Paper: arXiv 2310.01104

Authors: Purba Banerjee, Srikanth Iyer, Shashi Jain

Abstract

We consider the hedging of European options when the price of the underlying asset follows a single-factor Markovian framework. By working in such a setting, Carr and Wu \cite{carr2014static} derived a spanning relation between a given option and a continuum of shorter-term options written on the same asset. In this paper, we have extended their approach to simultaneously include options over multiple short maturities. We then show a practical implementation of this with a finite set of shorter-term options to determine the hedging error using a Gaussian Quadrature method. We perform a wide range of experiments for both the \textit{Black-Scholes} and \textit{Merton Jump Diffusion} models, illustrating the comparative performance of the two methods.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 5.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a solid theoretical extension of Carr and Wu’s spanning relation to multi-period static hedging using Gaussian Quadrature numerical methods. While it features rigorous mathematical derivations and numerical experiments under Black-Scholes and Merton Jump Diffusion models, it lacks extensive empirical backtesting on historical market data.

Research Flowchart

  flowchart TD
    A[Research Goal: Multi-period static hedging<br/>of European options using short-term contracts] --> B[Framework Setup: Single-factor Markovian model<br/>extended to multiple short maturities]
    B --> C[Inputs & Models: Black-Scholes &<br/>Merton Jump Diffusion models]
    C --> D[Computational Method: Discretize continuum via<br/>Gaussian Quadrature to finite option sets]
    D --> E[Empirical Experiments: Simulate static hedging performance<br/>and measure hedging error]
    E --> F[Key Outcome: Superior multi-period hedging efficiency<br/>and quantified error across asset dynamics]