Analysts in the finance industry are taking advantage
of advanced numerical analysis and data visualization initiatives in a
variety of areas including:
- Risk Management
- Portfolio Optimization
- Forecasting
- Trading Strategy Optimization
- Derivatives Pricing
- Fixed Income Analysis
- Interest Rate Modeling
- Equity Price Modeling and Analysis
- Exchange Rate Analysis
Quantitative analysts are using basic, but vitally necessary algorithms,
such as linear algebra, regression, and random number generation all
the way up to sophisticated algorithms, such as quadratic programming
and nonlinearly constrained optimization.
Below are several applications that demonstrate how quantitative organizations
are taking advantage of the reliable and accurate solutions provided
by Visual Numerics.
Forecasting
Many finance customers are employing
forecasting algorithms such as ARMA and GARCH to forecast in the areas
of equities, fixed income, currency and commodities. Quantitative researchers
also use Feed Forward Neural Networks, a technique that continuously
refines its forecasting model by applying knowledge gained from past
results, fine-tuning its forecasting accuracy over time.
Above: Accuracy of Neural Network model prediction compared
to historical and actual outcomes.
>> Learn
more about Forecasting
>> Read
white papers on Neural Network and other Forecasting
technologies
Trading
Organizations using the IMSL Libraries
for trading systems are obtaining optimal performance in their deployments.
These proprietary deployments often leverage quadratic programming and
nonlinear programming algorithms, sometimes in distributed computing
environments. One JMSL Library trading application with over 100 variables
runs in less than half a second with $1 billion worth of trades running
through it every week.
Portfolio Optimization
The goal of portfolio
optimization is to select a portfolio of assets that yields the highest
expected return for a given level of risk; alternatively, the problem
can be viewed as one of minimizing the level of risk for a given expected
rate of return.
The portfolio optimization problem may be formulated in various ways
depending on the selection of the objective function, the definition
of the decision variables, and the particular constraints underlying
the specific situation. The solution of the portfolio selection problem
may therefore involve one or more of the following optimization techniques:
- If the risk of the portfolio
can be measured as a ranking of assets or by the
linear distance from the target, then the portfolio
selection problem can be formulated as a linear programming
problem.
- Quadratic programming is applied when
the model is a mean variance model.
- Nonlinear programming is applied when
the portfolio selection model is characterized
by an objective function that seeks to maximize
utility as a function of the portfolio composition
with the utility function being nonlinear.
Above: The intuitive charting feature
in the JMSL Library is helping asset managers and
quantitative analysts develop versatile portfolio
optimization applications.
One portfolio optimization deployment reduced system execution time
from 10 hours to 10 minutes by moving from a software architecture that
wrapped a proprietary analytical package to a clean, pure-Java architecture
that utilizes the JMSL Numerical Library for the advanced analytics;
all while cutting development time by 20%.
Above: A global investment firm shifted from
a multi-language architecture to a single language architecture
(Java) and reduced performance time from 10 hours to
10 minutes.
Option Pricing
An options contract is characterized by its expiration date, i.e. the date
before which the option can be exercised. Options pricing analysts typically
value an American call option using the Black-Scholes partial differential
equation. Since the asset may be exercised at any time before its expiration
date, these analysts usually use algorithms to solve a free boundary problem.
Analysts will further set up a linear complementary problem and use a non-negative
constrained least-squares (NNLS) algorithm.
Above:
This PV-WAVE application compares the Black-Scholes price with the
actual market price and shows how much a call option is worth at any
given time.
Risk Management
Risk management analysts
use visual and numerical analysis to develop models and choose portfolios
with specified exposure to different risks. Well known risks include:
interest rate risks, liquidity risk, credit risk, and volatility
risk. Both linear programming and quadratic programming
techniques can be used in risk management applications.
Performance
Monitoring
In this example to the right, developers leveraged
a heat map charting capability to allow users to
gauge portfolio performance quickly over a selected
period of time. To make charts easily, developers
use the JMSL Library’s
Chart Programmers Guide, which contains a chart description,
chart example and code example. |
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| Above: Example of Heat Map Charting |
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