Pricing Mark-to-Market Basis Cross Currency Swaps and Subsequently Constant Notional

Hey guys,

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 (This post 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 :) ):

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.

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 maybe determine via historical data, as well as the volatility terms, in case data is 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 second question is how banks deal with this problem? Do they go for a convexity adjustment for pricing then CN CCS? 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,