Quanto Convexity in Notional-Reset Cross-Currency Swaps

Summary

The document considers whether valuation of a notional-reset cross-currency swap should account for the relationship between exchange rates and interest rates. In the example, one leg’s notional is reset using the spot exchange rate at the start of each coupon period. Although this construction removes direct exchange-rate exposure from the specified coupon payoff, the reset occurs before the coupon is paid, leaving a small convexity adjustment.

The answer attributes that adjustment to covariance between foreign exchange and the funding basis, defined as the difference between Libor and the discount rate. It also notes a separate adjustment associated with valuing JPY Libor under USD collateral rather than standard JPY Libor conventions. The common approximation omits these effects to avoid calibrating a diffusion model; the answer expects them to be small relative to currency basis delta. This is a simplified market-practice explanation, not a derivation or a claim that the adjustments are always negligible.

Key ideas

• A notional reset at the start of a period can create convexity when payment occurs later.
• The adjustment depends on covariance between foreign exchange and funding basis.
• USD collateralization of JPY Libor can add a further convexity adjustment.
• Ignoring these effects simplifies valuation by avoiding diffusion-model calibration.

Tags

# Quanto effect in cross currency mtm swaps


# Quanto effect in cross currency mtm swaps












Apparently the standard way to value these swaps involves ignoring the quanto effect, - ie the correlation between fx and rates. I wonder why this is - is this correl always so close to zero?

Eg of such a swap: swap 3m usd libor for 3m jpy libor, where jpy notional= 100mio jpy and usd notional for coupon i = 100mio x fxspot[jpyusd] at start of coupon i

(So usd leg coupon i notional is fixed in jpy - this is the quanto feature: the jpy p&l has zero fx exposure to usdjpy fx rate for such coupons) Note: these are aka notional-reset ccs

## Answer by AFK (score 2)

https://quant.stackexchange.com/a/37184

There is a small convexity adjustment coming from the fact that the notional resets at the beginning of a 3M period but is paid at the end. This convexity adjustment is driven by the covariance between FX and funding basis (Libor minus discount rate). Market also neglects the fact that JPY Libors are collateralised in USD which means there is a convexity adjustment compared to standard JPY Libors. The reason for this practice is that it makes the valuation much simpler as it avoids calibrating a diffusion model. The approximation is expected to be small compared to currency basis delta.

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