From maria@askari.com Thu Apr 10 11:33:00 1997
Date: Wed, 09 Apr 1997 18:53:51 -0400
From: Maria Berenguer <maria@askari.com>
To: gcf@postoffice.npac.syr.edu
Cc: paulc@boss.npac.syr.edu, peter@askari.com, zoran@askari.com
Subject: Monte-Carlo

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Geoffrey,

as discussed, I am enclosing the requirements for the Monte-Carlo system.
Please do not hesitate to contact me if you have questions in this regard.
My direct phone number is 212.2190730 X35.  

Paul sent me the Sailfish documentation.  I'll review it in more detail next
week but it looks quite good so far. It seems we are all quite excited about
getting started.

I'll be out of the office tomorrow, but I will give you a call on Friday to
define the next steps.

Best regards,

Maria   


Requirements for a Monte-Carlo Scenario Generator


Objectives

The purpose of the Monte-Carlo Scenario Generator is to model the dynamics
of risk variables though time.  These variables are typical financial market
rates, such as interest and foreign exchange rates and equity prices.
According to historical observations market rates do not evolve
independently from each other, but rather show correlated patterns.  The
simulation process has to have regard for these correlations. 

The ultimate usage of the simulated rates aims towards the market valuation
of financial portfolios, which are direct functions of these variables.  It
is therefore essential to ensure that the density space of the risk
variables has been covered accurately by the simulation process.  This
requires a methodology to assert the proper convergence towards the
distribution functions.  The Syracuse group favors the Metropolis algorithm
for this purpose and has implemented it in the current system.  It is
assumed that the same methodology will be initially adopted for Askari.

The following section lists the high level requirements for the scenario
generator.  They should serve as a guideline to the Syracuse group to
customize the current Monte-Carlo system (e.g. the Sailfish product) to
Askari's needs and to define the product specification.  Given the agreed
time frame for the delivery of the product (two months), the requirements
are not exhaustive.  It is therefore important that the product offers an
open platform to accommodate possible subsequent enhancements.


Requirements

· The scenario generator will simulate multi-dimensional explicit paths
though time for risk variables.
· The change in value of the variables from one step to the next will be
driven by distribution functions, which can vary from one variable to the
other.  For example, an interest rate could be simulated using a lognormal
distribution, whereas a foreign exchange rate could be simulated using
normal distributions.  The engine should be able to accommodate different
types of distributions. 
· The available functional forms the distribution functions can take should
encompass generic distribution types, such as normal, lognormal or binomial
distributions and customized distributions, such as explicit
parameterizations of historical data.  The number of parameters needed to
define the distribution should not be limited.
· The distribution functions will be dynamic, e.g. they will have an
explicit time dependency.
· The simulation process should be able to include a dynamic drift term in
addition to the stochastic part. This drift term should account for
collective effects, such as time value and mean reversion. The system should
allow this term to be dependent on factors, such as the average value of the
variable in a previous step.  The default drift term will be given by the
implied forward values of the risk variables, calculated under arbitrage
free conditions. 
· The relationship between the variables will be defined in terms of a
static correlation matrix.  Future enhancements will include a time
dependent correlation matrix.
· The simulated paths will be consistent at any time with the correlation
structure as defined through the correlation matrix.  
· The scenario generator should be able at least to simulate 2000 variables.
· The simulation horizon will vary between 1 day and 10 years and will be
user-defined.
· The simulation steps should be user-defined and can be either constant or
flexible.  For example for the first month the steps could be daily, from
the second month to the first year monthly and for the rest of the
simulation yearly.
· The development environment should be Microsoft NT.
· The simulation should be able to run in parallel mode.
· The simulation process should be partitionable as a multi-threaded process
on a single machine and a set of distributable processes on many machines.