A Model of Credit Value Adjustment Essay

Words: 6886
Pages: 28

9/21/2013

Modeling Credit Value
FX Forwards and Currency Swaps

Alexi Carlos and Zedrick Torres

Introduction
This paper is concerned with the generalization of the Credit Value Adjustment (CVA) equation for FX
Forwards and Currency Swaps. In addition, a model for CVA using Visual Basic for Applications (VBA) in
Microsoft Excel will be presented.
Counterparty credit risk (CCR) is the risk that the counterparty to a financial contract will default prior to the expiration of the contract and will not make all the payments required by the contract (Zhu and
Pykhtin, 2007). The issue regarding CCR is something inevitable for over-the-counter (OTC) derivative transactions that is why it is very important to know how
It is usually used with over-the-counter (OTC) derivatives such as swaps and options (Barbarican Consulting).

Calculation of Collateralized Exposure
A. Collateral Computation where is the collateral amount at a given simulation date is the uncollateralized exposure at time is the margin period of risk is the threshold value.

B. Collateralized Exposure where is the collateralized exposure at the simulation date t is the collateral amount at a given simulation date

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is the uncollateralized exposure at time

In the Cox-Ingersoll-Ross (CIR) Model, the short rate satisfies the stochastic differential equation
(
where

)

is the volatility factor is the drift factor is the mean around which mean reversion occurs is the short-term interest rate is a Brownian motion under the risk-neutral measure.

In the CIR Model, the price of a zero-coupon bond with maturity
(

)

(

(

)

at time

[

] is given by

) (