Why mante carlo simulation is important ?

?? A Monte Carlo simulation is a model used to predict the probability of a variety of outcomes when the potential for random variables is present.

?? Monte Carlo simulations help to explain the impact of risk and uncertainty in prediction and forecasting models.

?? A Monte Carlo simulation requires assigning multiple values to an uncertain variable to achieve multiple results and then averaging the results to obtain an estimate.

?? Monte Carlo simulations assume perfectly efficient markets.

?? Monte Carlo simulation that estimates the probable price movements of stocks or other assets. There are?two components to an asset’s price movement:-

1. Drift, which is its constant directional movement,

2. Random input, which represents market?volatility.

By analyzing historical price data, you can determine the drift,?standard deviation,?variance, and average price movement of a security.

?? How we create monte carlo simulaion ?

Follow four steps to create mante carlo simulation :-

? Step 1: Use the historical price data of the asset to generate a series of periodic daily returns using the natural logarithm (note ?? this equation differs from the usual percentage change formula)

?? Periodic?Daily?Return=???? ( Day’s?Price / Previous?Day’s?Price)

? Step 2: Next, use the AVERAGE, STDEV.P, and VAR.P functions on the entire resulting series to obtain the average daily return, standard deviation, and variance inputs, respectively.

?? Drift=(Average?Daily?Return?Variance/2 ) where : Average?Daily?Return=Produced?from?Excel’s AVERAGE?function?from?periodic?daily?returns?series Variance=Produced?from?Excel’sVAR.P?function?from?periodic?daily?returns? series.

? Step 3: Next, obtain a random input :-

?? Random?Value = ??×NORMSINV(RAND())

where :- ??=Standard?deviation,?produced?from?Excel’sSTDEV.P?function?from periodic?daily?returns?series NORMSINV?and?RAND=Excel?functions

?? The equation for the following day’s price is :- ?? Next?Day’s?Price=Today’s?Price×??(Drift+Random?Value)

?Step 4: To take?e?to a given power?x?in Excel, use the EXP function: EXP(x).?Repeat this calculation the desired number of times. (Each repetition represents one day.) The result is a simulation of the asset’s future price movement.

?? By generating an arbitrary number of simulations, you can assess the probability that a security’s price will follow a given trajectory.