Pricing Partners attends leading conference on inflation in London.Organized by Risk, this conference gathered leading professionals on inflation derivatives products. Leveraging on previous research works, Eric Benhamou presented his latest thoughts on inflation derivatives modeling and in particular the new generation inflation index model.

Risk Inflation Conference paper

Inflation Derivatives Series, Part 1: Inflation Seasonality

Inflation Derivatices Series, part 2: Inflation Market Model

Inflation Derivatices Series, Part 3: Inflation Index Model

Investment banks have an increasing need for computation power. Grid computing represents today a challenging technology for exploiting the capacity of thousands of interconnected computers. This set of papers presents the design and architecture of a complete distributed system for financial sensitivities computation. As Microsoft Excel is widely used in investment banks it appears necessary to allow users to submit computations to the grid directly from Excel. Pricing Partners develops an extensible and modular financial library for Excel named Price-it®. A primary objective is to distribute Price-it® computations on a grid; a more general purpose is to be able to distribute any C++ financial library such as Price-it®. This first paper deals with the technical aspects related to the use of Excel as a client for a grid computing system built on top of a C++ library.

In order to distribute computations initiated from Excel and executed in a library, special attention has to be given to the existing interfaces between Excel and the library. By building specific interfaces between Excel and the library, one extends the functionalities of Excel by providing functions to the user. Two interfaces commonly used in banks are going to be presented in details: the XLL interface (eXceL Library) and the...

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An Euler scheme approximation enables one to discretize virtually any jump diffusion process in a PIDE or Monte Carlo simulation. It is simply a first order Taylor approximation. It is well known that the discretization error increases as soon as we use a step different from a critical value because of round off error effect.An improvement of this method is to use a predictor corrector method. Much has been said about this method for Monte Carlo simulation for diffusion but very little for PIDE and jump diffusions processes. The contribution of this paper is to examine the Predictor Corrector Method for jump diffusion both for PIDE and Monte Carlo simulations.

In the case of the PIDE, the initial scheme results in a Crank-Nickolson for the diffusion and an explicit Euler scheme for the jump part. We show that we obtain a fourth order convergence rate for the jump part. We also show that we can improve the accuracy error using a Runge Kutta method and an extension of the Simpson's rule. We also present two methods for computing the jump term: the traditional FFT and a straight integration. We discuss the stability of the initial numerical scheme (see [2]). In the case of the Monte Carlo, we show that the convergence rate (for strong and weak convergence, see [3] and [4]) improves only for the local volatility term. We provide numerical results for a specific model, namely the AA model. This model is simply a local volatility model with a Poisson jump (see [1]). This enables us to favorably compare our method to existing ones and show that our method is 7 times faster or has a precision increased by 50 times.

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Stochastic volatility models are the new generation of option pricing models. These models can explain how certain pricing patterns emerged in the option markets, such as "smile" and "skew". In the world of stochastic volatility models, time-dependent parameters are indispensable to price complicated derivatives, such as exotics. This is so because exotics do not only depend on the distribution of the underlying at a particular point in time, but on its dynamics through time.

In this note, we work out closed forms solutions to effectively calibrate time dependent stochastic volatility models. We show how to adapt these to a dynamic version of the SABR model. Indeed, for a model with time-dependent parameters, calibration with numerical algorithms such as partial differential equations (PDE) and Monte Carlo can be too time-consuming.

This paper explains how to effectively calibrate stochastic volatility models leveraging on a recent work by Piterbarg which suggests the use of "effective" constant parameters such that European option prices match the model with time-dependent parameters. In this paper, we first work on a concrete example, square root model. In section 3, we describe the square root model. After solving the effective constant parameters in section 4, we give a standard result by Lewis in section 5 to treat the constant parameter stochastic volatility model. Then we compare the result with the result of the standard PDE method. In the appendix, we give an application on another stochastic model, SABR.

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Recently, various semi-analytical methods have been developed to offer less time consuming alternatives to Monte Carlo simulation for the pricing of correlation credit derivatives products (like single tranche CDO and CDO squared). The motivation of this note is to present and compare these methods and suggests quantitative insights into their relative efficiency both in terms of accuracy and computing time. 

In particular, we compare the standard recursive method originally developped by Hull and White with a new bred method that can provide more accurate result and based on Fourier transformation. This method referred to as the polynomial generating function turns out to be very accurate and is used as a benchmark for our various methods.

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