Pricing and hedging · Research by Gregory Pelts
A Markovian interpretation
of rough diffusion.
Markovian models and numerical methods for derivatives pricing and hedging. The research connects observed volatility behavior with tractable model states, market calibration and conditional valuation.
The purpose
Connect market dynamics
to prices and hedges.
Pricing a contingent contract requires a view of how the market can evolve before its obligations are settled. Volatility fluctuations, option skew and the relationship between returns and volatility all matter for that evolution.
The research develops Markovian models that capture features associated with rough volatility while retaining a finite-dimensional state. Stochastic clocks based on running maxima, local time and related boundary activity provide ways to describe irregular diffusion activity.
The aim is a coherent framework connecting observed market behavior, calibration and the conditional values needed for pricing and hedging. Each model specifies its own dynamics and numerical interpretation.
The approach
Mathematics and computation
developed together.
A tractable model state
Physical-time dynamics and additional stochastic clocks describe how uncertainty evolves. The enlarged Markov state provides the conditioning information for future model values; the contract retains its own record of observations and obligations.
Analytical structure and numerical methods
Model construction, analytical calculations, simulation and GPU computation form a connected research effort. Calibration to option prices, forward diagnostics and discretization studies provide separate checks on its numerical results.
From contract terms to valuation and hedging
The current focus is SPX-linked products, including memory autocalls and European options. SHTAR defines the contractual records and payments. The valuation engine interprets those obligations using the selected model; tradable forwards and options provide instruments for hedge construction.
The intended workflow
Quantitative research
within the client's workflow.
The product vision starts with a term sheet in a financial professional's existing AI application and connects product definition, market calibration, valuation and hedge quantities. The quantitative engine supplies the models and calculations; MCP provides an interface through which an AI client can use those capabilities.
The research engine already supports market calibration and GPU pricing. The public MCP currently provides retrieval and search of the published documents. The integrated valuation and hedging workflow is in development.
Research paper
Mathematical foundations
Gregory Pelts. Roughly Rough: Tractable Markov Processes Emulating Rough Volatility.
Working manuscript
The paper develops the stochastic-clock constructions, process variants and numerical interpretations underlying this research. Its model specifications provide the mathematical reference.
Read the paper PDFRelated research
Define the product before valuing it.
SHTAR connects terms, state and payments with the capabilities of a valuation provider.