Behind the Scenes: The Monte Carlo Simulation
The Monte Carlo Simulation (MCS) is a method of computational analysis employed by our Business Development team to ascertain how a given strategy is likely to perform in a range of different situations.
- What is it? A statistical technique used to model complicated systems (with complex interactions of many variables) and establish the odds for a variety of outcomes. Used by professionals in various fields incl. finance. Method translates uncertainties in model inputs into uncertainties in model output (results).
- Origin. Created by two mathematicians von Neumann and Ulam. The method was devised after WWII to simulate behaviour of atomic weapon. Named after Casino where Ulam’s uncle gambled.
- How it works. Uses random inputs to model the system and produce probable outcomes. Given a range of values for each variable, a MCS will randomly select a number within each range, and note the result – and repeat the process millions of times. When the simulation is complete with a large number of results from the model; results are used to describe the probability of reaching various results. No two iterations in the simulation might be identical, but collectively they build up a realistic picture.
- Random values are generated with a specified distribution. Opportunity to end the test when the distribution of all values within a parameter list is normal. Simulations are as good as their inputs.
Benefits of MCS
- Probabilistic results. Showing outcome and likelihood based on the input ranges of estimates.
- Graphical results. MCS data displayed as graphs of outcomes and chances of occurrences.
- Sensitivity analysis to see which input variable has the biggest impact on results.
- Scenario analysis with combination of different input values to estimate results.
- Correlation of inputs analysis. To understand interdependency between input variables.
- Use of random numbers has the additional advantage of avoiding unfair targeting of values that may be known in advance to perform well.
MCS applied to Forex (example and benefits)
- Use back-tests results to gain information about how good or bad a trading system is.
- When used to simulate trading, the trade distribution (represented by the historical list of trades) is sampled to generate a trade sequence. Thousands of different sequences of trades are randomised and analysed. Rate of return and drawdown are calculated and a probability is assigned to each result.
- Construct sequence of trades by random sampling with or without replacement.
- Risk simulator. Helpful in estimating likely rate of returns, drawdowns, risk of ruin, etc.
- Stress testing systems. Get estimate of worst possible outcomes/ behaviour of our systems, worst consecutive losing runs, worst drawdown