Jump risk premia in the presence of clustered jumps

Authors: Francis Liu, Natalie Packham, Artur Sepp

Abstract

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.

Complexity vs Empirical Score

Math Complexity: 7.5/10
Empirical Rigor: 6.0/10 (capped from 8.0: transaction costs not modelled; see penalty flags)
Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a rigorous mathematical framework using a bivariate Hawkes process to model self- and cross-exciting jumps in option pricing. It demonstrates high empirical rigor by calibrating to Bitcoin options and analyzing delta-hedged strategy performance, complemented by reproducible code provided via Quantlet.

Research Flowchart

  flowchart TD
    A[Research Goal: Capture jump clustering & asymmetric IV skew dynamics using Hawkes processes] --> B[Data Inputs: Bitcoin BTC Options & Futures Data]
    B --> C[Methodology: Bivariate Hawkes Process Model with Positive & Negative Jump Risk Premia]
    C --> D[Option Calibration & Jump Risk Premia Extraction]
    D --> E[Empirical Analysis: Predictive Modeling on Futures Cost of Carry & Delta-Hedged Strategies]
    E --> F[Key Outcomes: Model generates dynamic IV skews; Jump Premia predict Futures Carry & Strategy Performance]

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