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.

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.

On the efficacy of techniques for evaluating multivariate volatility forecasts

The performance of techniques for evaluating multivariate volatility forecasts are not yet as well understood as their univariate counterparts. This paper aims to evaluate the efficacy of a range of traditional statistical-based methods for multivariate forecast evaluation together with methods based on underlying considerations of economic theory. It is found that a statistical-based method based on likelihood theory and an economic loss function based on portfolio variance are the most effective means of identifying optimal forecasts of conditional covariance matrices.

Estimating the parameters of stochastic volatility models using option price data

This article describes a maximum likelihood method for estimating the parameters of the standard square-root stochastic volatility model and a variant of the model that includes jumps in equity prices. The model is fitted to data on the S&P 500 Index and the prices of vanilla options written on the index, for the period 1990 to 2011. The method is able to estimate both the parameters of the physical measure (associated with the index) and the parameters of the risk-neutral measure (associated with the options), including the volatility and jump risk premia. The estimation is implemented using a particle filter whose efficacy is demonstrated under simulation. The computational load of this estimation method, which previously has been prohibitive, is managed by the effective use of parallel computing using graphics processing units (GPUs). The empirical results indicate that the parameters of the models are reliably estimated and consistent with values reported in previous work. In particular, both the volatility risk premium and the jump risk premium are found to be significant.

Selecting volatility forecasting models for portfolio allocation purposes

Techniques for evaluating and selecting multivariate volatility forecasts are not yet understood as well as their univariate counterparts. This paper considers the ability of different loss functions to discriminate between a set of competing forecasting models which are subsequently applied in a portfolio allocation context. It is found that a likelihood-based loss function outperforms its competitors, including those based on the given portfolio application. This result indicates that considering the particular application of forecasts is not necessarily the most effective basis on which to select models.

Are combination forecasts of S&P 500 volatility statistically superior?

Forecasting volatility has received a great deal of research attention, with the relative performances of econometric model based and option implied volatility forecasts often being considered. While many studies find that implied volatility is the pre-ferred approach, a number of issues remain unresolved, including the relative merit of combining forecasts and whether the relative performances of various forecasts are statistically different. By utilising recent econometric advances, this paper considers whether combination forecasts of S&P 500 volatility are statistically superior to a wide range of model based forecasts and implied volatility. It is found that a combination of model based forecasts is the dominant approach, indicating that the implied volatility cannot simply be viewed as a combination of various model based forecasts. Therefore, while often viewed as a superior volatility forecast, the implied volatility is in fact an inferior forecast of S&P 500 volatility relative to model-based forecasts.

The benefit of modeling jumps in realized volatility for risk prediction : evidence from Chinese mainland stocks

Recent literature has focused on realized volatility models to predict financial risk. This paper studies the benefit of explicitly modeling jumps in this class of models for value at risk (VaR) prediction. Several popular realized volatility models are compared in terms of their VaR forecasting performances through a Monte Carlo study and an analysis based on empirical data of eight Chinese stocks. The results suggest that careful modeling of jumps in realized volatility models can largely improve VaR prediction, especially for emerging markets where jumps play a stronger role than those in developed markets.

A heterogeneous computing approach to simulation of the Heston Stochastic Volatility Model

Stochastic volatility models are of fundamental importance to the pricing of derivatives. One of the most commonly used models of stochastic volatility is the Heston Model in which the price and volatility of an asset evolve as a pair of coupled stochastic differential equations. The computation of asset prices and volatilities involves the simulation of many sample trajectories with conditioning. The problem is treated using the method of particle filtering. While the simulation of a shower of particles is computationally expensive, each particle behaves independently making such simulations ideal for massively parallel heterogeneous computing platforms. In this paper, we present our portable Opencl implementation of the Heston model and discuss its performance and efficiency characteristics on a range of architectures including Intel cpus, Nvidia gpus, and Intel Many-Integrated-Core (mic) accelerators.

Multicomponent kinetic spectrophotometric determination of pefloxacin and norfloxacin in pharmaceutical preparations and human plasma samples with the aid of chemometrics

A spectrophotometric method for the simultaneous determination of the important pharmaceuticals, pefloxacin and its structurally similar metabolite, norfloxacin, is described for the first time. The analysis is based on the monitoring of a kinetic spectrophotometric reaction of the two analytes with potassium permanganate as the oxidant. The measurement of the reaction process followed the absorbance decrease of potassium permanganate at 526 nm, and the accompanying increase of the product, potassium manganate, at 608 nm. It was essential to use multivariate calibrations to overcome severe spectral overlaps and similarities in reaction kinetics. Calibration curves for the individual analytes showed linear relationships over the concentration ranges of 1.0–11.5 mg L−1 at 526 and 608 nm for pefloxacin, and 0.15–1.8 mg L−1 at 526 and 608 nm for norfloxacin. Various multivariate calibration models were applied, at the two analytical wavelengths, for the simultaneous prediction of the two analytes including classical least squares (CLS), principal component regression (PCR), partial least squares (PLS), radial basis function-artificial neural network (RBF-ANN) and principal component-radial basis function-artificial neural network (PC-RBF-ANN). PLS and PC-RBF-ANN calibrations with the data collected at 526 nm, were the preferred methods—%RPET not, vert, similar 5, and LODs for pefloxacin and norfloxacin of 0.36 and 0.06 mg L−1, respectively. Then, the proposed method was applied successfully for the simultaneous determination of pefloxacin and norfloxacin present in pharmaceutical and human plasma samples. The results compared well with those from the alternative analysis by HPLC.

