Learning for infinitely divisible GARCH models in option pricing

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Fumin Zhu ◽  
Michele Leonardo Bianchi ◽  
Young Shin Kim ◽  
Frank J. Fabozzi ◽  
Hengyu Wu
Keyword(s):  
Option Pricing ◽  
Stock Returns ◽  
Bayesian Learning ◽  
Space Structure ◽  
Estimation Methods ◽  
Garch Models ◽  
Learning Approaches ◽  
Infinitely Divisible ◽  
Asymmetric Garch ◽  
Non Gaussian

AbstractThis paper studies the option valuation problem of non-Gaussian and asymmetric GARCH models from a state-space structure perspective. Assuming innovations following an infinitely divisible distribution, we apply different estimation methods including filtering and learning approaches. We then investigate the performance in pricing S&P 500 index short-term options after obtaining a proper change of measure. We find that the sequential Bayesian learning approach (SBLA) significantly and robustly decreases the option pricing errors. Our theoretical and empirical findings also suggest that, when stock returns are non-Gaussian distributed, their innovations under the risk-neutral measure may present more non-normality, exhibit higher volatility, and have a stronger leverage effect than under the physical measure.

scholarly journals OPTION PRICING AND HEDGING WITH TEMPORAL CORRELATIONS

2002 ◽  
Vol 05 (03) ◽  
pp. 307-320 ◽  
Author(s):  
LORENZO CORNALBA ◽  
JEAN-PHILIPPE BOUCHAUD ◽  
MARC POTTERS
Keyword(s):  
Option Pricing ◽  
Stock Returns ◽  
General Formula ◽  
Gaussian Processes ◽  
Risk Minimisation ◽  
Temporal Correlations ◽  
Hedging Strategies ◽  
Black Scholes ◽  
Non Gaussian

We consider the problem of option pricing and hedging when stock returns are correlated in time. Within a quadratic-risk minimisation scheme with history-dependent hedging strategies, we obtain a general formula, valid for weakly correlated non-Gaussian processes. We show that for Gaussian price increments, the correlations are irrelevant, and the Black-Scholes formula holds with the volatility of the price increments calculated on the scale of the re-hedging. For non-Gaussian processes, further non trivial corrections to the "smile" are brought about by the correlations, even when the hedge is the Black-Scholes Δ-hedge. We introduce a compact notation which eases the computations and could be of use to deal with more complicated models.

Bayesian option pricing using asymmetric GARCH models

2002 ◽  
Vol 9 (3) ◽  
pp. 321-342 ◽  
Author(s):  
Luc Bauwens ◽  
Michel Lubrano
Keyword(s):  
Option Pricing ◽  
Garch Models ◽  
Asymmetric Garch

scholarly journals INVESTIGATING VOLATILITY BEHAVIOUR: EMPIRICAL EVIDENCE FROM ISLAMIC STOCK INDICES

2020 ◽  
Vol 6 (4) ◽  
Author(s):  
Burhanuddin Burhanuddin
Keyword(s):  
Stock Returns ◽  
Risk Premium ◽  
Garch Models ◽  
Single Model ◽  
Volatility Risk ◽  
Stock Indices ◽  
Asymmetric Garch ◽  
Mean Square Errors ◽  
Forecasting Errors ◽  
Daily Returns

The main purpose of this research is to apply five univariate GARCH models to thedaily stock returns of four major sharia stock indices. Two symmetric versions of theGARCH model (GARCH and MGARCH) and three asymmetric versions (EGARCH,TGARCH and PGARCH) are employed to estimate and forecast the volatility of fourmajor sharia indices. The results provide strong evidence that all models can depictthe volatility behaviours in all four sharia index returns. The two symmetric modelsindicate that the volatility of a sharia index’s returns depend on its previous own lags,and statistically prove that a rise in volatility (risk) leads to an increase in mean(return), i.e. the risk premium effect. Meanwhile, the three asymmetric modelssuggest that negative shocks to daily returns tend to have higher impact on thevolatility of sharia indices than positive shocks of the same magnitude. Moreover,based on the values of forecasting errors – root mean square errors (RMSE) andmean absolute errors (MAE) – the asymmetric GARCH models outperform thesymmetric models in forecasting the volatility of four major sharia indices. However,the very small difference values of RMSE and MAE among the univariate GARCH-type models denote that no single model is superior to the others.

Early warning signals using AVaRs of infinitely divisible GARCH models — evidence from stock index markets

2015 ◽  
Vol 47 (43) ◽  
pp. 4630-4652 ◽  
Author(s):  
Chia-Chien Chang ◽  
Te-Chung Hu ◽  
Chiu-Fen Kao ◽  
Ya-Chi Chang
Keyword(s):  
Early Warning ◽  
Stock Index ◽  
Garch Models ◽  
Infinitely Divisible ◽  
Warning Signals ◽  
Early Warning Signals

scholarly journals Modelling volatility of Kuala Lumpur composite index (KLCI) using SV and garch models

2019 ◽  
Vol 13 (3) ◽  
pp. 1087
Author(s):  
Ezatul Akma Abdullah ◽  
Siti Meriam Zahari ◽  
S.Sarifah Radiah Shariff ◽  
Muhammad Asmu’i Abdul Rahim
Keyword(s):  
Stock Returns ◽  
Price Index ◽  
Financial Time Series ◽  
Composite Index ◽  
Garch Models ◽  
Financial Assets ◽  
Kuala Lumpur ◽  
Financial Decisions ◽  
Auto Regressive ◽  
Public Holidays

It is well-known that financial time series exhibits changing variance and this can have important consequences in formulating economic or financial decisions. In much recent evidence shows that volatility of financial assets is not constant, but rather that relatively volatile periods alternate with more tranquil ones. Thus, there are many opportunities to obtain forecasts of this time-varying risk. The paper presents the modelling volatility of the Kuala Lumpur Composite Index (KLCI) using SV and GARCH models.  Thus, the aim of this study is to model the KLCI stock market using two models; Stochastic Volatility (SV) and Generalized Auto-Regressive Conditional Heteroscedasticity (GARCH). This study employs an SV model with Bayesian approach and Markov Chain Monte Carlo (MCMC) sampler; and GARCH model with MLE estimator. The best model will be used to forecast the future volatility of stock returns. The study involves 971 daily observations of KLCI Closing price index, from 2 January 2008 to 10 November 2016, excluding public holidays. SV model is found to be the best based on the lowest RMSE and MAE values.

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