English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider approximate pricing formulas for European options based onapproximating the logarithmic return's density of the underlying by a linearcombination of rescaled Hermite polynomials. The resulting models, that can beseen as perturbations of the classical Black-Scholes one, are nonpararametricin the sense that the distribution of logarithmic returns at fixed times tomaturity is only assumed to have a square-integrable density. We extensivelyinvestigate the empirical performance, defined in terms of out-of-samplerelative pricing error, of this class of approximating models, depending ontheir order (that is, roughly speaking, the degree of the polynomial expansion)as well as on several ways to calibrate them to observed data. Empiricalresults suggest that such approximate pricing formulas, when compared withsimple nonparametric estimates based on interpolation and extrapolation on theimplied volatility curve, perform reasonably well only for options with strikeprice not too far apart from the strike prices of the observed sample.

Nonparametric estimates of option prices via Hermite basis functions