Implied Volatility (Put-Call Parity) [Market A(2), slide 67]

[mikey10011]

David,

Unfortunately I am using an ancient edition of Hull and thus do not have his chapter on volatility smile.

From slide 48 I know that implied volatility can be determined through "goal seeking."

I listened carefully to slide 67 but didn't understand what the second line means (e.g., "market" call/put, underlying S0). Could you say more about it and perhaps give a sample calculation? For example are the strike prices of the two equations the same?

 

[David Harper CFA FRM]

Mikey,

Agree, it's not well explained....next time i will use numbers to show that.

Here is a small XLS to show it.

Note, to your question, yes put-call parity does require strike prices and maturities to be identical.
So, in the XLS I have two columns.
The first column (BS model value of the call) takes 50% volatility as an input, then solves for black-scholes call and put.
The second column "simulates" implied volatility: it assumes we observe market price of call = $2.00, then goal seeks to find the implied volatility (you cannot do this in EditGrid, but it is just tweaking the volatility until the call option equals the market price). In this example, implied volatility = 46%.

The point of slide 67, from Hull Ch 16, is that the "error" of $0.14 ($2.14 BS model price - $2 observed market price of call) is the same for both the call and put.

Thanks, David