scholarly journals A Bayesian nonparametric approach to option pricing

2020 ◽  
Vol 18 (4) ◽  
pp. 115-137
Author(s):  
Zhang Qin ◽  
Caio Almeida
Keyword(s):  
Option Pricing ◽  
Implied Volatility ◽  
Kernel Functions ◽  
General Covariance ◽  
Bayesian Nonparametric ◽  
Market Data ◽  
Nonparametric Approach ◽  
Covariance Functions ◽  
Implied Volatility Surface ◽  
Volatility Surface

Accurately modeling the implied volatility surface is of great importance to option pricing, trading and hedging. In this paper, we investigate the use of a Bayesian nonparametric approach to fit and forecast the implied volatility surface with observed market data. More specifically, we explore Gaussian Processes with different kernel functions characterizing general covariance functions. We also obtain posterior distributions of the implied volatility and build confidence intervals for the predictions to assess potential model uncertainty. We apply our approach to market data on the S&P 500 index option market in 2018, analyzing 322,983 options. Our results suggest that the Bayesian approach is a powerful alternative to existing parametric pricing models

Empirical performance of stochastic volatility option pricing models

2021 ◽  
pp. 2050056
Author(s):  
Przemyslaw S. Stilger ◽  
Ngoc Quynh Anh Nguyen ◽  
Tri Minh Nguyen
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Implied Volatility ◽  
Model Performance ◽  
The Other ◽  
Heston Model ◽  
Pricing Models ◽  
Implied Volatility Surface ◽  
Empirical Performance ◽  
Volatility Surface

This paper examines the empirical performance of four stochastic volatility option pricing models: Heston, Heston[Formula: see text], Bates and Heston–Hull–White. To compare these models, we use individual stock options data from January 1996 to August 2014. The comparison is made with respect to pricing and hedging performance, implied volatility surface and risk-neutral return distribution characteristics, as well as performance across industries and time. We find that the Heston model outperforms the other models in terms of in-sample pricing, whereas Heston[Formula: see text] model outperforms the other models in terms of out-of-sample hedging. This suggests that taking jumps or stochastic interest rates into account does not improve the model performance after accounting for stochastic volatility. We also find that the model performance deteriorates during the crises as well as when the implied volatility surface is steep in the maturity or strike dimension.

scholarly journals Accounting for earnings announcements in the pricing of equity options

2014 ◽  
Vol 01 (04) ◽  
pp. 1450031 ◽  
Author(s):  
Tim Leung ◽  
Marco Santoli
Keyword(s):  
Option Pricing ◽  
Stock Price ◽  
Implied Volatility ◽  
Analytical Approximation ◽  
Price Impact ◽  
Equity Options ◽  
Announcement Date ◽  
Implied Volatility Surface ◽  
Before And After ◽  
Volatility Surface

We study an option pricing framework that accounts for the price impact of an earnings announcement (EA), and analyze the behavior of the implied volatility surface prior to the event. On the announcement date, we incorporate a random jump to the stock price to represent the shock due to earnings. We consider different distributions of the scheduled earnings jump as well as different underlying stock price dynamics before and after the EA date. Our main contributions include analytical option pricing formulas when the underlying stock price follows the Kou model along with a double-exponential or Gaussian EA jump on the announcement date. Furthermore, we derive analytic bounds and asymptotics for the pre-EA implied volatility under various models. The calibration results demonstrate adequate fit of the entire implied volatility surface prior to an announcement. We also compare the risk-neutral distribution of the EA jump to its historical distribution. Finally, we discuss the valuation and exercise strategy of pre-EA American options, and illustrate an analytical approximation and numerical results.

scholarly journals An Intuitive Introduction to Fractional and Rough Volatilities

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 994
Author(s):  
Elisa Alòs ◽  
Jorge A. León
Keyword(s):  
Malliavin Calculus ◽  
Numerical Experiments ◽  
Implied Volatility ◽  
Natural Approach ◽  
Volatility Models ◽  
Implied Volatility Surface ◽  
Short Memory ◽  
White Type ◽  
Volatility Surface ◽  
Theoretical Results

Here, we review some results of fractional volatility models, where the volatility is driven by fractional Brownian motion (fBm). In these models, the future average volatility is not a process adapted to the underlying filtration, and fBm is not a semimartingale in general. So, we cannot use the classical Itô’s calculus to explain how the memory properties of fBm allow us to describe some empirical findings of the implied volatility surface through Hull and White type formulas. Thus, Malliavin calculus provides a natural approach to deal with the implied volatility without assuming any particular structure of the volatility. The aim of this paper is to provides the basic tools of Malliavin calculus for the study of fractional volatility models. That is, we explain how the long and short memory of fBm improves the description of the implied volatility. In particular, we consider in detail a model that combines the long and short memory properties of fBm as an example of the approach introduced in this paper. The theoretical results are tested with numerical experiments.

scholarly journals Generalized Mean-Reverting 4/2 Factor Model

2019 ◽  
Vol 12 (4) ◽  
pp. 159 ◽  
Author(s):  
Yuyang Cheng ◽  
Marcos Escobar-Anel ◽  
Zhenxian Gong
Keyword(s):  
Value At Risk ◽  
Implied Volatility ◽  
Factor Model ◽  
Risk Measures ◽  
Risk Measure ◽  
Common Factor ◽  
Principal Component ◽  
Characteristic Functions ◽  
Implied Volatility Surface ◽  
Volatility Surface

This paper proposes and investigates a multivariate 4/2 Factor Model. The name 4/2 comes from the superposition of a CIR term and a 3/2-model component. Our model goes multidimensional along the lines of a principal component and factor covariance decomposition. We find conditions for well-defined changes of measure and we also find two key characteristic functions in closed-form, which help with pricing and risk measure calculations. In a numerical example, we demonstrate the significant impact of the newly added 3/2 component (parameter b) and the common factor (a), both with respect to changes on the implied volatility surface (up to 100%) and on two risk measures: value at risk and expected shortfall where an increase of up to 29% was detected.

Sign in / Sign up

Export Citation Format

Share Document