Our friend above as a newbie asked a simple question ... "What Implied Vol is and how it affects different Warrants. E.G. a Warrant with a Vol of 22 and a Warrant with a vol of 66."
I gave a simple definition of I/Volatility ... designed to help a newbie get a simple idea of I/Volatility ... it was not meant to be distorted by pedantic argument which is now seeing this thread heading for the bushes ...
BSOMP modeling are complex numbers that are be interpreted at a number of levels ... this is the beauty of the mathematics.
Your example of $12.00 NCP and 10.50 strike with 35% I/V is far too simplistic ... as was perhaps my definition. Obviously it is not meant to read strictly in the literal sense ... the 35% represents the probability ... the fact that the underlying has already gone beyond the Strike is not the point nor meant to be read that way.
The reference to Strike and Expiry is deliberate and BSOPM faithful would have realised this as definitive expressions delineating between H/Vol and I/Vol.
H/Vol is a completely different formula and not related to BSOPM.
Specifically, BSOPM models I/Vol (V) as the square root of the annualised variance V2.
NOW CRASHY MY SON ... READ MY LIPS ... the BSOPM theorum was written specifically for OPTIONS WRITERS ... and at the concept level, the PRICE and IMPLIED VOLATILITY elements were separated and designed to be DYNAMIC ... key in one you get the other and vice versa ...
The market determines both Price and I/Volatility.
An OPTIONS WRITER has an interest in VOLATILITY of the UNDERLYING as it relates to the likelihood or RISK to the WRITER of him being EXERCISED usually (original Euro. concept) at EXPIRY should the UNDERLYING REACH THE STRIKE.
The WRITER can determine his level of REWARD (PREMIUM) and RISK by varying the STRIKE and EXPIRY.
So, the connection between the Strike ... the Expiry and Volatility (Risk of being Exercised) have been established.
VOLATILITY at this concept level relates to the probability or RISK (to the WRITER) of the UNDERLYING reaching the STRIKE PRICE by EXPIRY= RISK OF EXERCISE. (original concept model).
BSOPM theorum introduces a THIRD element that DYNAMICALLY allows the WRITER to make a RISK JUDGEMENT for VOLATILITY of the UNDERLYING and COMPENSATES the WRITER where this higher RISK of EXERCISE occurs with a HIGHER PREMIUM and is DYNAMICALLY adjusted by IMPLIED VOLATILITY number.
At this CONCEPT level it is generally recognised that IMPLIED VOLATILITY does relate as a NUMBER represented as a PERCENTAGE (for ease of use) as being representative of the RISK of the UNDERLYING reaching the STRIKE by the EXPIRY date causing an EXERCISE of the OPTION for which the WRITER is compensated with a higher PREMIUM.
There maybe others who have a different interpretation but you now have an understanding of mine ...
