fairfolio
Saved Projects

Convergence Analysis of Deep BSDE Methods for Multi-Asset Option Pricing Under Heston Stochastic Volatility

CSEF · 2026 Mathematical Sciences (Senior Division)

Arav Rawat, Advait Kaimal

Overview

We present a systematic empirical analysis of the Deep BSDE method applied to multi-asset European basket option pricing under the Heston stochastic volatility model. Through 120 experiments spanning dimensions d ∈ {1, 2, 5, 10, 20} and volatility-of-volatility σv ∈ [0.1, 0.8], we characterize the accuracy boundary in the (d, σv) parameter space. Three principal findings emerge: (i) pricing error increases sharply past the Feller condition boundary σ ∗ v = √ 2κθ = 0.4, rising from sub-0.35% to over 3%; (ii) error decreases with dimension due to basket diversification, contradicting the expected curse of dimensionality; (iii) training loss diverges from pricing error at high dimensions, indicating reliable prices but unreliable hedging strategies. Ablation studies identify temporal discretization—not network capacity—as the primary error source. Comparison with S&P 500 calibrations shows the convergent regime covers 80% of market conditions. Keywords: High-dimensional PDEs, backward stochastic differential equations, neural networks, Heston model, option pricing, curse of dimensionality, Feller condition

Competition history

  • CSEF 2026 Mathematical Sciences (Senior Division) · Entry S-14-11

Related projects

Closest projects by meaning, across every fair and year in the corpus.

Browse more like this

Source: California Science & Engineering Fair public projects

Save projects to your library

Sign in with Google to keep track of projects you find interesting, organized into folders. An account also raises your daily allowance for “Has this been done?”, and lets you create a key for the MCP server with a much higher limit than anonymous use. Browsing stays public.

Continue with Google