The parallel solution of early-exercise Asian options with stochastic volatility

This paper describes an parallel semi-Lagrangian finite difference approach to the pricing of early exercise Asian Options on assets with a stochastic volatility. A multigrid procedure is described for the fast iterative solution of the discrete linear complementarity problems that result. The accuracy and performance of this approach is improved considerably by a strike-price related analytic transformation of asset prices. Asian options are contingent claims with payoffs that depend on the average price of an asset over some time interval. The payoff may depend on this average and a fixed strike price (Fixed Strike Asians) or it may depend on the average and the asset price (Floating Strike Asians). The option may also permit early exercise (American contract) or confine the holder to a fixed exercise date (European contract). The Fixed Strike Asian with early exercise is considered here where continuous arithmetic averaging has been used. Pricing such an option where the asset price has a stochastic volatility leads to the requirement to solve a tri-variate partial differential inequation in the three state variables of asset price, average price and volatility (or equivalently, variance). The similarity transformations [6] used with Floating Strike Asian options to reduce the dimensionality of the problem are not applicable to Fixed Strikes and so the numerical solution of a tri-variate problem is necessary. The computational challenge is to provide accurate solutions sufficiently quickly to support realtime trading activities at a reasonable cost in terms of hardware requirements.

Volatility Spillover and Multivariate Volatility Impulse Response Analysis of GFC News Events

This paper applies two measures to assess spillovers across markets: the Diebold Yilmaz (2012) Spillover Index and the Hafner and Herwartz (2006) analysis of multivariate GARCH models using volatility impulse response analysis. We use two sets of data, daily realized volatility estimates taken from the Oxford Man RV library, running from the beginning of 2000 to October 2016, for the S&P500 and the FTSE, plus ten years of daily returns series for the New York Stock Exchange Index and the FTSE 100 index, from 3 January 2005 to 31 January 2015. Both data sets capture both the Global Financial Crisis (GFC) and the subsequent European Sovereign Debt Crisis (ESDC). The spillover index captures the transmission of volatility to and from markets, plus net spillovers. The key difference between the measures is that the spillover index captures an average of spillovers over a period, whilst volatility impulse responses (VIRF) have to be calibrated to conditional volatility estimated at a particular point in time. The VIRF provide information about the impact of independent shocks on volatility. In the latter analysis, we explore the impact of three different shocks, the onset of the GFC, which we date as 9 August 2007 (GFC1). It took a year for the financial crisis to come to a head, but it did so on 15 September 2008, (GFC2). The third shock is 9 May 2010. Our modelling includes leverage and asymmetric effects undertaken in the context of a multivariate GARCH model, which are then analysed using both BEKK and diagonal BEKK (DBEKK) models. A key result is that the impact of negative shocks is larger, in terms of the effects on variances and covariances, but shorter in duration, in this case a difference between three and six months.

The meaning of implied volatility in pricing stock options traded in options markets

Ph.D. in the Faculty of Business Administration

Synthetic portfolio for event studies: Estimating the effects of volatility call auctions

We propose a method denoted as synthetic portfolio for event studies in market microstructure that is particularly interesting to use with high frequency data and thinly traded markets. The method is based on Synthetic Control Method and provides a robust data driven method to build a counterfactual for evaluating the effects of the volatility call auctions. We find that SMC could be used if the loss function is defined as the difference between the returns of the asset and the returns of a synthetic portfolio. We apply SCM to test the performance of the volatility call auction as a circuit breaker in the context of an event study. We find that for Colombian Stock Market securities, the asynchronicity of intraday data reduces the analysis to a selected group of stocks, however it is possible to build a tracking portfolio. The realized volatility increases after the auction, indicating that the mechanism is not enhancing the price discovery process.

Particle emissions, volatility, and toxicity from an ethanol fumigated compression ignition engine

Particle emissions, volatility, and the concentration of reactive oxygen species (ROS) were investigated for a pre-Euro I compression ignition engine to study the potential health impacts of employing ethanol fumigation technology. Engine testing was performed in two separate experimental campaigns with most testing performed at intermediate speed with four different load settings and various ethanol substitutions. A scanning mobility particle sizer (SMPS) was used to determine particle size distributions, a volatilization tandem differential mobility analyzer (V-TDMA) was used to explore particle volatility, and a new profluorescent nitroxide probe, BPEAnit, was used to investigate the potential toxicity of particles. The greatest particulate mass reduction was achieved with ethanol fumigation at full load, which contributed to the formation of a nucleation mode. Ethanol fumigation increased the volatility of particles by coating the particles with organic material or by making extra organic material available as an external mixture. In addition, the particle-related ROS concentrations increased with ethanol fumigation and were associated with the formation of a nucleation mode. The smaller particles, the increased volatility, and the increase in potential particle toxicity with ethanol fumigation may provide a substantial barrier for the uptake of fumigation technology using ethanol as a supplementary fuel.

Yield-factor volatility models

The term structure of interest rates is often summarized using a handful of yield factors that capture shifts in the shape of the yield curve. In this paper, we develop a comprehensive model for volatility dynamics in the level, slope, and curvature of the yield curve that simultaneously includes level and GARCH effects along with regime shifts. We show that the level of the short rate is useful in modeling the volatility of the three yield factors and that there are significant GARCH effects present even after including a level effect. Further, we find that allowing for regime shifts in the factor volatilities dramatically improves the model’s fit and strengthens the level effect. We also show that a regime-switching model with level and GARCH effects provides the best out-of-sample forecasting performance of yield volatility. We argue that the auxiliary models often used to estimate term structure models with simulation-based estimation techniques should be consistent with the main features of the yield curve that are identified by our model.

