Finance

Non-normal methods, Deep RL take on classical finance

I explore how modern mathematical and computational ideas reshape classical finance. My current work focuses on three connected directions:

  1. Beyond Normality: Asset returns often display heavy tails and volatility clustering. I study alternatives to the Gaussian paradigm, such as Lévy–Stable and Tempered Stable processes, and their implications for inference and pricing.
  2. Dependence and Systemic Risk: Linear correlation underestimates joint extremes. I use copulas and tail-dependence models to quantify multi-asset crash risk.
  3. Learning and Control in Finance: Reinforcement-learning frameworks can reinterpret classical problems in portfolio choice and market making.

1. Rethinking Distributional Assumptions

Mandelbrot and Fama questioned the lognormal model of asset prices.
Empirical evidence suggests that returns may follow heavy-tailed processes with infinite variance.
Our projects revisit this premise using both model-selection and pricing approaches.

🔹 Rolling AIC for Stable vs Normal

Tracking how market regimes switch between normal and stable distributions using rolling model-comparison techniques.
Collaborator: Hariharasudhan (B.A. Economics, MSE)

🔹 Event Study Analysis under Stable Tails

Analyzing stock price reactions around corporate and political events to evaluate market efficiency when returns exhibit stable tails, volatility clustering, and dependence.
Collaborator: Tania (B.A. Economics, MSE)

🔹 A Generalized Tempered Stable Approach to Option Pricing

Extending the Lévy–Stable framework by tempering its tails to create a tractable yet heavy-tailed model suitable for option pricing.
Compares traditional Black–Scholes pricing with a Generalized Tempered Stable (GTS) formulation using Fourier methods.
Collaborators: Mr. Sushant Singh and Mr. Jai Shivam (PGDM, MSE)

2. Modeling Dependence and Tail Risk

Classical correlation is inadequate for joint extremes.
This stream focuses on copulas and multivariate dependence structures to capture systemic vulnerability in Indian markets.

🔹 Copulas and Tail Risk

Measuring joint downside crashes across Nifty stocks using lower-tail-dependence copulas.
Collaborators: Ms. Amritha (M.A. Economics, MSE) and Dr. Ekta Selarka (MSE)

3. Portfolio Optimisation with Modern Reinforcement Learning

Classical portfolio theory assumes static rebalancing under fixed risk–return trade-offs.
In contrast, reinforcement learning treats portfolio management as a sequential decision process under uncertainty.
Our work explores how policy-gradient methods can dynamically learn allocation strategies that adapt to changing market conditions and transaction costs.

Collaborators: Ongoing work with Dr. Arun Selvan.

References