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 itself is discussed. The criterion for inclusion in this survey is that the method has been implemented by a software vendor (or indeed an inhouse developer) as a viable option for yield curve interpolation. As will be seen, many of these methods suffer from problems: they posit unreasonable expections, or are not even necessarily arbitrage free. Moreover, many methods lead one to derive hedging strategies that are not intuitively reasonable. In the last sections, two new interpolation methods (the monotone convex method and the minimal method) are introduced, which it is believed overcome many of the problems highlighted with the other methods discussed in the earlier sections.Yield curve, interpolation, bootstrap,

Recently the SABR model has been developed to manage the option smile which is observed in derivatives markets. Typically, calibration of such models is straightforward as there is adequate data available for robust extraction of the parameters required asinputs to the model. The paper considers calibration of the model in situations where input data is very sparse. Although this will require some creative decision making, the algorithms developed here are remarkably robust and can be used confidently for mark to market and hedging of option portfolios.SABR model, equity derivatives, volatility skew calibration, illiquid markets,

Abstract. Let M be a von Neumann algebra with a faithful, finite, normal tracial state τ , and let A be a finite, maximal subdiagonal algebra of M. Let H 2 be the closure of A in the noncommutative Lebesgue space L 2 (M, τ). Then H 2 possesses several of the properties of the classical Hardy space on the circle, including a commutant lifting theorem, some results on Toeplitz operators, an H 1 factorization theorem, Nehari's Theorem, and harmonic conjugates which are L 2 bounded.

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Let M be a von Neumann algebra with a faithful normal tracial state τ and let H ∞ be a finite maximal subdiagonal subalgebra of M. In previous work we defined a harmonic conjugate relative to H ∞ . Let H 1 be the closure of H ∞ in the noncommutative Lebesgue space L 1 (M). By analysing the behaviour of the harmonic conjugate in L 1 (M), we identify the dual space of H 1 as a concrete space of operators.