Implementation considerations

Path-dependence and received cashflows in the context of future valuation can create
difficulties in the implementation of VaR systems. The reason is that most instrument
implementations simply do not support future valuation in the sense described
above, distinguishing between anchor and target dates. Rather, all that is supported
is a spot valuation function, with dependence on past market data, e.g. resets,
embedded in the valuation function through a separate process. Thus the usual
practice is to generate samples of the instantaneous market data vector as of time T,
mT, and evaluate the instantaneous valuation function at time t0 or T, i.e. vt0 (mT) or
vT(mT). It is easy to think of cases where this practice gives seriously erroneous
results. An obvious problem with using vt0 (mT) as a proxy for a future valuation
function is that it will erroneously show market risk for a fixed cashflow payable at
time T. A better choice is probably vT(mT), but this will return a PV of zero for a
cashflow payable between t0 and T. In addition, one needs to be careful about resets.
For example, suppose there is a reset occurring at time tr with t0\tr\T. Since the
spot valuation function only has market data as of time T available to it, it cannot
determine the correct value of the reset, as it depends on past market data when
viewed from time T. (In normal operation, the value of this reset would have been
previously set by a separate process.) How the valuation function treats this missing
reset is, of course, implementation dependent. For example, it may throw an error
message, which would be the desired behavior in a trading environment or during a
revaluation process, but is not very helpful in a simulation. Even worse, it might just
fail silently, setting the missing reset to 0 or some other arbitrary value. To solve this
problem completely, instrument implementations would have to support future
valuation function with distinct anchor and target dates. Such a function would
potentially need to access market-data values for times between the anchor and
target date. As of today, valuation functions supporting these semantics are not
generally available. Even if they were, a rigorous extension of even the parametric
VaR methodology that would properly account for the intermediate evolutions of
variables would be quite involved.
We can, however, recommend a reasonably simple approximation that will at least
capture the gross effects. We will just sketch the idea at a conceptual level. First of
all, we construct DEAF proxies for all instruments based on the spot valuation
function as of the anchor date. We then modify the mapping procedure as follows:
1 Exposures are numerically equal to the forward value of the asset at the target
date rather than the present value at the anchor date. Forward values of assets
for delivery prior to the target date are computed by assuming that the asset is
reinvested until the target date at the forward price as of the anchor date.
2 Asset flows between the anchor and target dates do not result in discount-factor
risk. Asset flows after the target date are mapped to discount factors with
maturities equal to the difference between the delivery and target date.

Glossary of terms
Absolute Return: The change in value of an instrument or portfolio over the time
horizon.
Analytic VaR: Any VaR methodology in which the distribution of portfolio value is
approximated by an analytic expression. Variance/covariance VaR is a special case.
Anchor Date: Roughly speaking, ‘today’. More formally, the date up until which
market conditions are known.
DEAFs: Delta-equivalent asset flows. Primary asset flows that serve as proxies for
derivative instruments in a VaR calculation.
DTS: Discounting term structure. Data structure used for discounting of future asset
flows relative to their value today.
Exposure: The present value of the equivalent position in a fundamental asset.
Fundamental Asset: A fundamental market factor in the form of the market price
for a traded asset.
Future Valuation Function: A function that gives the value of a financial instrument
at the target date in terms of the evolution of the risk factors between the anchor
and target date.
FX: Foreign exchange.
Historical VaR: A value-at-risk methodology in which the statistical model for the
risk factors is directly tied to the historical time series of changes in these variables.
Maturity: The interval of time between the anchor date and the delivery of a given
cashflow, option expiration, or other instrument lifecycle event.
Monte Carlo VaR: A value-at-risk methodology in which the distribution of portfolio
values is estimated by drawing samples from the probabilistic model for the risk
factors and constructing a histogram of the resulting portfolio values.
Native Currency: The usual currency in which the price of a given asset is quoted.
PAV: Primary asset value. A variable that denotes the value of an asset flow for spot
or future delivery by a counterparty of a given credit quality.
PV: Present value. The value of a given asset as of the anchor date.
Relative Return: The change in value of an asset over the time horizon divided by
its value at the anchor date.
Risk Factors: A set of market variables that determine the value of a financial
portfolio. In most VaR methodologies, the starting point is a probabilistic model for
the evolution of these factors.
Spot Valuation Function: A function that gives the value of a financial instrument
at a given date in terms of the evolution of the risk factor vector for that date.
Target Date Date in the future on which we are assessing possible changes in
portfolio value.
Time Horizon: The interval of time between the anchor and target dates.
VaR: Value at risk. A given percentile point in the profit and loss distribution between
the anchor and target date.
Variance/Covariance VaR: A value-at-risk methodology in which the risk factors
are modeled as jointly normal and the portfolio value is modeled as a linear combination
of the risk factors and hence is normally distributed.
VTS: Volatility term structure. Data structure used for assigning spot and future
asset flows to exposure vectors.
ZCDF: Zero-coupon discount factor. The ratio of the value of a given asset for future
delivery with a given maturity by a counterparty of a given credit quality to the spot
value of the asset. 215