Simulation and sizing

MC, Monte Carlo

The MC panel runs geometric Brownian motion price simulations forward from the current spot. You configure:

• Drift, annualised expected return.
• Volatility, annualised IV or RV input.
• Horizon, days forward.
• Path count, typically 1,000 to 10,000.

Outputs:

• Fan chart, the cone of simulated paths with confidence bands (50%, 95%, 99%).
• Distribution at horizon, histogram of ending prices.
• VaR estimate, value-at-risk at standard confidence levels.

GARCH, volatility forecasting

The GARCH panel fits a GARCH (or GJR-GARCH) volatility model to the underlying's return series and forecasts vol forward. Outputs:

• In-sample fit, model vol overlaid on realised vol.
• Forecast cone, vol forecast over the next N days with confidence bands.
• News impact curve, for GJR-GARCH, the asymmetric response of vol to positive vs negative returns (the "leverage effect": down moves lift vol more than up moves).

Useful when you want a model-based view of where realised vol is heading, to compare against the option market's implied view (IV). If GARCH forecasts higher RV than IV is pricing, options are cheap; if lower, options are rich. See also VRP.

KELLY, position sizing

The KELLY panel computes the Kelly-criterion optimal bet size for a known edge and known win/loss distribution. Inputs: probability of winning, average win, average loss. Output: optimal fraction of bankroll to size on the bet.

Real-world traders typically use fractional Kelly (50% or 25% of full Kelly) because (a) edge estimates are uncertain and (b) full Kelly maximises geometric growth but accepts huge drawdowns along the way. The panel surfaces both full and fractional Kelly so you can see the difference.

RISKPAR, risk parity allocator

The RISKPAR panel takes a basket of assets and computes the weights that equalise their risk contribution to the portfolio (rather than equal dollar weights). The result is a portfolio where no single asset dominates the risk budget.

Inputs: the asset list and a covariance window. Output: the risk-parity weights, plus the realised risk contribution per asset under those weights.

Useful for multi-coin portfolios where naive equal-dollar weights would have one or two volatile assets dominating everything. Risk parity tilts away from those toward the stabler ones.