Implied Willow Tree

Bing Dong, Wei Xu, Zhenyu Cui

Research output: Contribution to journalArticlepeer-review

Abstract

Reconstructing the risk-neutral density (RND) of an underlying asset has been extensively studied using market-observed European option prices. However, the literature on reconstructing the corresponding implied stochastic process remains limited. To address this challenge, the authors propose an innovative approach that incorporates an implied willow tree (IWT) into market-observable options data across various maturities. Rather than solely focusing on recovering the RNDs, their method aims to reconstruct the risk-neutral process without relying on any prior parametric models. This unique feature enables data-driven model-free valuation of potentially path-dependent options, eliminating the need for specific parametric stochastic models. Through numerical experiments, the authors demonstrate the effectiveness of their approach in pricing American and Asian options, as well as computing Greeks. Furthermore, they demonstrate the resilience of their approach by assessing its performance when subjected to noise introduced into the original data. To conclude, the authors provide empirical evidence of the efficacy of the IWT method using data from S&P 500 index options.

Original languageEnglish
Pages (from-to)44-74
Number of pages31
JournalJournal of Derivatives
Volume31
Issue number4
DOIs
StatePublished - Jun 2024

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