Quant Lab

Interactive research surfaces

Live numerical experiments — closed-form Black-Scholes, Gatheral SVI smiles, GBM Monte Carlo, and stochastic backtests. Drag any slider; the math recomputes in your browser.

Interactive scenario engine

Strategy Lab

Stress a stylized equity-options strategy and watch expected return, drawdown risk, payoff convexity, and the efficient frontier respond in real time.

E[R]
+8.3%
scenario mean
Risk
13.3%
annualized vol
VaR 95
-13.6%
left tail
Sharpe
0.63
stylized

Return Distribution

Option Overlay Payoff

Efficient Frontier Under Stress

Black-Scholes engine

Options Pricer

European call/put pricer with the full Greek surface. All five Greeks recompute on every slider tick using closed-form Black-Scholes-Merton with continuous dividend yield.

Price
7.702
call
Δ Delta
0.565
∂V/∂S
Γ Gamma
0.0221
∂²V/∂S²
Vega
0.276
per 1 vol pt
Θ Theta
-0.023
per day
ρ Rho
+0.0024
per 1 bp

Price vs Spot

Delta vs Spot

Gatheral SVI

Volatility Smile

Raw SVI parametric curves: w(k) = a + b·(ρ(k−m) + √((k−m)² + σ²)). Three expiries share parameters; IV(k,T) = √(w/T).

ATM 1m
69.3%
implied vol
ATM 3m
40.0%
implied vol
ATM 12m
20.0%
implied vol

Implied Vol vs Log-Moneyness

Geometric Brownian motion

Monte Carlo Simulator

Exact log-Euler GBM with seedable PRNG. Path overlay shows 50 sample trajectories; histogram and risk metrics use the full ensemble.

E[Rₜ]
6.76%
terminal mean
Median
3.48%
50th pct
VaR 95
-26.40%
left tail
CVaR 95
-32.77%
expected shortfall

Sample Paths

Terminal Distribution

Drift Cone (mean ± 1σ ± 2σ)

Stochastic backtest

Strategy Backtest

Synthetic daily-bar strategy with adjustable hit rate and volatility. Equity curve, drawdown underwater, and the standard risk-adjusted return statistics recompute deterministically from the seed.

Sharpe
2.58
ann.
Sortino
2.66
downside
Calmar
5.57
annRet/MDD
Max DD
-11.1%
trough
Win rate
57.9%
of bars

Equity Curve

Drawdown (underwater)