Modelling the dynamics of Bitcoin and Litecoin: GARCH versus stochastic volatility models

We examine and compare a large number of generalized autoregressive conditional heteroskedastic (GARCH) and stochastic volatility (SV) models using series of Bitcoin and Litecoin price returns to assess the model fit for dynamics of these cryptocurrency price returns series. The various models examined include the standard GARCH(1,1) and SV with an AR(1) log-volatility process, as well as more flexible models with jumps, volatility in mean, leverage effects, t-distributed and moving average innovations. We report that the best model for Bitcoin is SV-t while it is GARCH-t for Litecoin. Overall, the t-class of models performs better than other classes for both cryptocurrencies. For Bitcoin, the SV models consistently outperform the GARCH models and the same holds true for Litecoin in most cases. Finally, the comparison of GARCH models with GARCH-GJR models reveals that the leverage effect is not significant for cryptocurrencies, suggesting that these do not behave like stock prices.     

Nonparametric estimation of stochastic volatility models

This letter introduces nonparametric estimators of the drift and diffusion coefficient of stochastic volatility models which exploit techniques for estimating integrated volatility with high-frequency data. The performance of the proposed estimators is assessed on simulations of two popular stochastic volatility models.     

Valuation of commodity derivatives in a new multi-factor model

This paper extends existing commodity valuation models to allow for stochastic volatility and simultaneous jumps in the spot price and spot volatility. Closed-form valuation formulas for forwards, futures, futures options, geometric Asian options and commodity-linked bonds are obtained using the Heston (1993) and Bakshi and Madan (2000) methodology. Stochastic volatility and jumps do not affect the futures price at a given point in time. However, numerical examples indicate that they play important roles in pricing options on futures. This revised version was published online in June 2006 with corrections to the Cover Date.     

Implied Volatility of Interest Rate Options: An Empirical Investigation of the Market Model

We analyze the empirical properties of the volatilityimplied in options on the 13-week US Treasury bill rate. These options havenot been studied previously. It is shown that a European style put optionon the interest rate is equivalent to a call option on a zero-coupon bond.We apply the LIBOR market model and conduct a battery of validity tests tocompare three different volatility specifications: contact, affine, and exponentialvolatility. It appears that the additional parameter in the affine and theexponential volatility function is not justified. Overall, the LIBOR marketmodel fares well in describing these options.     

Estimating daily volatility in financial markets utilizing intraday data

This study proposes a new approach to the estimation of daily realised volatility in financial markets from intraday data. Initially, an examination of intraday returns on S&P 500 Index Futures reveals that returns can be characterised by heteroscedasticity and time-varying autocorrelation. After reviewing a number of daily realised volatility estimators cited in the literature, it is concluded that these estimators are based upon a number of restrictive assumptions in regard to the data generating process for intraday returns. We use a weak set of assumptions about the data generating process for intraday returns, including transaction returns, given in den Haan and Levin [den Haan, W.J., Levin, A., 1996. Inferences from parametric and non-parametric covariance matrix estimation procedures, Working paper, NBER, 195.], which allows for heteroscedasticity and time-varying autocorrelation in intraday returns. These assumptions allow the VARHAC estimator to be employed in the estimation of daily realised volatility. An empirical analysis of the VARHAC daily volatility estimator employing intraday transaction returns concludes that this estimator performs well in comparison to other estimators cited in the literature.     

Contagion Effects from the 1994 Mexican Peso Crisis: Evidence from Chilean Stocks

The contagion, or informational spillover, effects of the 1994 peso crisis from the Mexican market to the Chilean market, and to the Chilean American Depository Receipts (ADRs) trading in the U.S., are examined. Significant excess returns are observed for Chilean stocks for the event dates of the Mexican Peso crisis, providing evidence of contagion effects. Significant excess returns on these Chilean ADRs are also observed for each of the five event dates associated with the Peso crisis, suggesting that the contagion effects spilled over to the ADRs. A multiple regression model shows that the spillover contagion effects were very efficiently transmitted from the Mexican market to the Chilean market to the Chilean ADRs. Multifactor regressions show that the most significant influence on the pricing of Chilean ADRs is the raw Chilean Index, rather than the Chilean Index expressed in U.S. dollars.     

A Closer Look at the Relation between GARCH and Stochastic Autoregressive Volatility

We show that, for three common SARV models, fitting a minimummean square linear filter is equivalent to fitting a GARCH model.This suggests that GARCH models may be useful for filtering,forecasting, and parameter estimation in stochastic volatilitysettings. To investigate, we use simulations to evaluate howthe three SARV models and their associated GARCH filters performunder controlled conditions and then we use daily currency andequity index returns to evaluate how the models perform in arisk management application. Although the GARCH models produceless precise forecasts than the SARV models in the simulations,it is not clear that the performance differences are large enoughto be economically meaningful. Consistent with this view, wefind that the GARCH and SARV models perform comparably in testsof conditional value-at-risk estimates using the actual data.     

Observable Consequences of Trading Structure Differences: On the Use of Variance Ratios in Microstructure Studies

This paper examines the variance ratio tests in studies of transitory volatility and concludes that the variance ratio is an appropriate test of trading structure differences only under certain assumptions regarding the evolution of underlying stock prices and the autocorrelation structure of returns. This result raises caution as to the interpretation of results bases upon the 24-hour variance ratio methodologies in studies of transitory volatility and trading structure effects. A numerical example indicates that errors in inferences can be severe.     

Dynamic analysis of stock return volatility in an integrated international capital market

This paper examines the dynamic behavior of the stock return volatility for Canada, Japan, Germany, and the United Kingdom. The evidence indicates that international stock return volatility is mainly influenced by the U.S. stock return volatility and the exchange rate volatility, supporting the international capital market integration hypothesis. There seems to be some correlation between stock return volatility and macroeconomic volatility, but the effect is relatively weaker. In addition to the economic fundamentals, the noise component is found to be time varying, confirming the AR(MA)CH specifications in the stock return models.     

R&D Progress, stock price volatility, and post-announcement drift: An empirical investigation into biotech firms

I investigate the effects of R&D progress on the dynamics of stock price volatility and the post announcement drift to provide insights into whether or not and how capital markets react to corporate R&D progress in the context of the biotech industry. I find both stock price volatility and the post announcement drift decrease in R&D progress. More importantly, the decrease is proportional to the increase in the drug development success rate driven by R&D progress. Findings suggest that R&D progress conveys useful risk-relevant information, and plays an important role in explaining stock price volatility change and market anomalies.