Building Predictive Models for Financial Outcomes

Core Concepts: Rate Processes

At its heart, financial modeling relies on rate processes – changes in quantity per unit of time. Just as momentum describes the change in velocity of a moving object, interest rates describe the change in value of an investment over time. This simulation allows you to manipulate these ‘rates’ and observe their effects.

Key concepts include present value (PV), future value (FV), compounding interest, and discount factors. These are all mathematically derived from basic physics principles relating to energy and time.

FV = PV * (1 + r)^t

Building a Simple Portfolio Model

Our simulator allows you to represent assets – stocks, bonds, or even simulated commodities – as dynamic systems. Each asset’s value is governed by its own rate process, influenced by factors like market volatility (represented as stochastic fluctuations) and interest rates.

You can define initial investment amounts for each asset and set the discount rate to reflect your risk tolerance. The simulation then iteratively updates the portfolio's value based on these parameters.

Portfolio Value = Σ (Asset i * FV_i)

Risk Assessment: Monte Carlo Simulation

To assess risk, we utilize a Monte Carlo simulation. This technique involves running the model thousands of times with randomly generated inputs for key variables like interest rates and market volatility.

By analyzing the distribution of resulting portfolio values, you can quantify potential upside and downside risks – creating probabilistic forecasts rather than single point estimates.

Probability Distribution = (Number of Simulations with Value > Threshold) / Total Number of Simulations

Expanding the Model: Incorporating External Factors

Advanced models can incorporate external factors such as inflation, exchange rates, and economic growth. These are represented as additional rate processes that influence asset values.

You can also introduce correlations between assets – reflecting how their prices tend to move together or against each other. This adds a layer of complexity and realism to the simulation.

Correlation (Asset A, Asset B) = Covariance(A,B) / (Standard Deviation(A) * Standard Deviation(B))

Frequently asked questions

Try it live

Everything above runs in your browser — open SPH Fluid and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.