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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.

We study international interbank spreads within a no-arbitrage dynamic term structure model and attempt to disentangle time-varying risk premia in the interbank market for major currencies. Our results suggest that, at the peak of financial crisis, the interbank spread was clearly driven by liquidity risk. In the aftermath of the crisis, credit risk has become the dominant driver of the spread. This effect is stronger in the Euro and UK markets, due to the escalation of the European sovereign debt crisis, and weaker in the Japanese market which experienced remarkably low credit pressures. Furthermore, we assess the effectiveness of monetary policy actions and demonstrate that the establishment of the unconventional policy programmes led to the deterioration of liquidity risk in the interbank market, and the policy of major Central banks to substantially cut interest rates kept credit pressures at low levels. We also partition the spread into expectation hypothesis and time-varying risk premium components and reject the hypothesis of constant risk premium. We find strong evidence of predictability inferred from the interbank spread model with time-varying risk premia.