Probability Theory Fundamentals › Key Parameters

The key parameters for simulating and analyzing financial returns are:

• annual_return: Annualized arithmetic mean of iid daily simple returns (10% here), so the daily mean is $0.10/252$. It is not an exact target for the one-year compounded return, which under this model has expectation $(1+0.10/252)^{252}-1$.
• annual_volatility: Annualized standard deviation under iid or zero-autocovariance scaling; daily volatility is the annual value divided by $\sqrt{252}$. This is the volatility convention for an additive sum of daily returns, not generally the exact standard deviation of a compounded annual simple return.
• trading_days: Modeling convention for trading days per year (commonly 252). Exact counts vary by market and calendar year.
• VaR confidence level: 95% and 99% are common choices, including the two used here. Higher confidence means more conservative risk estimates.
• initial_price: Starting price for the simulation. All subsequent prices are computed relative to this value.