Paper: arXiv 2303.17014
Authors: Yuan Hu, W. Brent Lindquist, Svetlozar T. Rachev, Frank J. Fabozzi
Abstract
Motivated by the Corns-Satchell, continuous time, option pricing model, we develop a binary tree pricing model with underlying asset price dynamics following Itô-Mckean skew Brownian motion. While the Corns-Satchell market model is incomplete, our discrete time market model is defined in the natural world; extended to the risk neutral world under the no-arbitrage condition where derivatives are priced under uniquely determined risk-neutral probabilities; and is complete. The skewness introduced in the natural world is preserved in the risk neutral world. Furthermore, we show that the model preserves skewness under the continuous-time limit. We provide numerical applications of our model to the valuation of European put and call options on exchange-traded funds tracking the S&P Global 1200 index.
Complexity vs Empirical Score
- Math Complexity: 7.0/10
- Empirical Rigor: 5.0/10
- Quadrant: Holy Grail — high math complexity, high empirical rigor
Why this score: The paper presents a solid theoretical bridge between Itô-McKean skew Brownian motion and discrete binomial trees, solving the market completeness issue present in the continuous model. While mathematically rigorous with derivations of risk-neutral probabilities and continuous limits, the empirical evaluation is somewhat limited to basic numerical pricing of European options on an ETF index.
Research Flowchart
flowchart TD
A[Research Goal: Develop complete discrete-time option pricing model capturing skewness] --> B[Data Inputs: S&P Global 1200 ETF Options Data]
B --> C[Methodology: Construct Skew Random Walk Binary Tree in Natural World]
C --> D[Computational Process: Apply No-Arbitrage Condition to derive unique Risk-Neutral Probabilities]
D --> E[Continuous-Time Limit Analysis: Prove preservation of Skew Brownian Motion]
E --> F[Key Outcomes: Complete market model, preserved skewness, accurate European Option valuation]