Calibration and Option Pricing with Stochastic Volatility and Double Exponential Jumps

TL;DR

This paper introduces a stochastic volatility model with double-exponential jumps that improves option pricing accuracy, especially for short-term implied volatility, and demonstrates its effectiveness for exotic options using Fourier techniques.

Contribution

It provides a thorough analysis of calibration and pricing performance of the model, highlighting its advantages over similar models and its tractability for exotic options.

Findings

Outperforms challenger models in fitting short-term implied volatility smile

Effective for pricing various exotic options using Fourier methods

Model captures richer dynamics due to asymmetric jump distribution

Abstract

This work examines a stochastic volatility model with double-exponential jumps in the context of option pricing. The model has been considered in previous research articles, but no thorough analysis has been conducted to study its quality of calibration and pricing capabilities thus far. We provide evidence that this model outperforms challenger models possessing similar features (stochastic volatility and jumps), especially in the fit of the short term implied volatility smile, and that it is particularly tractable for the pricing of exotic options from different generations. The article utilizes Fourier pricing techniques (the PROJ method and its refinements) for different types of claims and several generations of exotics (Asian options, cliquets, barrier options, and options on realized variance), and all source codes are made publicly available to facilitate adoption and future research. The results indicate that this model is highly promising, thanks to the asymmetry of the jumps distribution allowing it to capture richer dynamics than a normal jump size distribution. The parameters all have meaningful econometrics interpretations that are important for adoption by risk-managers.