Quanto Reverse Convertibles: FX Effects on the Put and Bond

Summary

The document raises a pricing question about a reverse convertible denominated in euros and linked to a US dollar stock. It frames the product as a zero-coupon bond combined with a put, and asks how quanto adjustment affects both components. For the stock-linked put, the author understands that the equity drift adjustment depends on the correlation between the stock and exchange rate and on their volatilities.

The unresolved issue is how to treat the bond component. The author proposes converting euros to dollars through an FX swap, lending in dollars, and discounting in euros, while questioning whether the appropriate adjustment can be reduced to a simple interest-rate differential. Illustrative one-year rates and an exchange rate are supplied for both currency orientations. The text contains no confirmed derivation, pricing model, or answer, so it is useful as a prompt about quanto valuation rather than evidence that the suggested funding treatment is correct.

Key ideas

• Quanto pricing can affect the equity-linked option through stock and FX dependence.
• The author models the reverse convertible as a zero-coupon bond plus a put.
• The treatment of the bond component under a quanto payoff remains unresolved in the document.
• The suggested FX swap and lending approach is a hypothesis, not a demonstrated valuation method.

Tags

# Reverse convertible quanto decomposition


# 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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.