arXiv subjects

Natalie Packham

Publications and source records attributed to Natalie Packham.

5 recordsLinked to original sources

arXiv2025

Jump risk premia in the presence of clustered jumps

This paper presents an option pricing model that incorporates clustered jumps using a bivariate Hawkes process. The process captures both self- and cross-excitation of positive and negative jumps, enabling the model to generate return dynamics with asymmetric, time-varying skewness and to produce positive or negative implied volatility skews. This feature is especially relevant for assets such as cryptocurrencies, so-called ``meme'' stocks, G-7 currencies, and certain commodities, where implied volatility skews may change sign depending on prevailing sentiment. We introduce two additional parameters, namely the positive and negative jump premia, to model the market risk preferences for positive and negative jumps, inferred from options data. This enables the model to flexibly match observed skew dynamics. Using Bitcoin (BTC) options, we empirically demonstrate how inferred jump risk premia exhibit predictive power for both the cost of carry in BTC futures and the performance of delta-hedged option strategies.

q-fin.MF↗

arXiv2024

A Markov approach to credit rating migration conditional on economic states

We develop a model for credit rating migration that accounts for the impact of economic state fluctuations on default probabilities. The joint process for the economic state and the rating is modelled as a time-homogeneous Markov chain. While the rating process itself possesses the Markov property only under restrictive conditions, methods from Markov theory can be used to derive the rating process' asymptotic behaviour. We use the mathematical framework to formalise and analyse different rating philosophies, such as point-in-time (PIT) and through-the-cycle (TTC) ratings. Furthermore, we introduce stochastic orders on the bivariate process' transition matrix to establish a consistent notion of "better" and "worse" ratings. Finally, the construction of PIT and TTC ratings is illustrated on a Merton-type firm-value process.

q-fin.RM↗

arXiv2023

Risk factor aggregation and stress testing

Stress testing refers to the application of adverse financial or macroeconomic scenarios to a portfolio. For this purpose, financial or macroeconomic risk factors are linked with asset returns, typically via a factor model. We expand the range of risk factors by adapting dimension-reduction techniques from unsupervised learning, namely PCA and autoencoders. This results in aggregated risk factors, encompassing a global factor, factors representing broad geographical regions, and factors specific to cyclical and defensive industries. As the adapted PCA and autoencoders provide an interpretation of the latent factors, this methodology is also valuable in other areas where dimension-reduction and explainability are crucial.

q-fin.RM↗

arXiv2021

Hedging Cryptocurrency Options

The cryptocurrency market is volatile, non-stationary and non-continuous. Together with liquid derivatives markets, this poses a unique opportunity to study risk management, especially the hedging of options, in a turbulent market. We study the hedge behaviour and effectiveness for the class of affine jump diffusion models and infinite activity Levy processes. First, market data is calibrated to stochastic volatility inspired (SVI)-implied volatility surfaces to price options. To cover a wide range of market dynamics, we generate Monte Carlo price paths using an SVCJ model (stochastic volatility with correlated jumps), a close-to-actual-market GARCH-filtered kernel density estimation as well as a historical backtest. In all three settings, options are dynamically hedged with Delta, Delta-Gamma, Delta-Vega and Minimum Variance strategies. Including a wide range of market models allows to understand the trade-off in the hedge performance between complete, but overly parsimonious models, and more complex, but incomplete models. The calibration results reveal a strong indication for stochastic volatility, low jump frequency and evidence of infinite activity. Short-dated options are less sensitive to volatility or Gamma hedges. For longer-dated options, tail risk is consistently reduced by multiple-instrument hedges, in particular by employing complete market models with stochastic volatility.

q-fin.PR↗

arXiv2018

A factor-model approach for correlation scenarios and correlation stress-testing

In 2012, JPMorgan accumulated a USD~6.2 billion loss on a credit derivatives portfolio, the so-called `London Whale', partly as a consequence of de-correlations of non-perfectly correlated positions that were supposed to hedge each other. Motivated by this case, we devise a factor model for correlations that allows for scenario-based stress testing of correlations. We derive a number of analytical results related to a portfolio of homogeneous assets. Using the concept of Mahalanobis distance, we show how to identify adverse scenarios of correlation risk. In addition, we demonstrate how correlation and volatility stress tests can be combined. As an example, we apply the factor-model approach to the "London Whale" portfolio and determine the value-at-risk impact from correlation changes. Since our findings are particularly relevant for large portfolios, where even small correlation changes can have a large impact, a further application would be to stress test portfolios of central counterparties, which are of systemically relevant size.

q-fin.RM↗