# Black (1976) model: boundary conditions with non-convergence of spot and forward prices

Let's suppose we have a futures contract F in a market where the relation

$$F(t,T)=S(t)e^{r(T−t)}$$ doesn't hold.

What are the the boundary conditions for the derivation of the Black (1976) formula??

• @MattWolf: I probably mislead you with the title. Imagine we have convergence but $F(t,T)=S(t)\exp (r(T−t))$ does not hold. From what was told to me, we can still apply the Black model. Therefore, I want to know how can we specify yhe boundary conditions. Aug 20, 2013 at 10:41
• I see. But if we have the Black formula $C=\exp(-r(T-t))(FN(d_1)-KN(d_2))$, does this mean we are assuming the relation $F(t,T)=S(t)\exp(r(T−t))$ is verified? or can we get the exact same expression for C without using that relation? Aug 20, 2013 at 14:11
• @JoaoSerafim please use the math formatting feature of the site it really makes quesations and comments more readable.
– SRKX
Aug 20, 2013 at 15:50
• @SRKX Ok. I will do that. Aug 20, 2013 at 18:42
• @MattWolf: I'm sorry but I'm getting a little bit confused. I'm going to reformulate my question. For example, in the context of stock markets, the price for an european call option on futures is given by the previous $C$ expression. Now let's imagine we are going to study another market and in this market the relation doesn't hold. Is it possible that the price of the options (in that new market) is still given by the exact $C$ expression? Aug 22, 2013 at 12:01