C# for Financial Markets

16

Multi-curve Building

16.1 INTRODUCTION AND OBJECTIVES

In this chapter we introduce and discuss multi-curve building. We build on the material in Chapter 15 that focused on traditional interest-rate models. These models assume some no-arbitrage conditions, in particular a strong relationship between forward rates and discount factors and between forward rates of different tenors. During the 2007 crisis it became clear that these no-arbitrage assumptions could break down due to counterparty and liquidity risk, for example. Moreover, it became more important to collateralise OTC deals in order to reduce the risk involved in bilateral transactions. The multi-curve framework was introduced precisely for the purpose of dealing with collateralised derivatives and with the new behaviour of the forward rates. The traditional framework, using the same curve for discounting and for estimating forward rates, was not flexible enough to capture these features; some ‘new’ formulae are required. The approach in this chapter is hands-on and we pay attention to the code design by focusing on practical cases related to interest rate derivatives evaluation.

This is a large and important chapter; we have created a number of applications and have used several .NET libraries in order to show how multi-curve technology can be used. For this reason, we develop the theory and we give numerous examples of use. Some of the examples can be found in this chapter while more advanced examples are to be found ...