Risk-Neutral Pricing of Random-Expiry Options Using Trinomial Trees

ArXiv ID: 2508.17014 “View on arXiv”

Authors: Sebastien Bossu, Michael Grabchak

Abstract

Random-expiry options are nontraditional derivative contracts that may expire early based on a random event. We develop a methodology for pricing these options using a trinomial tree, where the middle path is interpreted as early expiry. We establish that this approach is free of arbitrage, derive its continuous-time limit, and show how it may be implemented numerically in an efficient manner.

Keywords: Random-expiry options, Trinomial tree, Derivative pricing, Arbitrage-free pricing, Numerical methods, Derivatives/Options

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper uses advanced mathematical tools like subordinated Brownian motion and risk-neutral measures in incomplete markets, with complex derivations for tree convergence, warranting high math complexity. It also provides a full numerical implementation (Python code on GitHub) and discusses practical applications like insurance-linked securities, indicating strong empirical rigor.

  flowchart TD
    A["Research Goal<br>Price Random-Expiry Options"] --> B["Methodology<br>Develop Trinomial Tree Framework"]
    B --> C{"Data/Inputs<br>Underlying Process Parameters &<br>Random Expiry Distribution"}
    C --> D["Computational Process<br>Build Trinomial Tree<br>with Middle Path as Early Expiry"]
    D --> E{"Arbitrage-Free<br>Check?"}
    E -- Yes --> F["Key Findings/Outcomes<br>Arbitrage-Free Pricing Methodology"]
    E -- No --> G["Refine Node Probabilities"]
    G --> D