Listed Volatility and Variance Derivatives

CHAPTER 14 DX Analytics – Square-Root Jump Diffusion

14.1 Introduction

Similarly to the previous chapter, this chapter again uses DX Analytics to model the VSTOXX index, but this time by the square-root jump diffusion (SRJD) process as introduced in chapter 7, Advanced Modeling of the VSTOXX Index. The study this chapter implements is actually the same as in the previous one using the very same data set. However, the challenge is increased in that we require multiple VSTOXX option maturities to be calibrated simultaneously and over time.

14.2 Modeling the VSTOXX Options

DX Analytics provides a class for the deterministic shift square-root jump diffusion model. It is called dx.square_root_jump_diffusion(). Although the calibration we are implementing in this chapter is more or less the same as in the previous one, we need nevertheless to adjust the code significantly in many places. Therefore, we are stepping through the single elements again in what follows. All the code used in this chapter is found in the Python script dx_srjd_calibration.py (see sub-section 14.6.1, dx_srjd_calibration.py).

The beginning of the script is rather similar to the one implementing the calibration of the square-root diffusion model. A major difference is that we need three additional parameters lambda, mu and delta.

The function srjd_get_option_selection() selects the options used for the calibration. ...