Abstract: This project develops a high-performance quantitative framework for systematic asset management, emphasizing rigorous statistical validation and multi-model risk engineering. While the primary objective is to demonstrate a robust methodology for strategy lifecycle management—from signal generation to portfolio optimization—the framework is applied to a momentum-based investment universe within the Indian NSE (National Stock Exchange).
Abstract: This project provides a robust implementation and comparative analysis of the SABR (Stochastic Alpha, Beta, Rho) model—a sophisticated stochastic volatility framework designed to capture the “volatility smile” and “skew” prevalent in modern financial markets. While the traditional Black-Scholes model assumes constant volatility, this work demonstrates how the SABR model mathematically accounts for the dynamic relationship between an asset’s price and its volatility, offering a more accurate representation of market reality.
Abstract: The study begins with the Binomial model, demonstrating how its step-by-step backward induction allows for the valuation of early exercise features in American options—a capability lacking in the standard Black-Scholes formula. It further investigates the Trinomial Tree model, which introduces a “stay” node to improve convergence stability and computational efficiency. Key comparative analyses include:
Early Exercise Incentives: Evaluating how dividend yields ($q$) and interest rates ($r$) create price premiums for American options compared to their European counterparts.
Put-Call Parity: Demonstrating that while strict parity holds for European options, American options are governed by specific price inequalities.
The Greeks: Implementing methodologies to calculate price sensitivities, including Delta, Gamma, and Theta via internal tree nodes, and Vega and Rho using numerical finite difference (bumping) methods.
Results confirm that the Trinomial model provides a smoother convergence to Black-Scholes-Merton values as the number of time steps ($N$) increases, establishing it as a robust industry standard for complex exotic and American options.
Abstract: This project investigates the valuation of a USDEUR Cross-Currency FX Swaption by comparing the widely used closed-form pricing solution, the Black ’76 model (Benchmark), against the advanced Merton Jump-Diffusion (JD) model (Alternative). The goal was to quantify the pricing impact of assuming fat-tailed (leptokurtic) distributions over the Black model’s standard log-normal assumption. Key financial engineering procedures, including yield curve bootstrapping and Vanna-Volga surface interpolation, were performed. The primary finding is that the Merton JD model yields a price that is 8.06% higher than the Black model, accurately capturing a Jump Risk Premium necessary for a more robust and prudent valuation in volatility-sensitive markets.
This notebook develops a quantitative framework for stochastic asset price modelling, derivatives pricing, and portfolio risk management, completed as part of the Erdős Institute Quantitative Finance Boot Camp. Beginning from first principles, it implements Geometric Brownian Motion for correlated multi-asset portfolios and uses Monte Carlo simulation to estimate Value-at-Risk, demonstrating how correlation structure governs tail risk. The Black–Scholes model is derived and implemented, with implied volatility extracted from live TSLA option data and visualised as a volatility smile across strikes and maturities. To address the empirical failure of constant volatility, the Heston stochastic volatility model is introduced: its mean-reverting variance process is simulated via Euler–Maruyama discretisation, and European option prices are computed semi-analytically through Fourier inversion of the characteristic function. The model is then calibrated to real market option prices by minimising mean squared pricing error using the L-BFGS-B algorithm. The project concludes with an empirical delta hedging backtest on a real historical stock path, reporting the discounted profit-and-loss of the strategy.
