Non-parametric method for European option bounds

Hsuan Chu Lin*, Ren Raw Chen, Oded Palmon

*Corresponding author for this work

Research output: Contribution to journalJournal Article peer-review

4 Scopus citations


There is much research whose efforts have been devoted to discovering the distributional defects in the Black-Scholes model, which are known to cause severe biases. However, with a free specification for the distribution, one can only find upper and lower bounds for option prices. In this paper, we derive a new non-parametric lower bound and provide an alternative interpretation of Ritchken's (J Finance 40:1219-1233, 1985) upper bound to the price of the European option. In a series of numerical examples, our new lower bound is substantially tighter than previous lower bounds. This is prevalent especially for out of the money options where the previous lower bounds perform badly. Moreover, we present how our bounds can be derived from histograms which are completely non-parametric in an empirical study. We discover violations in our lower bound and show that those violations present arbitrage profits. In particular, our empirical results show that out of the money calls are substantially overpriced (violate the lower bound).

Original languageEnglish
Pages (from-to)109-129
Number of pages21
JournalReview of Quantitative Finance and Accounting
Issue number1
StatePublished - 01 2012
Externally publishedYes


  • Black-Scholes model
  • Non-parametric
  • Option bounds


Dive into the research topics of 'Non-parametric method for European option bounds'. Together they form a unique fingerprint.

Cite this