The relationship between implied and realized volatility : evidence from the Australian stock index option market

This paper examines the relationship between the volatility implied in option prices and the subsequently realized volatility by using the S&P/ASX 200 index options (XJO) traded on the Australian Stock Exchange (ASX) during a period of 5 years. Unlike stock index options such as the S&P 100 index options in the US market, the S&P/ASX 200 index options are traded infrequently and in low volumes, and have a long maturity cycle. Thus an errors-in-variables problem for measurement of implied volatility is more likely to exist. After accounting for this problem by instrumental variable method, it is found that both call and put implied volatilities are superior to historical volatility in forecasting future realized volatility. Moreover, implied call volatility is nearly an unbiased forecast of future volatility.

Evaluating multivariate volatility forecasts : how effective are statistical and economic loss functions?

Multivariate volatility forecasts are an important input in many financial applications, in particular portfolio optimisation problems. Given the number of models available and the range of loss functions to discriminate between them, it is obvious that selecting the optimal forecasting model is challenging. The aim of this thesis is to thoroughly investigate how effective many commonly used statistical (MSE and QLIKE) and economic (portfolio variance and portfolio utility) loss functions are at discriminating between competing multivariate volatility forecasts. An analytical investigation of the loss functions is performed to determine whether they identify the correct forecast as the best forecast. This is followed by an extensive simulation study examines the ability of the loss functions to consistently rank forecasts, and their statistical power within tests of predictive ability. For the tests of predictive ability, the model confidence set (MCS) approach of Hansen, Lunde and Nason (2003, 2011) is employed. As well, an empirical study investigates whether simulation findings hold in a realistic setting. In light of these earlier studies, a major empirical study seeks to identify the set of superior multivariate volatility forecasting models from 43 models that use either daily squared returns or realised volatility to generate forecasts. This study also assesses how the choice of volatility proxy affects the ability of the statistical loss functions to discriminate between forecasts. Analysis of the loss functions shows that QLIKE, MSE and portfolio variance can discriminate between multivariate volatility forecasts, while portfolio utility cannot. An examination of the effective loss functions shows that they all can identify the correct forecast at a point in time, however, their ability to discriminate between competing forecasts does vary. That is, QLIKE is identified as the most effective loss function, followed by portfolio variance which is then followed by MSE. The major empirical analysis reports that the optimal set of multivariate volatility forecasting models includes forecasts generated from daily squared returns and realised volatility. Furthermore, it finds that the volatility proxy affects the statistical loss functions’ ability to discriminate between forecasts in tests of predictive ability. These findings deepen our understanding of how to choose between competing multivariate volatility forecasts.

Essays on volatility and liquidity in financial markets

The price formation of financial assets is a complex process. It extends beyond the standard economic paradigm of supply and demand to the understanding of the dynamic behavior of price variability, the price impact of information, and the implications of trading behavior of market participants on prices. In this thesis, I study aggregate market and individual assets volatility, liquidity dimensions, and causes of mispricing for US equities over a recent sample period. How volatility forecasts are modeled, what determines intradaily jumps and causes changes in intradaily volatility and what drives the premium of traded equity indexes? Are they induced, for example, by the information content of lagged volatility and return parameters or by macroeconomic news, changes in liquidity and volatility? Besides satisfying our intellectual curiosity, answers to these questions are of direct importance to investors developing trading strategies, policy makers evaluating macroeconomic policies and to arbitrageurs exploiting mispricing in exchange-traded funds. Results show that the leverage effect and lagged absolute returns improve forecasts of continuous components of daily realized volatility as well as jumps. Implied volatility does not subsume the information content of lagged returns in forecasting realized volatility and its components. The reported results are linked to the heterogeneous market hypothesis and demonstrate the validity of extending the hypothesis to returns. Depth shocks, signed order flow, the number of trades, and resiliency are the most important determinants of intradaily volatility. In contrast, spread shock and resiliency are predictive of signed intradaily jumps. There are fewer macroeconomic news announcement surprises that cause extreme price movements or jumps than those that elevate intradaily volatility. Finally, the premium of exchange-traded funds is significantly associated with momentum in net asset value and a number of liquidity parameters including the spread, traded volume, and illiquidity. The mispricing of industry exchange traded funds suggest that limits to arbitrage are driven by potential illiquidity.

Volatility timing : how best to forecast portfolio exposures

This paper investigates how best to forecast optimal portfolio weights in the context of a volatility timing strategy. It measures the economic value of a number of methods for forming optimal portfolios on the basis of realized volatility. These include the traditional econometric approach of forming portfolios from forecasts of the covariance matrix, and a novel method, where a time series of optimal portfolio weights are constructed from observed realized volatility and directly forecast. The approach proposed here of directly forecasting portfolio weights shows a great deal of merit. Resulting portfolios are of equivalent economic benefit to a number of competing approaches and are more stable across time. These findings have obvious implications for the manner in which volatility timing is undertaken in a portfolio allocation context.