In-Arrears Term Structure Products: No Arbitrage Pricing Bounds and the Convexity Adjustments
25 Pages Posted: 19 Oct 2009 Last revised: 16 Nov 2012
Date Written: October 16, 2009
When pricing an in-arrears term structure product, the valuation usually boils down to determining the price of a vanilla product and of some additional part. To computer the price of the additional part, sometimes a specific term structure (like Gaussian or LIBOR) is assumed. Sometimes approximation methods are applied to achieve model-independent valuation formulae. In the present paper, we show that these valuation formulae (the price of vanilla products plus convexity adjustments resulting from approximation) are in effect model-independent pricing bounds in every arbitrage-free model. More specifically, they are proven to be a lower pricing bound for in-arrears payer swaps and in-arrears caps and an upper bound for in-arrears receiver swaps and in-arrears floors. To address the goodness/tightness issue of the bounds, convexity adjustments are compared with the exact pricing formulae obtained in LIBOR market model.
Keywords: In-arrears Swaps, In-arrears Caps and Floors, Convexity Adjustments, Pricing Bounds, Risk-neutral Pricing, Change of Measure.
JEL Classification: G12
Suggested Citation: Suggested Citation