More Numerix Quantitative Research

Mar 23, 2012


In this paper, authors Alexander Antonov, PhD, and Michael Spector, PhD, present advanced analytical formulas for SABR model option pricing.The first technical result consists of a new exact formula for the zero correlation case. This closed...
May 1, 2010

In this article, we present the analytical approximation of zero-coupon bonds and swaption prices for general short rate models. The approximation is based on regular and singular expansions with respect to the small volatility and contains a low-...
Jun 25, 2009

In this article,we introduce a method for volatility computation from listed prices of American options on a un- derlying close to log-normal. From prices of American calls and puts, traded at an exchange at multiple strikes we compute the...
Jun 25, 2009

In this article, we give a general treatment of the Vanna-Volga mark-to-market volatility smile correction in application to pricing of contracts with European exercise on a single underlying. The method remains applicable in cases of delayed or...
May 6, 2009

In this article, we present a simple bottom-up dynamic credit model that can be calibrated simultaneously to the market quotes on CDO tranches and individual CDSs constituting the credit portfolio. The model is most suitable for the purpose of...
Jan 1, 2009

In this paper, we develop a series of approximations for a fast analytical pricing of European constant maturity swap (CMS) products, such as CMS swaps, CMS caps/floors, and CMS spread options, for the LIBOR Market Model (LMM) with stochastic...
Jun 16, 2008


In this article, we develop a technique of parameter averaging and Markovian projection on a quadratic volatility model based on a term-by-term matching of the asymptotic expansions of option prices in volatilities. In doing so, we revisit...
Mar 12, 2008


Markovian Projection is an optimal approximation of a complex underlying process with a simpler one, keeping essential properties of the initial process. The Heston process, as the Markovian Projection target, is an example.

In this...
Aug 29, 2007


In this article, we propose a new model for the dynamics of the aggregate credit portfolio loss. The model is Markovian in two dimensions with the state variables being the total accumulated loss Lt and the stochastic default intensity λt....
Aug 29, 2007


In this paper, we develop a systematic approach to Markovian projection onto an effective displaced diffusion, and work out a set of computationally efficient formulas valid for a large class of non-Markovian underlying processes. The generic...

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