A Practical Approach to XVA

The following sections are included:

• Dedication
• Foreword
• Preface
• About the Author
• Contents
• List of Figures
• List of Tables
• Introduction

XVA is valuation adjustments to the traditional (risk-free) derivative valuation. Therefore before discussing XVA, traditional derivatives valuation theory will be briefly explained in this chapter (Tan, 2012).

Following the impact of the 2008 financial crisis, the environment of the derivatives trading business has changed dramatically. This change also dramatically affects the practice of derivatives valuation. One of the changes is the adoption of Overnight Index Swap (OIS) discounting of collateralized trades, and the other is a far more comprehensive inclusion of valuation adjustments (XVA — cross-valuation adjustment) in derivatives valuation…

In the previous chapter, valuation adjustment arises from the counterparty default risk of the clients of the bank (Credit Valuation Adjustment or CVA). Whereas the valuation adjustment from the default risk of the clients is necessary, we also need that from the default risk of the bank as a matter of course. The adjustment which corresponds to the default risk of the bank is called the Debit Valuation Adjustment (DVA)…

In the previous chapter, Debit-Valuation Adjustment (DVA) and Funding Valuation Adjustment (FVA) were introduced. FVA is sometimes divided into Funding Cost Adjustment (FCA), which has negative value and Funding Benefit Adjustment (FBA), which has positive value. DVA and FVA are closely related to each other. Actually FBA and DVA are mirror images of the same thing. Hereafter, we refer to both FVA and DVA jointly as FVA…

Ultimately, XVA can be thought of as a set of adjustments to the price of an instrument to fully take into account costs (and benefits) pertaining to various activities needed to maintain and risk manage the position (i.e. funding, potential default, margining, etc.). But what is the base (e.g. potentially but not necessarily “risk-free”) case to which these adjustments are made? This naturally needs us to consider the construction of the modern yield curve, post 2008 (Bianchetti, 2010).

In Chapters 3 and 4, we have discussed about FVA. FVA is the funding cost related to derivatives trading. Here, funding is necessary for collateral margin and/or cash flows from derivatives. Collateral margin here is (a function of) exposure of derivatives. This collateral margin is called Variation Margin (VM). In addition, there are certain important circumstances where Initial Margin (IM) is posted on top of VM in derivative trading. VM protects derivative counterparties from loss with the amount of positive exposure when the opposite counterparty defaults. On the other hand, IM protects counterparties from potential losses from market movements in the Margin Period of Risk (MPOR) (i.e. the short period of time required for margin to be posted in response to market moves). MPOR is well captured by VAR, SVAR or Expected Shortfall…

Whereas prior to 2008, derivatives pricing was very much based on the concept of efficient markets (i.e. ability to borrow and lend large amounts at the same rate, existence of deep markets which allows one to trade in size without affecting market prices) and costs were seen as an afterthought; it has now been well established that pricing must reflect a lot of the costs associated with maintaining the position (i.e. CVA, DVA, FVA and MVA). Indeed, markets have become less efficient since 2008 (i.e. scarcity of capital leading to a high cost in funding, reduction in market depth as players exit unprofitable businesses and higher capital charges take hold), so that such adjustments become more significant…

A typical financial institution engages with a range of counterparties. Typically, there are collateral arrangements with fellow financial institutions and larger funds and some major corporates. Also, deals done across different assets tend to have different maturities (with interest rates including cross-currency swaps being long dated and equities being short dated in nature). The different types of business arrangements and maturity profile of deals across assets have significant implications on the importance of XVA and also the computational challenges that one will face in implementing this. We thus wish to explore this topic here…

In this chapter, we shall sketch a framework for computing XVA in practice. Whereas traditional derivatives pricing is analyzed from the perspective of individual deals, XVA needs to be understood at the portfolio level. This naturally suggests a different perspective and presents challenges in terms of computational constraints and data availability and consistency…

As has already been stated in previous chapters, calculation of KVA (and MVA) is computationally intense when the internal model (or even the Standardized Approach under Basel III) is used. In this section, we will discuss the computational burden. KVA is given by…

Derivatives pricing has been based on the idealized world where arbitrage can be eliminated by locking in a payoff via other instruments. Among other things, this assumes the existence of deep markets where actions of a participant will not move the market, the ability to borrow and lend at the same rate, and that market variables are continuous. Whereas in practice, none of the above strictly hold, derivatives pricing still works in general because the above “approximately” holds…

By now, it should be clear that XVA is very much something to be considered at the level of large portfolios — all portfolios in a netting set for CVA and DVA, funding set for FVA, capital set for KVA and other segregated set (to which initial margin applies) for MVA. Ring fencing and integration of different regulatory environments are adding another layer of complexity. Clearly, there are operational considerations in light of this — namely data requirements and computational requirements. We shall start with a brief discussion of the setup of a financial institution to give further context to the subsequent discussion.

The following sections are included:

• Appendix A: Sample Appendix
  • Credit Risk Model in XVA
  • Interest Rate and Fx Models in XVA
    • Hull–White model
    • Swaption volatility in the Hull–White model
    • Two-factor Hull–White model
    • Correlation structure of two-factor Hull–White model
      • Better approximation
    • Interest rate skew in XVA
    • Cross-currency Hull–White Model
      • Quanto adjustment
• Appendix B: A Brief Outline of Regulatory Capital Charges for Financial Institutions
  • The Latest Prescribed Regulatory Framework
    • Leverage ratio
    • Output floor
  • Operational Risk Capital
  • Credit Risk, Market Risk and the Various Components of Capital
  • Counterparty Risk
    • CCR element (part of credit risk)
    • CVA element (part of market risk)
  • Market Risk Capital
    • General market risk RWA
    • Default risk charge for non-securitization
    • Securitization framework
    • Relevant calculations

The following sections are included:

• Conclusion
• References
• Index