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- W3123669393 abstract "Our first main results are the existence and uniqueness of solutions to a `generalised CIR initial-value problem', which originates from the classical Cox-Ingersoll-Ross (CIR) stochastic differential equation after a time-change. These results hold on a pathwise basis for any continuous driver, and solutions are shown to accommodate any practicable continuous volatility path. We then prove a certain `fast reversion' pathwise convergence of our solutions to a hitting-time limit on the $(D,M)$ topologies of Skorokhod (1956), thereby also accommodating discontinuous paths. In the classical Wiener setting, this limit is an inverse Gaussian L'evy process. By continuous mapping, analogous results follow for any functional, such as a derivative payoff or price, of our volatility paths. As an example, the classical Heston log-price limit is shown to be very closely related, but not equivalent, to the normal-inverse Gaussian L'evy process. This exposes the origin of the marginal connection between these two processes revealed in Mechkov (2015)." @default.
- W3123669393 created "2021-02-01" @default.
- W3123669393 creator A5026235486 @default.
- W3123669393 date "2019-02-01" @default.
- W3123669393 modified "2023-09-27" @default.
- W3123669393 title "Foundations of a pathwise volatility framework with explicit fast reversion limits" @default.
- W3123669393 hasPublicationYear "2019" @default.
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