Paper: arXiv 2301.08232

Authors: Andrew Na, Justin Wan

Abstract

We propose a deep Recurrent neural network (RNN) framework for computing prices and deltas of American options in high dimensions. Our proposed framework uses two deep RNNs, where one network learns the price and the other learns the delta of the option for each timestep. Our proposed framework yields prices and deltas for the entire spacetime, not only at a given point (e.g. t = 0). The computational cost of the proposed approach is linear in time, which improves on the quadratic time seen for feedforward networks that price American options. The computational memory cost of our method is constant in memory, which is an improvement over the linear memory costs seen in feedforward networks. Our numerical simulations demonstrate these contributions, and show that the proposed deep RNN framework is computationally more efficient than traditional feedforward neural network frameworks in time and memory.

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces an innovative RNN-based framework for pricing high-dimensional American options, effectively improving both computational time complexity (to linear) and memory complexity (to constant) relative to traditional feedforward networks. It combines solid mathematical modeling of spacetime option values and deltas with convincing numerical efficiency demonstrations.

Research Flowchart

  flowchart TD
    A[Goal: Efficient High-Dimensional American Option Pricing & Delta Calculation] --> B[Inputs: Option Parameters & Simulated Asset Price Paths]
    B --> C[Dual Deep RNN Framework]
    C --> D[RNN 1: Learns Spacetime Option Prices <br> RNN 2: Learns Spacetime Deltas]
    D --> E[Optimization: Sequential Timestep Training]
    E --> F[Outcomes: Linear Time & Constant Memory Efficiency vs. Feedforward Networks]