From maria@askari.com Thu Apr 10 11:33:00 1997 Date: Wed, 09 Apr 1997 18:53:51 -0400 From: Maria Berenguer To: gcf@postoffice.npac.syr.edu Cc: paulc@boss.npac.syr.edu, peter@askari.com, zoran@askari.com Subject: Monte-Carlo [The following text is in the "iso-8859-1" character set] [Your display is set for the "US-ASCII" character set] [Some characters may be displayed incorrectly] 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.