Tri-Segmented Monte Carlo Simulation
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Monte Carlo simulation
Financial firms and others who advise or regulate them often
need estimates of the value of portfolios of assets and/or liabilities or of
risk measures quantifying the risks to which such portfolios are exposed.
Common risk measures used to quantify risk for such portfolios include value-at-risk (VaR), expected
shortfall and tail
value-at-risk (TVaR). For portfolios involving sufficiently simple payoffs,
the relevant valuation and risk metrics may be expressible using just
analytical formulae and the runtimes needed to calculate them may be quite low.
However, for more complicated portfolios it is typically necessary to use simulation
techniques. Simulation techniques are also used extensively in non-financial
fields.
The traditional workhorse for this purpose is Monte Carlo
simulation. In its most basic form, simulations are drawn randomly from the
relevant probability distribution(s) characterising the economic drivers
impacting the (present) value of the portfolio payoff. The payoff present
values arising from each simulation are then calculated. The portfolio value is
estimated as the average of these values. The portfolio VaR can be estimated by
identifying the outcome below which only a specified fraction of losses arising
from such simulations lie, in other words, from the relevant percentile
(quantile) of the observed distribution of these simulated losses.
Unfortunately, the accuracy of results derived from (basic)
Monte Carlo simulation exercises typically improves only in proportion to the
square root of the number of simulations used. To improve accuracy 10-fold we
thus need to use 100 times as many simulations. If the portfolio includes many
more complicated assets or liabilities or if nested calculations are involved (in
which quantification of the value of a payoff for a given simulation itself
requires a simulation exercise) runtimes can easily become excessive. Firms may
then use proxy models, approximating full book simulations, for
day-to-day decision-making and monitoring. But proxy modelling comes with other
complications such as a need to select a suitable proxy model and to justify
why that model should be a suitable approximation to a full book simulation for
the purpose in question.
Tri-segmented Monte Carlo
(TSMC)
Nematrian has developed an approach, called tri-segmented
Monte Carlo, that for many relevant problems seems capable of materially improved
runtimes. Instead of applying all simulations to the portfolio, the simulations
are split into 3 subsets, (1) an “underlying”, (2) an “added” and (3) an
“extended” simulation set. The extended set is usually by far the largest of
these three sets. Only the underlying and added sets are actually applied to
the portfolio; the extended set is instead applied to only to a fast to
evaluate approximation derived principally from the underlying simulation set.
The added simulation set helps to correct for inaccuracies in this
approximation.
A presentation summarising tri-segmented (trisegmented)
Monte Carlo is available here: Efficient
Monte Carlo simulation of portfolio value, value-at-risk and other portfolio
metrics.
Demonstration tool
To help organisations unfamiliar with tri-segmented Monte
Carlo (TSMC) understand better how it might help them, Nematrian has included
on its website several Nematrian web service tools:
(a) MnDemoTSMC. This tool provides
a cut-down demonstration version of Nematrian’s full TSMC engine. Users can
enter simulation data and other parameters that are similar in form to a subset
of those needed by the full engine but with size limits on datasets and
parameters to limit the CPU resources required to run the demonstration
version.
(b) MnDemoTSMCSimGen.
This tool allows users to create a simulation set of the sort needed for MnDemoTSMC.
(c) MnDemoTSMCValueSim.
This tool allows users to apply simulations from MnDemoTSMCSimGen to a
simplified portfolio which MnDemoTSMC
uses to illustrate TSMC. The strikes, terms and underlyings of each of the
instruments in this portfolio are available through MnDemoTSMCStrikes, MnDemoTSMCTerms and MnDemoTSMCUnderlyings.
Licensing
If you are interested in licensing this intellectual
property then please speak to your contact at Nematrian or email us at ContactUs@nematrian.com.*
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