The Gaussian affine interest rate models are widely used in the financial industry for pricing, hedging and also risk management purposes. We consider the multifactor models with time dependent parameters. Usually the models are simulated using some appropriate discretization schema because the...

We give explicit algorithms and source code for extracting factors underlying Treasury yields using (unsupervised) machine learning (ML) techniques, such as nonnegative matrix factorization (NMF) and (statistically deterministic) clustering. NMF is a popular ML algorithm (used in computer...

We derive expected bond return equations for various structural credit valuation models with alternative stochastic processes and boundary conditions for default given in Merton [1974], Merton [1976], Black and Cox [1976], Heston [1993], Longstaff and Schwartz [1995], and Collin-Dufresne and...

The shape of the VIX term structure conveys information about the price of variance risk rather than expected changes in the VIX, a rejection of the expectations hypothesis. A single principal component, Slope, summarizes nearly all this information, predicting the excess returns of S&P 500...

Term premiums, defined as the excess return of long-dated contracts over short-dated contracts, in commodity futures are strongly predictable, both in the time series and in the cross section, by roll yield spreads. Strategies that exploit this predictability show sizable Sharpe ratios and are...

This paper presents a critical review of the different versions of the LIBOR market model (LMM). Based on the new taxonomy of the term structure models (see Nawalkha, Beliaeva, and Soto [2007a, 2007b]) the typical application of the LMM are shown to triple-plus type, exposing these to the...

Does the selection of a specific interest rate model to use for pricing, hedging, and risk-return analysis depend upon whether the user is a buy-side institution or a sell-side dealer bank? Sanjay Nawalkha and Riccardo Rebonato debate this question in this paper and provide some insightful...

We study the risk-reversal premium, where out-of-the-money puts are over-priced relative to out-of-the-money calls. This effect is driven by investors’ utility preferences which lead them to over-pay for the risk reduction benefits of long puts instead of valuing options on the basis of...

Quanto CDS spreads are differences in CDS premiums of the same reference entity but in different currency denominations. Such spreads can arise in arbitrage-free models and depend on the risk of a jump in the exchange rate upon default of the underlying and the covariance between the exchange...

SABR stochastic volatility model is appealing for modeling smile and skew of option prices. Hagan, who first proposed this model, derived a closed form approximation for european options and showed that it provides consistent and stable hedges. Here I prove a new exact closed formula for the...