How can we price options on index futures. I think we should take Black model instead of Black Scholes model for pricing of these contracts. The term ln(F/K) becomes zero for these contracts.For index futures, you need to pay only some percentage of the Notional as margin money (not the full amount when you hedge with Stocks) Suppose 3m treasury rates are 3% , how would you take interest free rates for short term futures in Black Scholes or Black Model.This becomes a bigger issue in pricing, when we see Index Futures trading at discount compared with the spot. How should we take up this.

QuoteOriginally posted by: FinBeeHow can we price options on index futures. I think we should take Black model instead of Black Scholes model for pricing of these contracts. The term ln(F/K) becomes zero for these contracts.Could you please explain why / how the term ln(F/K) = 0?

QuoteOriginally posted by: VegawizardQuoteOriginally posted by: FinBeeHow can we price options on index futures. I think we should take Black model instead of Black Scholes model for pricing of these contracts. The term ln(F/K) becomes zero for these contracts.Could you please explain why / how the term ln(F/K) = 0?This is only true for ATMF options (F = K).

QuoteI think we should take Black's model instead of Black ScholesYes sort-of, since the underlying is a future, but keep in mind that the CME S&P 500 options are American Exercise not European.

Thanks for the replies. Vega and Fretty , sorry for the error. I made a wrong notion about ln(F/K). It will be Zero if the Future and Strike is the same. Here, we would be taking directly the future's price rather than Forwards since Future price is already available to us.How do we decide on the risk free interest rates if the futures are being traded at discount (may be due to depressed markets). Do we still take the riskfree rate at prevalent 3 month treasury rate for short term options. The question arises because we need to block a small fraction of money as Future's margin.

And I am trading in a market where Index Options are European in nature.Its really hard on Sellers to give quote for American options.

If you are trading Margined options on Index Futures, then yes, you should be using the Black (76) model. You should not require a risk free rate. The clearing house (usually) pays interest on cash margin balances, or you can lodge approved assets (typically sovereign bonds) that are interest earning, so there is no 'cost of funds' to model with respect to initial margin. Variation margin would, theoretically, be normally distributed with a mean of zero, therefore not worth modelling interest on variation margin.Keep it straight and simple - use the black 76 model. Since the options are on the future, the future and not the spot index is the underlying, so the fact that the future is trading discount to fair value should be of no consequence or interest to you, that should be for the index arb guys - delta one desk.

Vegawizard:QuoteKeep it straight and simple - use the black 76 model.I agree.