Currently I'm working on my Master Thesis in Quant Finance in cooperation with a company. I would like to thank you very much for your time and help in advance!

In my thesis I want to price Mark-to-Market (MtM) Basis Cross Currency Swaps (CCS) and subsequently the Constant Notional (CN) version. So far, I'm following the multi curve framework described here

Fujii, Masaaki; Shimada, Yasufumi; Takahashi, Akihiko (2010): A Note on Construction of Multiple Swap Curves with and without Collateral. In FSA Research Review 6, pp. 139–157.

My first question is, whether this is in general a good approach, i.e. applied by the majority of practitioners? Or is there something else out there you have heard about? The goal is to price these products precisely and to follow market practice.

The rest is addressed to people who know the multi curve approach very well, because it is a very detailed question. However, if you would like to know more about this approach don't hesitate to ask me :). So far, I followed this approach and the last ingredient missing is the convexity adjustment mentioned p.14-16. The JPY discounting curve USD collateralized need to be derived via MtM CCS because the CN data is not available (I'm applying this on EURUSD and not JPYUSD). For that purpose I found a paper, which specifies the convexity adjustment analytical, i.e. did the whole derivation for me on p. 29/30 :D

Moreni, Nicola; Pallavicini, Andrea (2015): FX Modelling in Collateralized Markets: foreign measures, basis curves, and pricing formulae. In SSRN Journal.

To specify the volatility of the diffusion terms, I would like to use market data of FX Options EURUSD and Options on 3M USD Libor. The correlation term I will determine via historical data. Is that data available? I checked Bloomberg and Reuters, and it seems that Options on 3M USD Libor are not available.

Another goal of the thesis is, to check how much influence the convexity adjustment has and whether it can be neglected. I thought that neglecting the convexity adjustment is actually not a problem, because the derived discounting curve (in my case: EUR discounting collateralized with USD) might be slightly wrong, because it neglects the adjustment. But when pricing other MtM swaps I will ignore again the convexity adjustment, which kind of equalizes the first error. In other words, I calibrate my curve on market data, which I hit in the end; therefore, I will price MtM swaps correctly even though I ignore the convexity adjustment. If this is correct, the only reason for a convexity adjustment is to price CN swaps in the end, because they don't contain such an adjustment and I would use a curve discounting curve containing a bias because of an ignored adjustment. My third question is how banks deal with this problem? Do they go for a convexity adjustment for pricing subsequently CN CCS? Are there other easier ways for estimating it? Or is it possible that they say, ok there is an adjustment, but the influence is so small, that we can hide this adjustment in wider spreads?

Again, thank you very much for your time!

Kind regards, Pablo


2 Answers 2


Most banks consider this convexity too small to worry about. A typical approach is to model a mtm basis swap using notionals that correspond to the fx forward rates for each period. Every day these notionals are adjusted for moves in fx. If there were significant convexity effects, those adjustments would cause a material pnl, but I haven't seen that in practice.


As to "precise pricing" ACT Treasurer's Wiki shows that in practise the reason a swap is cheaper than 2 outrights is the hedging cost - with a swap the market maker need not hedge in the FX market at all.

As to which interest rate curve you choose, in my view that's all about the hedging cost in the money markets, and as to why there's a convexity it's all about predicting cash flow payments for the hedge. You've got this quant finance answer, and this one

How much influence does a convexity adjustment have? How does the bank deal with the problem of convexity? I guess that if the bank loses money on hedging these deals then they either get out of the swap pricing business or replace the traders.


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