P. S. Hagan

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We study the SABR model of stochastic volatility [10]. This model is essentially an extension of the local volatility model [6], [4], in which a suitable volatility parameter is assumed to be stochastic. The SABR model admits a large variety of shapes of volatility smiles, and it performs remarkably well in the swaptions and caps / floors markets. We refine(More)
SFI Working Papers contain accounts of scientific work of the author(s) and do not necessarily represent the views of the Santa Fe Institute. We accept papers intended for publication in peer-reviewed journals or proceedings volumes, but not papers that have already appeared in print. Except for papers by our external faculty, papers must be based on work(More)
This paper surveys a wide selection of the interpolation algorithms that are in use in financial markets for construction of curves such as forward curves, basis curves, and most importantly, yield curves. In the case of yield curves the issue of bootstrapping is reviewed and how the interpolation algorithm should be intimately connected to the bootstrap(More)
We analyze an increasingly popular NMR method analogous to the black lipid membrane (BLM) isotopic tracer experiment for the study of mediated cation transport but involving the preparation of vesicles with an environment asymmetric in that paramagnetic metal ions are present only outside the vesicles. This asymmetry is manifest in the NMR spectrum as two(More)
Microbialites are sedimentary deposits formed by the metabolic interactions of microbes and their environment. These lithifying microbial communities represent one of the oldest ecosystems on Earth, yet the molecular mechanisms underlying the function of these communities are poorly understood. In this study, we used comparative metagenomic and(More)
input is perturbed (the method is not local). In Hagan and West [2006] we introduced two new interpolation methods—the monotone convex method and the minimal method. In this paper we will review the monotone convex method and highlight why this method has a very high pedigree in terms of the construction quality criteria that one should be interested in.(More)
This paper describes the oxidation of iron-rich uranium-bearing rocks by infiltration of groundwater. A reaction-diffusion model is set up to describe the sequence of reactions involving iron oxidation, uranium oxidation and reduction, sulphuric acid production, and dissolution of the host rock that occur. On a geological timescale of millions of years, the(More)
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