A Quantization Approach to the Counterparty Credit Exposure Estimation

Abstract

During recent years the counterparty risk subject has received a growing attention because of the so called Basel Accord. In particular the Basel III Accord asks the banks to fulfill finer conditions concerning counterparty credit exposures arising from banks' derivatives, securities financing transactions, default and downgrade risks characterizing the Over The Counter (OTC) derivatives market, etc. Consequently the development of effective and more accurate measures of risk have been pushed, particularly focusing on the estimate of the future fair value of derivatives with respect to prescribed time horizon and fixed grid of time buckets . Standard methods used to treat the latter scenario are mainly based on ad hoc implementations of the classic Monte Carlo (MC) approach, which is characterized by a high computational time, strongly dependent on the number of considered assets. This is why many financial players moved to more enhanced Technologies, e.g., grid computing and Graphics Processing Units (GPUs) capabilities. In this paper we show how to implement the quantization technique, in order to accurately estimate both pricing and volatility values. Our approach is tested to produce effective results for the counterparty risk evaluation, with a big improvement concerning required time to run when compared to MC approach.

A Rbsdes Approach for the Numerical Evaluation of the American Option Pricing Problem

“…In what follows, mainly exploiting the results given in [2], see also [7] and references therein, we describe a probabilistic method for pricing American style options on multidimensional baskets of traded assets and we see the connection between this method and RBSDEs. First of all the asset dynamics follow a d-dimensiona, d ≥ 1, diffusion model in the time interval [0, T ], where T is the maturity time.…”

“…The latter is the case, just to give concrete examples, of the evaluation of expectation of known random variables by mean of polynomial chaos decomposition, as happens for relevant financial models like, e.g., the Vasicek model, or the Cox-IngersollRoss (CIR) model, see [8]. Concerning the quantization method, see, e.g., [7] and references therein, it is worth to mention that it is well-adapted for the pricing and hedging of American options. Its purpose is to compute a large number of conditional expectations by projection of the diffusion on optimal grid designed to minimize the (square mean) projection error.…”

Estimating the Counterparty Risk Exposure by Using the Brownian Motion Local Time

“…To overcome latter drawbacks, the literature has recently proposed new techniques, e.g., the Vector Quantization [8,12,13,14], or more enhanced hardware technologies, such in the case of grid computing and Graphics Processing Units (GPUs) capabilities, see, e.g., [16], [41] and references therein. In the context of American option pricing, other methods recently investigated are the martingale-based approach à la Rogers, see e.g.…”

“…It is also worth to mention that there exists an extended literature dealing with the theoretical applications of BLT such as an extension of Itô's formula to convex functions, the definition of the density of the occupation measure for a Brownian Motion with respect to the Lebesgue measure, see e.g. [8], etc. On the other hand, a relatively limited literature has been devoted to concrete applications of BLT and its properties.…”