# Reverse convertible quanto decomposition

I'm trying to decompose the pricing of a reverse convertible when quantoed. Say my domestic currency is EUR and the stock $S$ currency is USD. The quanto reverse convertible, structured as a ZC bond and a put then needs to be adjusted in the pricing.

The dynamic of the stock for the put, from what I understood, is adjusted with $\rho\sigma_X\sigma_S$, where $X$ is the exchange rate.

My question is what about the ZC part ? I guess the answer is not as basic as "do a rates differential". My feeling is that if the investment is in EUR, trader will have to fxswap, therefore changing EUR in USD, lending USD, and discounting in EUR. Am I correct ?

With a practical example, my EUR and USD 1Y rates are around -0.25% and 2.8%, the spot EUR/USD 1.17, this would give a differential of 360 bps. In the case the quanto was USD and stock EUR, the differential would be around 250 bps.

• The short put is a EUR put on a USD asset. The asset dynamics need to be adjusted to account for the quanto effect. The ZC remains a vanilla ZC in EUR. – Ivan Jul 17 '18 at 21:52
• What about the put then, which flows are payed in USD, don't they have to be swapped in EUR ? I have access to an Excel Black Scholes quanto pricer and a quanto reverse pricer from a bank. The reason why I'm asking is that the difference between a plain vanilla and a quanto reverse is close to the gap between interest rates, but I can't reproduce: the BS pricer gives me an adjustment that widens the gap. Any clue ? @Ivan – Cedric_W Jul 18 '18 at 6:48