# Quanto Factor - FX Forward

In the paper Quanto Options by Uwe Wystup the "quanto factor" $Q$ is used to describe forwards/options when quanto-ed into a different currency, e.g.

$$\text{Quanto Forward Value} = Q \cdot e^{-r_Q T}\cdot \phi \cdot (S_0 \cdot e^{\tilde\mu T}-K)$$

where $K$ denotes the strike, $T$ the expiration time, $\phi=\pm1$ the usual long-short indicator, $S_0$ the underlying and $Q$ the quanto factor.

The paper never explicitly says (or at least I don't see it), what $Q$ is. Do we have something like $$Q = e^{\rho \cdot \sigma_{1} \cdot \sigma_{2}}$$ ?

• According to the book FX Options by Wystup "A Quanto Option can be any type of cash settled option, whose payoff is converted into a third currency at maturity at a pre-specified rate called the Quanto Factor". So whereas an ordinary FX option involves 2 currencies, a Quanto Option involves 3. HTH. – noob2 Aug 24 '18 at 12:46