Kriging of financial term-structures

Abstract

Due to the lack of reliable market information, building financial term-structures may be associated with a significant degree of uncertainty. In this paper, we propose a new term-structure interpolation method that extends classical spline techniques by additionally allowing for quantification of uncertainty. The proposed method is based on a generalization of kriging models with linear equality constraints (market-fit conditions) and shape-preserving conditions such as monotonicity or positivity (no-arbitrage conditions). We define the most likely curve and show how to build confidence bands. The Gaussian process covariance hyper-parameters under the construction constraints are estimated using cross-validation techniques. Based on observed market quotes at different dates, we demonstrate the efficiency of the method by building curves together with confidence intervals for term-structures of OIS discount rates, of zero-coupon swaps rates and of CDS implied default probabilities. We also show how to construct interest-rate surfaces or default probability surfaces by considering time (quotation dates) as an additional dimension. JEL classification C63; E43; G12

Gaussian processes for computer experiments

“…where the covariance parameters (σ and θ) have been estimated using the suited cross validation method described in [14] and [37]. We getθ = 30 andσ = 0.93.…”

“…The suggested model (1) has been applied to finance and economic domain to estimate discount factors and default probabilities [14]. In this section, we focus on discount factors.…”

“…For example, in Banking and Finance, the discount factor is known to be monotone (non-increasing) with respect to time-to-maturities [14]. In computer experiment framework, Gaussian Process (GP) is a popular model [50].…”

“…The contributions which are presented in Sections 2, 3 and 4 correspond to the references [14,35], [49] and [12,13].…”

Fifty Years of Kriging

“…Other paradox: originating from mining estimation problems, and very close to statistical regression from a theoretical standpoint, it was not obvious that kriging would be considered in other domains than mining and earth sciences. However applications now consider, for example, the design of aircrafts (Chung and Alonso 2002), the prediction of the mechanical properties of nanomaterials (Yan et al 2012), the optimization of supply chain networks (Dixit et al 2016), the construction of financial term-structures (Cousin et al 2016), the modeling of social systems (Oliveira et al 2013), and in all cases the quantification of the uncertainty.…”