For time-changed Markov processes built from the undershooting of a subordinator, expected payoffs solve a coupled non-local equation; for α-stable subordinators this yields a fractional Black-Scholes equation and a renewal formula for seasoned options.
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Time-changed Markov processes and space-time coupled non-local equations
For time-changed Markov processes built from the undershooting of a subordinator, expected payoffs solve a coupled non-local equation; for α-stable subordinators this yields a fractional Black-Scholes equation and a renewal formula for seasoned options.