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

Journal Article


Abstract


  • 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.

Publication Date


  • 2021

Citation


  • Rodrigo, M. R. (2021). On a strongly continuous semigroup for a Black-Scholes integro-differential operator: European options under jump-diffusion dynamics. Applicable Analysis. doi:10.1080/00036811.2021.1948536

Scopus Eid


  • 2-s2.0-85110019147

Web Of Science Accession Number


Volume


Issue


Place Of Publication


Abstract


  • 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.

Publication Date


  • 2021

Citation


  • Rodrigo, M. R. (2021). On a strongly continuous semigroup for a Black-Scholes integro-differential operator: European options under jump-diffusion dynamics. Applicable Analysis. doi:10.1080/00036811.2021.1948536

Scopus Eid


  • 2-s2.0-85110019147

Web Of Science Accession Number


Volume


Issue


Place Of Publication