# 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

• Pls try to explain why you think this is exposed to the correlation between fx and rates. There is no fixed rate leg in the basis swap so I don't see where that is coming from.
– dm63
Dec 2, 2017 at 11:23
• value of interest in coupon i in usd for usd leg = E(Fi * 100mio jpy x jpy/usd[i]) where Fi = 3m usd libor for cpn i. so we can see here that this expectation must take into account the correlation between 3m usd libor and the fx rate Dec 3, 2017 at 18:18
• dm63 can you answer? Dec 7, 2017 at 12:29

## 1 Answer

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.

• I dont fully understand your answer and its not what i was expecting ! what does it matter if the notional fixes in advance or in arears ? in both cases there is a quanto affect. can you show mathematically your point maybe? Dec 3, 2017 at 18:13
• AFK can you answer? Dec 7, 2017 at 12:29
• When the notional resets, you change the USD floating leg notional, which means that you borrow or lend some dollars at libor flat until maturity. What is the value of this loan? Zero, if you are discounting at libor. If you are discounting at Fed Funds (more likely), then the value depends on what is happening with the libor-fed funds basis. If that is correlated with the currency basis, you may have a small convexity adjustment.
– dm63
Dec 7, 2017 at 17:35