UD @ World Finance Conference (Buenos Aires, July 2015)

We are happy to announce that our work from last year on interest rate risk has been accepted for presentation at the World Finance Conference. The conference will take place in Buenos Aires (Argentina) on 21-24 July, where we will talk about our geometry paper (and maybe mention our related works).

More detailed information about the content of the conference will follow in future posts. Stay tuned!
 

Curiosities on the Monotone Preserving Cubic Spline

In this paper we describe some new features of the monotone-preserving cubic splines and the Hyman’s monotonicity constraint, that is implemented into various spline interpolation methods to ensure monotonicity. We find that, while the Hyman constraint is in general useful to enforce monotonicity, it can be safely omitted when the monotone-preserving cubic spline is considered. We also find that, when computing sensitivities, consistency requires making some specific assumptions about how to deal with non-differentiable locations, that become relevant for special values of the parameter space.

Keywords: Yield curve, fixed-income, interpolation, Hyman, monotone preserving cubic splines.

Click here for the full paper.

The Geometry of Interest Rate Risk

In this paper we consider the process of interest rate risk management. The yield curve construction is revisited and emphasis is given to aspects such as input instruments, bootstrap and interpolation. For various financial products we present new formulas that are crucial to define sensitivities to changes in the instruments and/or in the curve rates. Such sensitivities are exploited for hedging purposes. We construct the risk space, which eventually turns out to be a curve property, and show how to hedge any product or any portfolio of products in terms of the original curve instruments.

Keywords: Yield curve, hedging, interest rate risk management.

Click here for the full paper.

On the non-differentiability of Hyman Monotonicity constraint

In this paper we describe some new features of Hyman’s monotonicity constraint, which is implemented into various cubic spline interpolation methods. We consider the problem of understanding how sensitive such methods are to small changes of the input y-values and, in particular, how relevant Hyman’s constraint is with respect to such changes. We find that many things cancel out and that eventually Hyman’s constraint can be safely omitted when the monotone-preserving cubic spline is used. We also find that consistency requires including some specific boundary conditions that become relevant for special values of the parameter space.

Keywords: Yield curve, interpolation, monotone preserving cubic splines.

Click here for the full paper.