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

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

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Juvina Maggie answered.
3 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 fall 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)

25.00%

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

0.219

d2

0.109

d2

0.147

N(d1)

0.578

N(d1)

0.587

N(d2)

0.544

N(d2)

0.558

Call Price (Vc)

? 45.77

Call Price (Vc)

? 39.52

-d1

-0.196

-d1

-0.219

-d2

-0.109

-d2

-0.147

N(-d1)

0.422

N(-d1)

0.413

N(-d2)

0.456

N(-d2)

0.442

Put Price (Pp)

? 31.21

Put Price (Pp)

? 24.96

Let us look at an alternate scenario when the volatility of the stock goes down. What do we see in the table above? The values of the call and the put option have gone down proportionately when the volatility of the stock has gone down. Why is it that both the call and the put have reacted in the same manner? The answer is quite simple. When volatility goes down, the prospects of the stock moving sharply either ways goes down. In case of a call, it becomes less valuable if it is less likely to fluctuate on the downside. However, on the other side the risk is limited to the premium paid. Similarly, in case of a put option, falling volatility means a reduction in the probability of the stock price going down but if the price goes the other way then the loss is anyways limited to the premium paid. That is the reason the value of the call and the put options goes down with the fall in volatility.
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