# Expectation of expression with two currencies under forward measure

I'm trying to calculate the expected value, at time $0$, of a cashflow paid at time $T$, resetting at time $t$. The coupon is of the form:

$V_0=\mathbb{E}^{T_2}\left[\frac{A_t^y(T_1,T_2)}{B_t^x(T_1,T_2)}C^y_t(T_1,T_2)\right]$

in which:

$A^y_t(T_1,T_2)$ is the price of a discount bond from $T_1$ paying at $T_2$, observed at $t$, in currency $y$,

$B^x_t(T_1,T_2)$ is the price of a discount bond from $T_1$ paying at $T_2$, observed at $t$, in currency $x$,

$C^y_t(T_1,T_2)$ is a floating rate for the period $T_1$ to $T_2$, observed at $t$ and paying at $T_2$, in currency $y$,

$\mathbb{E}^{T_2}$ represents the expectation taken in the $T_2$ forward measure in currency $y$.

We have that the processes $A$ and $C$ are martingale in the chosen measure. Assuming that the prcesses $A$, $B$ and $C$ are log-normal, how can we calculate the expectation taking account of the fact that $B$ is denominated in the currency $x$?

Any pointers or suggestions would be very much appreciated!

• Hi Drax81, welcome to Quant.SE! – Bob Jansen Nov 30 '15 at 6:52
• Your conditions are not enough. For example, you may need the correlation between the bonds, or floating rates, of currencies $x$ and $y$, and the respective volatilities. Can you please provide more informations? – Gordon Nov 30 '15 at 18:38
• Any reference for your question. If you can provide more background information, it may also be helpful. – Gordon Dec 1 '15 at 16:07