Multi-Curve Convexity

16 Pages Posted: 1 Oct 2015

Date Written: September 30, 2015


In this paper we analyse the impact of tenor basis in a multi-curve environment on the pricing of CMS instruments. CMS derivatives may be priced by means of a replication approach. Doing so the derivative is translated into a portfolio of Vanilla swaptions. On the one side multi-curve pricing enters into this approach by valuing the replicating vanilla swaptions. On the other side the basis between forward and discount curves also impacts the specification of the replication portfolio.

The specification of the replication portfolio is driven by the definition of an annuity mapping function. That function links the quotient of the discount factor for the pay date and the underlying swap rate annuity to the underlying swap rate. In this study we investigate the impact of the multi-curve setting on the specification of the annuity mapping function. As a result we find that the impact of multi-curve setting on the annuity mapping function is small compared to the impact of the multi-curve setting on the underlying Vanilla swaption prices.

Keywords: CMS replication, multi-curve pricing, tenor and funding basis

JEL Classification: E43, G12, G13

Suggested Citation

Schlenkrich, Sebastian, Multi-Curve Convexity (September 30, 2015). Available at SSRN: or

Sebastian Schlenkrich (Contact Author)

d-fine GmbH ( email )

An der Hauptwache 7
Frankfurt, 60313

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