Tootfinder

Pricing Fractal Derivatives under Sub-Mixed Fractional Brownian Motion with Jumps
Nader Karimi
https://arxiv.org/abs/2506.24111 https://

Pricing Fractal Derivatives under Sub-Mixed Fractional Brownian Motion with Jumps
We study the pricing of derivative securities in financial markets modeled by a sub-mixed fractional Brownian motion with jumps (smfBm-J), a non-Markovian process that captures both long-range dependence and jump discontinuities. Under this model, we derive a fractional integro-partial differential equation (PIDE) governing the option price dynamics. Using semigroup theory, we establish the existence and uniqueness of mild solutions to this PIDE. For European options, we obtain a closed-form …