Finance
Projects
American Option & Longstaff–Schwartz
17 Sep 2025 by Tom Gilgenkrantz
- Simulation of geometric Brownian motion paths
- Estimation of continuation values using linear regression
- Detection and visualization of early exercise points and the exercise boundary
- Pricing of the American option using the estimated continuation values and early exercise points
Option Pricing Dashboard
5 Sep 2025 by Tom Gilgenkrantz
- Interactive Plotly dashboard to explore Call/Put pricing sensitivities
- Grid of effects of S, K, T, r, σ
- Greeks bar chart
- Dynamic KPIs: price, intrinsic, time value, moneyness, break-even, max loss/profit
Convertible Bond Pricer
26 Aug 2025 by Tom Gilgenkrantz
- Implementation of a closed-form Black–Scholes model for convertible bond pricing
- Derivation of sensitivities to volatility, interest rates, dividends, and stock price
- Visualization of the payoff structure (bond floor + conversion option)
- Monte Carlo simulation of stock price trajectories to analyze risk distribution
Millennium Market Making Challenge
23 Jul 2025 by Tom Gilgenkrantz
- Python implementation of a automated Market Maker within Amplify’s Quant Trading simulator in 24 hours
- Object-oriented design of a quoting engine returning two-sided bid/ask quotes
- Backtest of synthetic ETF vs. real FAANG benchmark with normalization for comparability
- Implementation of a systematic trading strategy based on spread between FAANG ETF and its components
- Live exposure & PnL monitoring of the trading strategy
Markowitz Portfolio Optimization
18 May 2025 by Tom Gilgenkrantz
- Implementation of the Markowitz mean-variance portfolio theory
- Construction of the efficient frontier with Monte Carlo simulations
- Estimation of covariance matrix and expected returns from historical data (Yfinance)
- Visualization of efficient frontier, minimum variance portfolio and tangency portfolio
SPX & VIX joint smile calibration
11 Feb 2025 by Tom Gilgenkrantz & Ranim Knaissi
- Joint calibration of SPX & VIX volatility smiles using a Quintic OU stochastic volatility model
- Forward variance term structure ξ₀(t) extracted from market using Carr-Madan formula
- VIX options priced semi-analytically via Gauss-Hermite quadrature exploiting polynomial structure
- Monte Carlo simulation for SPX derivatives with variance reduction (antithetic paths, control variates)
- Optimization via differential evolution to fit real volatility surfaces (CBOE data)
- Analysis of parameter sensitivity and implications of skew/asymmetry in smiles
- Exploration of model extensions: forward calibration, stress testing, real-time arbitrage detection
Stocks time series analysis
21 Dec 2024 by Tom Gilgenkrantz & Yassine Boicra
- Data preprocessing and computation of derived series Y(m) for m ∈ {1, 2, 3, 4}
- AR(1) modeling with structural break detection
- Visualization of residuals before and after the break
- Comparison with a normal density & QQ-plots to assess residual normality
- Economic analysis of market regime shifts (SVB crisis, Credit Suisse, ...)
Stock portfolio tracking software
17 Jul 2024 by Tom Gilgenkrantz
- Access to stock prices with Yfinance
- Storing positions in a CSV
- Graphical user interface with Tkinter
- Summary of portfolio performance and diversific'ation
