Just one spot question: I've been told about an "at the money forward strike" in pricing options... anyone could advise why and how this one has to be used?Many thanks!

ATMF is simply where your forward price lies. The reason you use that, is because that's where your vol is centered.If you are ATMF, call & put are worth the same. Alot of expressions simplify dramatically when you are ATMF.But, obviously you can use any old strike you want. It just makes some things simpler that's all.Regards.

BM -Not sure if you were also wondering why the forward is used instead of the spot price. By using the forward, one can price the option without worrying about the time value of money, as the interest rate is already embedded in the forward price. The sum of all of these simplifications is to remove as many extraneous parameters as possible, so that the option price is a direct reflection of the volatility of the underlying. (In a very oversimplified way...)

With reference to currency options, At the Money Spot (ATMS) are options with a strike equal to the spot exchange rate. I think delta of this options is really influencend by dynamics of interest rate differential. At the Money Forward (ATMF) options have strike equal to the traded forward exchange rate; usually delta of these options are close to 0.5. Interesting is the right delta of ATMF options:given the BS european call value C = S.N(d1) - K.e(-r.(T-t)).N(d2)in a precedent thread regarding mathematical basis of atmf options delta was demonstrated that being d1 = 1/2.v.((T-t)^0.5) both v and (T-t) are greater than zeo => N(d1) must be bigger than 0.5. We are talking about spot delta for atmf, and spot-delta for atmf is converging towards 50%.If I understood correctly,Collector criticized this position giving a market reason to ATMF delta=>0.5, in particular substaining that at expiration date buyers of calls could choose the quantity of options to be exercised and the best choice for sellers is offering 0.5 delta. Do you subscribe to this point of view?

Thanks for your answers.I'd also like to know if it is a common market practice...

yes, it is.

QuoteOriginally posted by: mrbadguyWith reference to currency options, At the Money Spot (ATMS) are options with a strike equal to the spot exchange rate. I think delta of this options is really influencend by dynamics of interest rate differential. At the Money Forward (ATMF) options have strike equal to the traded forward exchange rate; usually delta of these options are close to 0.5. Interesting is the right delta of ATMF options:given the BS european call value C = S.N(d1) - K.e(-r.(T-t)).N(d2)in a precedent thread regarding mathematical basis of atmf options delta was demonstrated that being d1 = 1/2.v.((T-t)^0.5) both v and (T-t) are greater than zeo => N(d1) must be bigger than 0.5. We are talking about spot delta for atmf, and spot-delta for atmf is converging towards 50%.If I understood correctly,Collector criticized this position giving a market reason to ATMF delta=>0.5, in particular substaing that at expiration date buyers of calls could choose the quantity of options to be exercised and the best choice for sellers is offering 0.5 delta. Do you subscribe to this point of view?OTC currency options are considered at-the-money for the delta-neutral straddle. This is either slightly above or below the forward (by approx a factor of exp(0.5*vol^2*T) depending on the premium conventions used for the particular pair.

>OTC currency options are considered at-the-money for the delta-neutral straddle. This is either slightly above or below the >forward (by approx a factor of exp(0.5*vol^2*T) depending on the premium conventions used for the particular pair. You are close! The delta neutral strike is X=S*exp((b+v^2/2)T) where b is cost of carry underlying security, in case of fx options cost of carry is the interest rate differential. This is for the Black-Scholes-Merton formula. Or in other words the delta neutral spot price is naturally S=X*exp((-b-v^2/2)T)PS this is not at-the-money spot, neither at-the-money forward. But in practice one typically assume at-the-money-forward X=S*exp(bT) to give approx delta neutral straddle. This is only good approx as long as relatively short time to maturity and relatively low vol, as we typically have in FX. And yes I have seen traders gotting confused here in more extreme situations, long maturity high vol.

QuoteOriginally posted by: Collector>OTC currency options are considered at-the-money for the delta-neutral straddle. This is either slightly above or below the >forward (by approx a factor of exp(0.5*vol^2*T) depending on the premium conventions used for the particular pair. You are close! The delta neutral strike is X=S*exp((b+v^2/2)T) where b is cost of carry underlying security, in case of fx options cost of carry is the interest rate differential. This is for the Black-Scholes-Merton formula. Or in other words the delta neutral spot price is naturally S=X*exp((-b-v^2/2)T)PS this is not at-the-money spot, neither at-the-money forward. But in practice one typically assume at-the-money-forward X=S*exp(bT) to give approx delta neutral straddle. This is only good approx as long as relatively short time to maturity and relatively low vol, as we typically have in FX. And yes I have seen traders gotting confused here in more extreme situations, long maturity high vol.Yeah I think we have the same strike there - I was multiplying the fx forward (S*exp(bT) in your notation?) by exp(0.5*vol^2*T). That's cool for RHS prems like eur/usd which trades in usd prem. usd/jpy would also be usd prem but then taking account the premia into the delta we get strike of forward * exp (-0.5*vol^2*T) (ie below the forward)