arXiv subjects

Ryan McCrickerd

Publications and source records attributed to Ryan McCrickerd.

4 recordsLinked to original sources

arXiv2026

Fast-excursion limit of the Heston model

This article introduces an unconventional model for price processes in finance that emerges from the classical Heston model under Mechkov's fast-reversion limit. This new fast-excursion Heston model exhibits instantaneous (i.e. fast) excursions through an interval of prices at each time, which are invisible to vanilla options but critical for hitting probabilities and continuously monitored exotics. Theoretically, the model provides a rare example of a non-degenerate limit of stochastic volatility models that escapes the Skorokhod topologies. This leads to a class of interval-valued processes which exist as lifts of subordinated Levy processes, through the concept of selections in the theory of random closed sets. On the practical side, we show how the model can be simulated using price-time parametric representations, and utilise a purpose-built classical Heston simulation scheme in order to visualise convergence. Finally we demonstrate how this model raises hitting probabilities for barrier options considerably (of order 10% for one-month EURUSD options), due to taking excursion risk into account.

q-fin.MF↗

arXiv2025

The fundamental representation of pricing adjustments

This article consolidates and extends past work on derivative pricing adjustments, including XVA, by providing an encapsulating representation of the adjustment between any two derivative pricing functions, within an Ito SDE/parabolic PDE framework. We give examples of this representation encapsulating others from the past 20 years, ranging from a well known option pricing adjustment introduced by Gatheral, to the collection of semi-replication XVA originating from Burgard & Kjaer. We show that this fundamental representation can be applied to quantify and mitigate XVA model risk, providing a novel approach to estimating CVA wrong-way risk as an example application.

q-fin.MF↗

arXiv2019

On spatially irregular ordinary differential equations and a pathwise volatility modelling framework

This thesis develops a new framework for modelling price processes in finance, such as an equity price or foreign exchange rate. This can be related to the conventional Ito calculus-based framework through the time integral of a price's squared volatility, or `cumulative variance'. In the new framework, corresponding processes are strictly increasing, solve random ordinary differential equations (ODEs), and are composed with geometric Brownian motion. The new framework has no dependence on stochastic calculus, so processes can be studied on a pathwise basis using probability-free ODE techniques and functional analysis. The ODEs considered depend on continuous driving functions which are `spatially irregular', meaning they need not have any spatial regularity properties such as Holder continuity. They are however strictly increasing in time, thus temporally asymmetric. When sensible initial values are chosen, initial value problem (IVP) solutions are also strictly increasing, and the solution set of such IVPs is shown to contain all differentiable bijections on the non-negative reals. This enables the modelling of any non-negative volatility path which is not zero over intervals, via the time derivative of solutions. Despite this generality, new well-posedness results establish the uniqueness of solutions going forwards in time. Motivation to explore this framework comes from its connection with a time-changed Heston volatility model. The framework shows how Heston price processes can converge to a generalisation of the NIG Levy process, and reveals a deeper relationship between integrated CIR processes and the IG process. Within this framework, a `Riemann-Liouville-Heston' martingale model is defined which generalises these relationships to fractional counterparts. This model's implied volatilities are simulated, and exhibit features characteristic of leading volatility models.

q-fin.MF↗

arXiv2017

Turbocharging Monte Carlo pricing for the rough Bergomi model

The rough Bergomi model, introduced by Bayer, Friz and Gatheral [Quant. Finance 16(6), 887-904, 2016], is one of the recent rough volatility models that are consistent with the stylised fact of implied volatility surfaces being essentially time-invariant, and are able to capture the term structure of skew observed in equity markets. In the absence of analytical European option pricing methods for the model, we focus on reducing the runtime-adjusted variance of Monte Carlo implied volatilities, thereby contributing to the model's calibration by simulation. We employ a novel composition of variance reduction methods, immediately applicable to any conditionally log-normal stochastic volatility model. Assuming one targets implied volatility estimates with a given degree of confidence, thus calibration RMSE, the results we demonstrate equate to significant runtime reductions - roughly 20 times on average, across different correlation regimes.

q-fin.CP↗