Black Sholes formula vs Black formula

[quantlego]

For equity and FX, people often use BS formula where the underlying is spot, while for commodity, the Black formula is often used where the underlying is forward price.

SO my question is, when using forward price as underlying, how to defne at-the money? It means strike = spot or strike = forward? Also, when using Black formula, the calculated implied volatility is the volatility of forward price or spot price?

Thanks for clarification.

 

[themarketprofessor]

It's all trading conventions! I suggest that before you use BS/B formula, you should throughly understand the fundamental intruments that are quoted/traded in the markets including equities spot markets, index futures, fx forward outrights, commodities futures, and how these contracts are traded and where. Importantly understand the relationship between spot and its counter part contracts (ie forwards and futures). Next is to know what are the vanillas traded in each markets (Eq, Fx, Com), whether it is vanilla on forwards (eg equities and fx), vanillas on futures ( commodities). This is a good exercise, why? Because you don't need a model or formula to understand all these.

When using a model or formula, one must know all the hidden assumptions, which are very often contradictive to the real world.

BS is equivalent to B which is written in terms of forward. Implied vol is simply an inversion of price thru BS/B formula.

ATM is a well-defined convention in each asset class. Different ATMs conventions are used in FX. You just need to know what ATM convention is used, then the equivalent imp vol follows.

Good luck!

 

[Gavin Bird]

For equity and FX, people often use BS formula where the underlying is spot, while for commodity, the Black formula is often used where the underlying is forward price.

SO my question is, when using forward price as underlying, how to defne at-the money? It means strike = spot or strike = forward? Also, when using Black formula, the calculated implied volatility is the volatility of forward price or spot price?

Thanks for clarification.

Hi there! I think it depends on the underlying. If the underlying is the spot, then the strike price is all about the spot price and so does the implied vol.

 

[themarketprofessor]

There are holes in the Black-Scholes formula, so use and trust Black formula!!!

 

[pingu]

There are holes in the Black-Scholes formula, so use and trust Black formula!!!

do you mean the Blacksc formula?