Implied volatility-How

the book says you can get that from BSM, how??

BSM has 5 parameters -

C=SN(d1) - N(d2) * K * e^(-rt)

r = Risk free rate

S = Stock Price

K = Strike Price

C = Call Premium

d1 and d2 use the std deviation of the stock price -> which is the volatility.

and d1 and d2 are both related.

If C, S, K and t are known - you can arrive at d1, d2 and thus work back to -> the volatility.

This thus becomes the implied volatility based on the other params.

OHHHH that! ha, is calculation of this required? how much of BSM details we need to know?

i do not think they required us to know the calculation using BSM … but what are the variables, what is the meaning was required to be known when I wrote the exam. Check the LOSs to see if anything requiring you to know the calculations is present now.

The call premium isn’t a parameter; it’s the result of the calculation.

The five parameters are:

  • Time to expiration
  • Strike price
  • Market price of the underlying
  • Risk-free rate
  • Volatility of returns of the underlying

If you know the time to expiration, the strike price, the market price of the underlying, the risk-free rate, and the option price (five things), you can compute the necessary volatility of returns of the underlying.

That’s the implied volatility: the volatility implied by the BSM model _ assuming that the option is fairly priced _.

The call premium is the observed price in the market, the other parameters either we can observe (time to expiration, stock price), we know (strick price) or we can assume (risk free rate). Implied vol is the plug-in number to make the BSM balance. As S2000magician mentioned, it’s the volatilly assuming options are priced correctly.

I believe you need a computer / program to calculate it, so I don’t think you’ll be asked to do it in CFA exam.

You _ will not have to do this _ on the exam.