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 a Black-Scholes integro-differential operator associated with a partial integro-differential equation for pricing European options with a jump-diffusion process for the underlying asset. Using the theory of one-parameter semigroups, we prove that the operator is the infinitesimal generator of a strongly continuous semigroup and express the semigroup explicitly as a convolution of a jump function, the Black-Scholes kernel and the payoff function. This is analogous to the Gauss-Weierstrass and Poisson semigroups. Then we investigate the pricing of European options under jump diffusion for two broad classes of payoff functions. A generalised put-call parity relating the functions from both classes is also obtained.

On a strongly continuous semigroup for a Black-Scholes integro-differential operator: European options under jump-diffusion dynamics