This article is to document what I have learned about XVA. I will first layout a few idea and continue to improve this as I find out more. Source of these information are from books such as
1 ) The XVA Challenge
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For an introduction, the point of calculating XVA is to find out the various cost of transaction in banks, from inception to maturity. Various stakeholders are involved in this process:
1) Dealers
a. Traders
There are different kind of traders in a bank, some are just doing flow business, others are doing proprietary trading. Typically, the head of desk will treat the desk trading business as any other business. He/She will consider the cost of operating this desk. XVA will form part of the operation cost.
b. Structurers
The trades done by structures are huge chunky trades as compared to traders. These are typically longer term as well. The counterparties involved are typically entities such as fund house, security firms and corporates. These counterparties have significant credit risk compared to interbanks trades. Therefore, XVA will form an important cost to the desk.
2) CVA Desk
This desk is responsible for hedging the CVA (one part of XVA) which is directly linked to the credit risk of counterparties. Hedges are typically done using CDS or proxy trades which is correlated to counterparties. Traders and Structurer will pay CVA cost to this desk and as such the credit risk associated with the trade is taken to be hedged out with this desk. This desk will be interested in the CVA Greeks as they are required to managed the CVA according to the movement in the market.
3) Risk Managers
This function is involved in computing, monitoring and reporting the exposure of the bank to management and regulators.
XVA Components
CVA
Simpliest among these, just go Google
Simpliest among these, just go Google
DVA
The flip side of CVA.
The flip side of CVA.
FVA
KVA
For every trade done in bank, there is a capital charge associate with it. These charges are amount which banks are required to set aside for mitigating counterparty credit risk. In the past, banks ignore this cost and uses quick and dirty way such as using minimum charges to transactions. Today, banks have became more sophisticated and implements KVA is to properly price the cost of setting aside such Capital for regulatory purposes.
3 factors to Capital Requirement for OTC Derivatives
- Default risk capital charge
Potential default charge of counterparty i.e. CCR
- CVA capital Charge
CVA sensitivity due to movement in Credit Spread
- Market Risk Capital Charge (insignificant since regulator has implement rule to reduce this)
These are capital charges arises from doing hedges.
- Capital Charge on exposure to CCP is very little.
Formula
KVA =-$\sum_{i=1}^{m} $EC(t_i)xCC(t_i)X(t_i-t_(i-1))XS(t_i)
For every trade done in bank, there is a capital charge associate with it. These charges are amount which banks are required to set aside for mitigating counterparty credit risk. In the past, banks ignore this cost and uses quick and dirty way such as using minimum charges to transactions. Today, banks have became more sophisticated and implements KVA is to properly price the cost of setting aside such Capital for regulatory purposes.
3 factors to Capital Requirement for OTC Derivatives
- Default risk capital charge
Potential default charge of counterparty i.e. CCR
- CVA capital Charge
CVA sensitivity due to movement in Credit Spread
- Market Risk Capital Charge (insignificant since regulator has implement rule to reduce this)
These are capital charges arises from doing hedges.
- Capital Charge on exposure to CCP is very little.
Formula
KVA =-$\sum_{i=1}^{m} $EC(t_i)xCC(t_i)X(t_i-t_(i-1))XS(t_i)
Margin Valuation Adjustment (MVA)
As the name suggest, this adjustment is related to margin associated with trades. Margin are charged to protect against default, so it is expensive and not re-hypothecated; it is regarded as a separate amount.
It consist of:
1) Initial Margin (and other financial resources required by Central Counterparty (CCP)
When a bank (Clearing Member) deal with counterparty via CCP, they are required to post an Initial Margin (IM) so that if they default, this margin can help buffer against the lost suffered by CCP.
These are cost to banks as the interest paid by CCP are less than the funding cost required.
Questions:
What benchmark is used by CCP to pay clearing members for IM?
2) Bilateral IM
This is required when both parties are required to post initial margin to each other.
3) Contingent IM
How are IM calculated?
IM calculation are determined by using VAR or expected shortfall. This means they need to specify % confidence interval and time horizon.
MVA =-$\sum_{i=1}^{m} $EIM(t_i)x(FC(t_i)-S_im)X(t_i-t_(i-1))XS(t_i)
Where $EIM = discounted expected IM, $FC is funding cost and $S_IM is the remuneration from posting IM.
EIM are calculated using simulation over 99% confidence interval with 10 days horizon.
Comparison with FCA
- MVA is the funding cost associated with worst-case movement of portfolio during a 10 day horizon. This is due to the fact that the trade is collateralized and the 10 days is to cover the situation where there is a default discovered only after 10 days, by which the market would have moved.
-FCA is the funding requirement over the life of the trade.
Where $EIM = discounted expected IM, $FC is funding cost and $S_IM is the remuneration from posting IM.
EIM are calculated using simulation over 99% confidence interval with 10 days horizon.
Comparison with FCA
- MVA is the funding cost associated with worst-case movement of portfolio during a 10 day horizon. This is due to the fact that the trade is collateralized and the 10 days is to cover the situation where there is a default discovered only after 10 days, by which the market would have moved.
-FCA is the funding requirement over the life of the trade.
Questions:
What is the flow of calculating MVA?XVA consists of a few components summarized in the table below:
Obtained from the book: The XVA Challenge
