Valuation Adjustments - XVAs — Martialis Consulting

Valuation Adjustments, XVAs for Derivatives

Valuation Adjustments (VAs) have been part of financial markets for many years.

More recently, the calculation methodologies for VAs have been significantly advanced and are now very quantitative involving complex models across a wide range of VAs.

As the number of VAs has expanded, they are collectively described as ‘XVAs’.

This blog is the first of a series which explains the types, uses and calculation methodologies for many XVAs. The blogs will not cover all the XVAs but will describe those frequently encountered by clients. The calculation methodologies are described in basic terms without excessive detail: if you want that level of explanation, feel free to contact me. The calculations in most XVAs vary from analytic approximations to full simulations.

This blog introduces some XVAs I regularly see for clients.

Following blogs will look at each XVA in more detail covering uses and calculation.

Why are XVAs important for derivatives?

Derivatives (e.g., interest rate swaps) have characteristics which are different to other assets and liabilities:

They have 2-way exposures, you can have payments or receipts
ii.This makes the calculation of exposure sensitive to market levels and future directions
The calculations and approaches are therefore different and often more complex than one-sided exposures such as bonds.

Note: Some XVAs are applied to collateralised transaction and some to uncollateralised transactions.

CVA – Credit Valuation Adjustment

CVA = -LGD * ∑ (EPE * PDc)

LGD = Loss given default (assumed to be 40%)

EPE = Expected discounted positive exposure where only positive exposures are included

PDc = Probability of default of counterparty (market input)

Calculation is done in discreet time steps so that the EPE and PD are specific to that time step, and this is summed over the entire trade until maturity.
Applied to uncollateralised transactions.

DVA – Debit Valuation Adjustment

DVA = -LGD * ∑ (ENE * PDs)

LGD = Loss given default (assumed to be 40%)

ENE = Expected discounted negative exposure where only negative exposures are included

PDs = Probability of your default (market input)

Only used for accounting and generally for corporates.
Applied to uncollateralised transactions.

FVA – Funding Valuation Adjustment

FVA = ∑ (EE * FSs)

EE = Expected exposure, sum of EPE and ENE

FSs = Your funding spread

Calculation is done in discreet time steps so that the EE and FS are specific to that time step, and this is summed over the entire trade until maturity.
No LGD used
Applied to uncollateralised and some collateralised transactions.

KVA – Capital (K) Valuation Adjustment

KVA = ∑ (EC * CC * ti)

EC = Discounted expected capital profile

CC = Cost of capital

This is often a theoretical calculatio. Most banks replace KVA with RoC (Return on Capital)

MVA – Margin Valuation Adjustment

MVA = ∑ (EIM * FSs * ti)

EIM = Discounted expected initial margin (often calculated from ISDA SIMM)

FSs = Your funding spread (as per FVA)

Used only for collateralised transactions

CollVA – Collateral Valuation Adjustment

ColVA = ∑ (ECB * FSs * ti)

ECB = Discounted expected collateral balance (EE from FVA)

FSs = Funding spread of collateral x relative to discount rate

Applied to collateralised transactions.
Discount rate is the actual rate in your system, e.g., SOFR
FSs accounts for different collateral and currency
Is usually very idiosyncratic – it is your cost of collateral
E.g., discount cross currency against SOFR (mkt standard) but collateral is in JPY

Summary of Valuation Adjustments, XVAs

Uncollateralised

CVA (always a cost)
DVA (always a benefit)
FVA (cost or benefit)

Collateralised

MVA (always a cost)
CollVA (cost or benefit)
FVA (if term funding is required)

Both

KVA (always a cost)

Valuation Adjustments - XVAs