Volatility Timing: Pricing Barrier Options on DAX XETRA Index

Carlos Esparcia,Francisco Jareño,Elena Ibañez

doi:10.3390/math8050722

Carlos Esparcia, Francisco Jareño + Show 1 more

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https://doi.org/10.3390/math8050722

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Abstract

This paper analyses the impact of different volatility structures on a range of traditional option pricing models for the valuation of call down and out style barrier options. The construction of a Risk-Neutral Probability Term Structure (RNPTS) is one of the main contributions of this research, which changes in parallel with regard to the Volatility Term Structure (VTS) in the main and traditional methods of option pricing. As a complementary study, we propose the valuation of options by assuming a constant or historical volatility. The study implements the GARCH (1,1) model with regard to the continuously compound returns of the DAX XETRA Index traded at daily frequency. Current methodology allows for obtaining accuracy forecasts of the realized market barrier option premiums. The paper highlights not only the importance of selecting the right model for option pricing, but also fitting the most accurate volatility structure.

Highlights

Instability in asset prices and periods of volatility or turbulence are two key elements that characterize and define the trend of financial markets
We consider that risk-neutral probabilities and multiplicative shocks are defined differently, depending on whether we introduce historical (σ) or Generalized Autoregressive Conditional Heterocedasticity (GARCH) volatility, obtaining fixed parameters with regard to the former (u, d, panels show the upward (Pu), Pd ) and time-varying vectors for the latter
In the same vein as the Binomial model, in the Trinomial tree, we consider that risk-neutral probabilities and multiplicative shocks are defined differently, depending on whether we introduce historical (σ) or GARCH volatility, obtaining fixed parameters with regard to the former (u, d, Pu, Pm, Pd ) and time-varying vectors for the latter

Summary

Introduction

Instability in asset prices and periods of volatility or turbulence are two key elements that characterize and define the trend of financial markets. According to [3], a financial option is a contract that gives the holder the right, but not the obligation, to buy or sell an underlying at a price and for a period of time. These instruments represent a right for the buyer and an obligation for the issuer. There are certain categories or exotic derivatives that are currently booming in the financial markets Such is the case of barrier options, whose particularity can be seen in the activation or deactivation of its value when the price of the underlying (S0 ) reaches a certain barrier level (H). Reference [25] studied the valuation of barrier options in contexts of uncertainty

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