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

TL;DR

This paper introduces a trinomial tree method for arbitrage-free pricing of random-expiry options, capturing early expiry events and providing an efficient numerical implementation with a continuous-time limit.

Contribution

It develops a novel trinomial tree approach for pricing random-expiry options, ensuring arbitrage-freeness and linking to continuous-time models.

Findings

Method is arbitrage-free

Provides a continuous-time limit derivation

Enables efficient numerical implementation

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.