A Kramers-Moyal approach to the analysis of third-order noise with applications in option valuation.

Clicks: 170
ID: 30617
2015
Article Quality & Performance Metrics
Overall Quality
Not rated
Combines reader engagement with the AI quality analysis. This article has not been analysed, so there is no overall score — reader engagement is measured and shown alongside.
AI Quality Assessment
Not analyzed
Readership in this journal
Popular

Ranked #1,829 of 2,056 articles by views in PloS one

Most read Least read

Bar heights use a square-root scale. Only the 120 most-read articles are drawn; the journal has 2,056 in total.

Mint this article as an NFT
Not yet minted

Create a permanent, verifiable on-chain record of this article on the Scimatic Network. The NFT is held in your Journament account, and you can withdraw it to your own wallet at any time.

5 SUSD one-off · no wallet required
Sign in to mint
Abstract
We propose the use of the Kramers-Moyal expansion in the analysis of third-order noise. In particular, we show how the approach can be applied in the theoretical study of option valuation. Despite Pawula's theorem, which states that a truncated model may exhibit poor statistical properties, we show that for a third-order Kramers-Moyal truncation model of an option's and its underlier's price, important properties emerge: (i) the option price can be written in a closed analytical form that involves the Airy function, (ii) the price is a positive function for positive skewness in the distribution, (iii) for negative skewness, the price becomes negative only for price values that are close to zero. Moreover, using third-order noise in option valuation reveals additional properties: (iv) the inconsistencies between two popular option pricing approaches (using a "delta-hedged" portfolio and using an option replicating portfolio) that are otherwise equivalent up to the second moment, (v) the ability to develop a measure R of how accurately an option can be replicated by a mixture of the underlying stocks and cash, (vi) further limitations of second-order models revealed by introducing third-order noise.
Reference Key
popescu2015aplos Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Popescu, Dan M;Lipan, Ovidiu;
Journal PloS one
Year 2015
DOI
10.1371/journal.pone.0116752
URL
Keywords Keywords not found

Citations

No citations found. To add a citation, contact the admin at info@scimatic.org

Comments

No comments yet. Be the first to comment on this article.