goes up or moves up?

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Deepa Salunkhe answered.
2 years ago
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Volatility is the extent to which the stock price fluctuates. When a stock is volatile, there are greater prospects of the stock price moving up or moving down. On the downside there is no risk as your loss is limited to the premium paid on the option. Let us look at the table below on how the value of the option is impacted by a rise in volatility.

Inputs

Inputs

Stock Price Now (Ps)

? 1,110

Stock Price Now (Ps)

? 1,110

Standard Dev - Annual (s)

30.00%

Standard Dev - Annual (s)

40.00%

Risk free Rate - Annual (R)

6.00%

Risk free Rate - Annual (R)

6.00%

Exercise Price (E)

? 1,100

Exercise Price (E)

? 1,100

Time To Maturity - Years (T)

0.0833

Time To Maturity - Years (T)

0.0833

Dividend yield (d)

1.00%

Dividend yield (d)

1.00%

Outputs

Outputs

d1

0.196

d1

0.172

d2

0.109

d2

0.057

N(d1)

0.578

N(d1)

0.568

N(d2)

0.544

N(d2)

0.523

Call Price (Vc)

? 45.77

Call Price (Vc)

? 58.33

-d1

-0.196

-d1

-0.172

-d2

-0.109

-d2

-0.057

N(-d1)

0.422

N(-d1)

0.432

N(-d2)

0.456

N(-d2)

0.477

Put Price (Pp)

? 31.21

Put Price (Pp)

? 43.77

What do we see in the table above? The values of the call and the put option have gone up proportionately when the volatility of the stock has gone up. Why is it that both the call and the put have reacted in the same manner? The answer is quite simple. When volatility goes up, the prospects of the stock moving sharply either ways goes up. In case of a call, it becomes more valuable when it fluctuates on the upside. However, on the downside the risk is limited to the premium paid. Similarly, in case of a put option, rising volatility means an increase in the probability of the stock price going down but if the price goes up then the loss is limited to the premium paid. That is the reason the value of the call and the put options goes up with the rise in volatility.
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