# Work out example of Valuation adjustment

Currently, there are many valuation adjustments for the fair price of a derivative instrument, when pricing is based on RFR. One of such adjustment is Prudential Valuation Adjustment.

This adjustment are performed for various reasons e.g. uncertainly in the market price (captured from the fact that, there may be many providers of market prices for the same instrument) or close out price (relevant bid-ask spreads to exit the valuation position)

Let consider a valuing a plain vanilla Interest Rate Swap where float leg defined as 3 month libor. Can someone point me to some work out example on how exactly I should calculate the adjustments for 1) market price uncertainty and 2) close out uncertainty?

Any pointer will be highly appreciated

I will attempt to answer partially - sorry, I don't know enough about this accounting stuff to give a more comprehensive answer, but I can share some pointers that I hope will help. This is more of an accounting question, than a math/quant question.

"Additional valuation adjustment" (AVA) is the difference between "fair" and "prudent" valuation.

Informally, "fair" is what you get if you unwind under normal market positions. (See FASB Topic 820 and similar IFRS 13), while "prudent" is what you get under "fire sale" market conditions, e.g. rapid liquidation (not exactly).

EU regulations (not U.S. yet) require banks to apply "prudent valuation" standards to all positions that are measured at "fair value": trading book and to fair value option banking book positions.

They describe a number of categories of valuation adjustments in context of prudent valuation (model risk is one of them). The goal is to demonstrate with the appropriate degree of certainty that the valuation is not higher than true realizable value.

Regulatory Technical Standards (RTS) on prudent valuation https://eba.europa.eu/sites/default/documents/files/documents/10180/642449/1d93ef17-d7c5-47a6-bdbc-cfdb2cf1d072/EBA-RTS-2014-06%20RTS%20on%20Prudent%20Valuation.pdf

90% confidence regarding prudency applied means that under the orderly exit of exposure (not fire sale) 9 out of 10 times you would be able to transact at better than the prudent value.

As usual, there are two approaches:

Simplified approach: 0.1% * net absolute value of fair-valued positions (if less than EUR 15 billion fair valued assets + liabilities)

Core approach (internal model): 90% prudency based on market data or expert judgment, with with the list of uncertainties to which AVA should be individually calculated and later aggregated:

The list of AVA components is:

• Market price uncertainty

• Close-out costs

• Model risk

• Investing and funding costs

• Concentrated positions

• Early termination

• Operational risk

For example, consider model risk AVA (Article 11)

For each valuation model the bank must consider model risk arising from potential existence of range of different models/model calibrations.

Again, two approaches are allowed:

Either: Determine range of plausible valuations produced from alternative appropriate modelling/calibration approaches. Estimate point within resulting range of valuations associated to 90% confidence level (paragraph 3)

Or: Expert-based approach (which sounds like a lot of work not worth the effort, so most banks/models will go for the first one) (paragraph 4)

For market data, article 3 specifies a hierarchy of pricing sources when calculating AVAs:

1. Exchange prices in a liquid market

2. Trades in the exact same or very similar instrument, either from internal records or from the market

3. Tradable quotes from brokers and other market participants

4. Consensus service data

5. Indicative broker quotes

6. Counterparty collateral valuations

This consultation paper: https://www.eba.europa.eu/sites/default/documents/files/documents/10180/336425/bf20c680-6e46-4de7-a5c4-19c1942cc478/EBA_CP_2013_28.pdf has a worked example of the calculation of market price uncertainty and close-out costs AVAs under the core approach (section 5.1).