Quantitative Finance Projects — Python

A collection of quantitative finance models built in Python (Google Colab), covering portfolio risk measurement, derivatives pricing, and yield curve analysis.

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1. Portfolio Risk — VaR & CVaR (Three Methodologies)

Notebook: Var+Cvar+Monte_carlo.ipynb

What it does

Implements and compares three industry-standard methodologies to estimate Value at Risk (VaR) and Conditional VaR (CVaR / Expected Shortfall) at the 99% confidence level on real market data fetched via yfinance.

Methodologies compared

Method	Approach	Key assumption
Historical Simulation	Sorts actual log-returns and reads the 1st percentile	No distributional assumption
Parametric (Variance-Covariance)	Fits a normal distribution using the covariance matrix	Returns are normally distributed
Monte Carlo Simulation	Generates 50,000 correlated daily paths via Cholesky decomposition	Normality + covariance structure

Portfolios tested

• Single asset — UBS Group:
  Historical VaR 99%: -5.64% | CVaR 99%: -8.51%

• Single asset — Bitcoin (BTC-USD):
  Historical VaR 99%: -8.91% | CVaR 99%: -13.24%

• Diversified portfolio (9 assets):
  LVMH, Sanofi, L'Oréal, Airbus (FR, 40%) + Apple, Microsoft, NVIDIA (US, 30%) + TLT bonds (20%) + Ethereum (10%)
  Historical VaR 99%: -3.24% | CVaR 99%: -4.58%

Key result

The three methodologies diverge most on fat-tailed assets (BTC): Historical Simulation captures extreme tail events better than Parametric, which underestimates tail risk by assuming normality. Monte Carlo and Parametric converge on near-Gaussian assets (UBS, diversified portfolio), confirming the model's coherence.

Stack

Python · NumPy · pandas · SciPy · yfinance · Plotly

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2. Options Pricing Engine — Black-Scholes & Binomial Tree

Notebook: option.ipynb

What it does

A full options pricing engine built around two models and an object-oriented architecture (VanillaOption, MarketEnvironment, BlackScholesPricer, BinomialTreePricer).

Model 1 — Black-Scholes (European options)

Analytical closed-form pricing with dividends (q) for European calls and puts, including four Greeks:

Greek	Formula basis	Normalisation
Delta (Δ)	e^{-qT} · N(d1)	Raw (0 to ±1)
Gamma (Γ)	e^{-qT} · N'(d1) / (S·σ·√T)	Raw
Vega (ν)	S · e^{-qT} · N'(d1) · √T	Divided by 100 (per 1% vol move)
Theta (Θ)	Full expression with both carry terms	Divided by 365 (daily decay)

Model 2 — Binomial Tree CRR (American options)

Cox-Ross-Rubinstein binomial tree with backward induction and early exercise check at each node. Convergence to Black-Scholes confirmed on European options.

Example output (S=100, K=100, T=1y, r=5%, q=2%, σ=20%):

BSM Call European      : 10.4506
Binomial Call European : 10.4502  → converges to BSM
Binomial Call American : 10.4502  → no early exercise premium on non-dividend call

Visualisations

• Interactive Greeks dashboard (ipywidgets sliders): real-time Price / Delta / Gamma / Theta curves for any Call or Put, with ATM strike line
• American vs European price comparison: side-by-side curves + early exercise premium filled area
• 3D Implied Volatility Surface: Strike × Maturity grid with moneyness skew (-0.12 × (K/S - 1)) and term structure (0.04 / √T)
• 3D American Premium Surface: Spot × Maturity grid of Price_American - Price_BSM (Inferno colorscale)

Stack

Python · NumPy · SciPy · Plotly · ipywidgets

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3. EUR/US Yield Curve Analysis

Notebook: EUR_US_Yield_Curveipynb.ipynb

What it does

Analyses and visualises the EUR and USD government yield curves across maturities, exploring the term structure of interest rates and key spread dynamics.

Stack

Python · pandas · Matplotlib

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4. On-Chain Market Microstructure — Nascent AMM Pool vs Mature Market

Folder: on-chain-market-microstructure/ · Report (PDF): report/rapport.pdf

What it does

A comparative market-microstructure study of two Automated Market Maker (AMM) regimes, using real on-chain data: a freshly-deployed illiquid token pool (HLD/ETH, Uniswap V4 on Base) characterised analytically, versus a deep, actively-traded pool (ETH/USDC, Uniswap V3 on Ethereum) estimated econometrically on 6,737 real swaps.

Highlights

Area	What was done
On-chain data engineering	Read a Uniswap V4 pool's raw state from the Singleton PoolManager via extsload — deriving poolId (keccak256), locating the storage slot, decoding the packed Slot0 (no public getter).
AMM microstructure model	Constant-product model → slippage, market depth, impermanent loss, execution cost.
Econometrics on real data	Extracted 6,737 Uniswap V3 Swap events; estimated Kyle's price-impact λ, realised volatility and effective spread (OLS, t-stats, R²).

Key result

Moving the price +1% costs ~$0.03 on HLD vs ~$3.2M on ETH/USDC (a ~10⁸ depth gap). Kyle's λ on ETH/USDC is estimated at 0.011 $/ETH² (t = 317, R² = 0.94) on 6,737 real swaps — a near-zero, statistically-significant impact typical of a deep market. Methodological point: classical price-series analytics (volatility, GARCH) are not identifiable on the newborn pool, so it is modelled, not estimated — the study only estimates where real data exists.

Stack

Python · NumPy · pandas · web3 · eth-abi · on-chain data · econometrics

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Setup

All notebooks run directly in Google Colab — no local installation required. Click any Open in Colab badge above.

To run locally:

pip install numpy pandas scipy yfinance matplotlib plotly ipywidgets

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Author

Gianni Pilotti — quantitative finance, portfolio risk & derivatives pricing. University of Luxembourg (Economics & Finance, Bachelor, expected January 2027). LinkedIn · GitHub