Stochastic models · Research by Gregory Pelts
Rough behavior.
A Markovian state.
Research into tractable Markov processes that emulate features of rough volatility through additional stochastic clocks.
The question
Can irregular clock activity
retain a tractable state?
Short-expiry option smiles motivate volatility models with more than a single diffusion time scale. The research considers Markov constructions with additional clocks based on running maxima or local times.
The aim is to emulate rough-volatility behavior while retaining a state that supports conditional calculations and numerical simulation. Different clock constructions lead to different processes and approximations.
The manuscript sets out the process specifications and their numerical interpretations. It treats these constructions as research models to be examined through their mathematics, calibration and diagnostics.
Inside the research
Processes, numerical methods
and financial interpretation.
Clocks and state
Physical time and additional process clocks describe how diffusion activity evolves. The construction specifies the state and dependence needed for future conditional values.
Simulation and calibration
Numerical implementations connect process definitions to option prices. Calibration, martingale diagnostics and discretization checks serve different roles in assessing a model.
Path-dependent products
Autocalls connect market observations to dated contingent deliveries. SHTAR defines those obligations independently of the model used to value them.
Working manuscript
Roughly Rough
Tractable Markov Processes Emulating Rough Volatility
Gregory Pelts
The full paper contains the mathematical constructions, process variants and implementation discussion. Its specifications are the reference for each model.
Open the manuscript PDFRelated research
Define the product before valuing it.
SHTAR connects terms, state and payments with the capabilities of a valuation provider.