Robust Volatility Estimation and Analysis of the Leverage Effect

<p>Using volatility estimation as the underlying commonality this thesis traverses the statistical problem of robust estimation of scale, through to the financial problem of valuing call options over stock. We use a large simulation study of robust scale estimators to benchmark a nonparametric volatility estimation procedure, which not only uses techniques which are particularly suited to observed financial returns, but also addresses the problem of bias in any robust volatility estimation procedure. Existing option pricing models are discussed with careful study of the assumed volatility and elasticity of volatility with respect to stock price relationships for each of these models. An option pricing formula is derived which extends existing methods, and provides a closed form solution which can be readily computed. Preliminary analysis of real price data suggests this model is able to explain observed leverage phenomena.</p>

Robust Volatility Estimation and Analysis of the Leverage Effect

<p>Using volatility estimation as the underlying commonality this thesis traverses the statistical problem of robust estimation of scale, through to the financial problem of valuing call options over stock. We use a large simulation study of robust scale estimators to benchmark a nonparametric volatility estimation procedure, which not only uses techniques which are particularly suited to observed financial returns, but also addresses the problem of bias in any robust volatility estimation procedure. Existing option pricing models are discussed with careful study of the assumed volatility and elasticity of volatility with respect to stock price relationships for each of these models. An option pricing formula is derived which extends existing methods, and provides a closed form solution which can be readily computed. Preliminary analysis of real price data suggests this model is able to explain observed leverage phenomena.</p>

Stock Price Volatility Estimation Using Regime Switching Technique-Empirical Study on the Indian Stock Market

Volatility is the degree of variation in the stock price over time. The stock price is volatile due to many factors, such as demand, supply, economic policy, and company earnings. Investing in a volatile market is riskier for stock traders. Most of the existing work considered Generalized Auto-regressive Conditional Heteroskedasticity (GARCH) models to capture volatility, but this model fails to capture when the volatility is very high. This paper aims to estimate the stock price volatility using the Markov regime-switching GARCH (MSGARCH) and SETAR model. The model selection was carried out using the Akaike-Informations-Criteria (AIC) and Bayesian-Information Criteria (BIC) metric. The performance of the model is evaluated using the Root mean square error (RMSE) and mean absolute percentage error (MAPE) metric. We have found that volatility estimation using the MSGARCH model performed better than the SETAR model. The experiments considered the Indian stock market data.

Excess Volatility in Bitcoin: Extreme Value Volatility Estimation

This article investigates the excess volatility in Bitcoin prices using an unbiased extreme value volatility estimator. We capture the time-varying nature of the excess volatility using bootstrap, multi-horizon, sub-sampling and rolling-window approaches. We observe that Bitcoin price changes are almost efficient. Although Bitcoin prices exhibit high volatility and show signs of excess volatility for a few periods, it is decreasing over time. After controlling for the outliers, we also notice that the Bitcoin market shows signs of increasing maturity. Overall, Bitcoin prices show a sign of increasing efficiency with decreasing volatility. Our findings have implications for investors making investment decisions and for regulators making policy choices.

Forward-Looking Volatility Estimation for Risk-Managed Investment Strategies during the COVID-19 Crisis

Under the impact of both increasing credit pressure and low economic returns characterizing developed countries, investment levels have decreased over recent years. Moreover, the recent turbulence caused by the COVID-19 crisis has accelerated the latter process. Within this scenario, we consider the so-called Volatility Target (VolTarget) strategy. In particular, we focus our attention on estimating volatility levels of a risky asset to perform a VolTarget simulation over two different time horizons. We first consider a 20 year period, from January 2000 to January 2020, then we analyse the last 12 months to emphasize the effects related to the COVID-19 virus’s diffusion. We propose a hybrid algorithm based on the composition of a GARCH model with a Neural Network (NN) approach. Let us underline that, as an alternative to standard allocation methods based on realized and backward oriented volatilities, we exploited an innovative forward-looking estimation process exploiting a Machine Learning (ML) solution. Our solution provides a more accurate volatility estimation, allowing us to derive an effective investor risk-return profile during market crisis periods. Moreover, we show that, via a forward-looking VolTarget strategy while using an ML-based prediction as the input, the average outcome for an investment in a drawdown plan is more sustainable while representing an efficient risk-control solution for long time period investments.