Abstract
In this paper we propose a double curving setup with distinct forward and discount curves to price constant maturity swaps (CMS). Using separate curves for discounting and forwarding, we develop a new convexity adjustment, by departing from the restrictive assumption of a flat term structure, and expand our setting to incorporate the more realistic and even challenging case of term structure tilts. We calibrate CMS spreads to market data and numerically compare our adjustments against the Black and SABR (stochastic alpha beta rho) CMS adjustments widely used in the market. Our analysis suggests that the proposed convexity adjustment is significantly larger compared to the Black and SABR adjustments and offers a consistent and robust valuation of CMS spreads across different market conditions.
Highlights
The recent financial crisis has led, among others, to unprecedented behavior in the money markets, which has created important discrepancies on the valuation of interest rate financial instruments
In this paper we have developed a new constant maturity swaps (CMS) convexity adjustment in a double-curve framework, that separates the discounting and forwarding term structures
The motivation of our study comes from the unprecedented increase in the Libor-overnight index swap (OIS) spread that was experienced during the financial crisis, which has questioned the legitimacy of considering both (Libor and OIS) quotes as risk-free, and has raised valid issues in the construction of zero-coupon curves, which clearly, can no longer be based on traditional bootstrapping procedures
Summary
The recent financial crisis has led, among others, to unprecedented behavior in the money markets, which has created important discrepancies on the valuation of interest rate financial instruments.
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