Monte Carlo Simulation: Application to Financial Markets Part I


Author: Tanya Rawat

The application to financial markets is arguably fairly straight forward.

Monte Carlo Simulation using Geometric Brownian Motion.
We define the path of the price in two parts: drift and volatility.

Drift is the most highly likelihood of expected return (constant) and volatility is the shock (stochastic).

Formula is:
Expected Future Return = Expected Return + Z (random Z value)*Volatility
Future price = Current price*Exponent(Expected Future Return)

We can make 3 assumptions about drift:
1. Risk neutral argument as used in the Black-Scholes model. Here we assume the returns will be the risk-free return
2. Random walk. Here we assume 0 returns as the past is not a precedence to the future
3. Efficient Market Hypothesis (EMH)

1. Take 10Y price history (if available or the maximum)
2. Find the return and volatility over the 10Y period
3. Find the 1D return and volatility from this sample
4. Run simulation 1000 times

The next post will discuss application to our markets with 1 month price forecasts with three scenarios viz. bull, base and bear case.

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