Dataset Information

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

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.

SUBMITTER: Popescu DM

PROVIDER: S-EPMC4308111 | biostudies-literature | 2015

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

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

Popescu Dan M DM Lipan Ovidiu O

PloS one 20150127 1

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 involv ...[more]

PMID: 25625856

Similar Datasets

Project description:Proteins adopt different higher-order structures (HOS) to enable their unique biological functions. Understanding the complexities of protein higher-order structures and dynamics requires integrated approaches, where mass spectrometry (MS) is now positioned to play a key role. One of those approaches is protein footprinting. Although the initial demonstration of footprinting was for the HOS determination of protein/nucleic acid binding, the concept was later adapted to MS-based protein HOS analysis, through which different covalent labeling approaches "mark" the solvent accessible surface area (SASA) of proteins to reflect protein HOS. Hydrogen-deuterium exchange (HDX), where deuterium in D2O replaces hydrogen of the backbone amides, is the most common example of footprinting. Its advantage is that the footprint reflects SASA and hydrogen bonding, whereas one drawback is the labeling is reversible. Another example of footprinting is slow irreversible labeling of functional groups on amino acid side chains by targeted reagents with high specificity, probing structural changes at selected sites. A third footprinting approach is by reactions with fast, irreversible labeling species that are highly reactive and footprint broadly several amino acid residue side chains on the time scale of submilliseconds. All of these covalent labeling approaches combine to constitute a problem-solving toolbox that enables mass spectrometry as a valuable tool for HOS elucidation. As there has been a growing need for MS-based protein footprinting in both academia and industry owing to its high throughput capability, prompt availability, and high spatial resolution, we present a summary of the history, descriptions, principles, mechanisms, and applications of these covalent labeling approaches. Moreover, their applications are highlighted according to the biological questions they can answer. This review is intended as a tutorial for MS-based protein HOS elucidation and as a reference for investigators seeking a MS-based tool to address structural questions in protein science.

Dataset Information

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

Publications

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

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure