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Non-Martingale Dynamics for Two Curve Derivatives Pricing

Mauricio Alvarez-Manilla

Mitsubishi UFJ Securities International plc

April 16, 2012

Given a forwarding LIBOR-style curve F corresponding to a fixed tenor (e.g. 6m) and an exogenous discounting curve D (e.g. an OIS curve or cross-currency basis swap curve) we build on Bianchetti's results to propose dynamics for the forward LIBOR-style rate collateralized by D.

In contrast with what other authors do (Bianchetti, Mercurio, Fujii, et al.) we do not assume that the collateralized forward rate is a martingale process under the corresponding forward risk neutral measure associated with the discount process. At time zero the collateralized forward rate is the forwarding curve rate multiplied by a quanto adjustment, but at reset time the expectation of the collateralized forward aligns with the forwarding curve rate.

In order to calculate the quanto adjustment we show how to construct a deterministic drift, which can be computed with the information available at time zero by bootstrapping (under certain assumptions on the spot swap rates). We extend the result to forward swap rates in the context of swap market models.

Number of Pages in PDF File: 20

Keywords: non-martingale, two curve framework, multi-curve, collateralized forward rates, curve bootstrapping, multiple yield curves, forward curve, discount curve, basis adjustment, quanto adjustment, swap market models, LIBOR market models, interest rate derivatives, FRAs, swaps, swaptions, overnight index

JEL Classification: E43, G12, G13

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Date posted: April 16, 2012  

Suggested Citation

Alvarez-Manilla, Mauricio, Non-Martingale Dynamics for Two Curve Derivatives Pricing (April 16, 2012). Available at SSRN: https://ssrn.com/abstract=2040581 or http://dx.doi.org/10.2139/ssrn.2040581

Contact Information

Mauricio Alvarez-Manilla (Contact Author)
Mitsubishi UFJ Securities International plc ( email )
Ropemaker Place
25 Ropemaker Street
London, EC2Y 9AJ
United Kingdom
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