Depression, anxiety and body image after treatment for invasive stage one epithelial ovarian cancer

Background: Diagnosis of epithelial ovarian cancer (EOC) in young women has major implications including those to their reproductive potential. We evaluated depression, anxiety and body image in patients with stage I EOC treated with fertility sparing surgery (FSS) or radical surgery (RS). We also investigated fertility outcomes after FSS.----- Methods: A retrospective study was undertaken in which 62 patients completed questionnaires related to anxiety, depression, body image and fertility outcomes. Additional information on adjuvant therapy after FSS and RS and demographic details were abstracted from medical records. Both bi and multivariate regression models were used to assess the relationship between demographic, clinical and pathological results and scores for anxiety, depression and body image.----- Results: Thirty-nine patients underwent RS and the rest, FSS. The percentage of patients reporting elevated anxiety and depression (subscores ≥ 11) were 27 % and 5% respectively. The median (inter quartile range) score for body image scale (BIS) was 6 (3-15). None of the demographic or clinical factors examined showed significant association with anxiety and BIS with the exception of ‘time since diagnosis’. For depression, post-menopausal status was the only independent predictor. Among those 23 patients treated by FSS, 14 patients tried to conceive (7 successful), resulting in 7 live births, one termination of pregnancy and one miscarriage.----- Conclusion: This study shows that psychological issues are common in women treated for stage I EOC. Reproduction after FSS is feasible and lead to the birth of healthy babies in about half of patients who wished to have another child. Further prospective studies with standardised instruments are required.

Prognostic significance of IGF and ECM induced signalling proteins in breast cancer patients

Breast cancer is a leading contributor to the burden of disease in Australia. Fortunately, the recent introduction of diverse therapeutic strategies have improved the survival outcome for many women. Despite this, the clinical management of breast cancer remains problematic as not all approaches are sufficiently sophisticated to take into account the heterogeneity of this disease and are unable to predict disease progression, in particular, metastasis. As such, women with good prognostic outcomes are exposed to the side effects of therapies without added benefit. Furthermore, women with aggressive disease for whom these advanced treatments would deliver benefit cannot be distinguished and opportunities for more intensive or novel treatment are lost. This study is designed to identify novel factors associated with disease progression, and the potential to inform disease prognosis. Frequently overlooked, yet common mediators of disease are the interactions that take place between the insulin-like growth factor (IGF) system and the extracellular matrix (ECM). Our laboratory has previously demonstrated that multiprotein insulin-like growth factor-I (IGF-I): insulin-like growth factor binding protein (IGFBP): vitronectin (VN) complexes stimulate migration of breast cancer cells in vitro, via the cooperative involvement of the insulin-like growth factor type I receptor (IGF-IR) and VN-binding integrins. However, the effects of IGF and ECM protein interactions on the dissemination and progression of breast cancer in vivo are unknown. It was hypothesised that interactions between proteins required for IGF induced signalling events and those within the ECM contribute to breast cancer metastasis and are prognostic and predictive indicators of patient outcome. To address this hypothesis, semiquantitative immunohistochemistry (IHC) analyses were performed to compare the extracellular and subcellular distribution of IGF and ECM induced signalling proteins between matched normal, primary cancer, and metastatic cancer among archival formalin-fixed paraffin-embedded (FFPE) breast tissue samples collected from women attending the Princess Alexandra Hospital, Brisbane. Multivariate Cox proportional hazards (PH) regression survival models in conjunction with a modified „purposeful selection of covariates. method were applied to determine the prognostic potential of these proteins. This study provides the first in-depth, compartmentalised analysis of the distribution of IGF and ECM induced signalling proteins. As protein function and protein localisation are closely correlated, these findings provide novel insights into IGF signalling and ECM protein function during breast cancer development and progression. Distinct IGF signalling and ECM protein immunoreactivity was observed in the stroma and/or in subcellular locations in normal breast, primary cancer and metastatic cancer tissues. Analysis of the presence and location of stratifin (SFN) suggested a causal relationship in ECM remodelling events during breast cancer development and progression. The results of this study have also suggested that fibronectin (FN) and ¥â1 integrin are important for the formation of invadopodia and epithelial-to-mesenchymal transition (EMT) events. Our data also highlighted the importance of the temporal and spatial distribution of IGF induced signalling proteins in breast cancer metastasis; in particular, SFN, enhancer-of-split and hairy-related protein 2 (SHARP-2), total-akt/protein kinase B 1 (Total-AKT1), phosphorylated-akt/protein kinase B (P-AKT), extracellular signal-related kinase-1 and extracellular signal-related kinase-2 (ERK1/2) and phosphorylated-extracellular signal-related kinase-1 and extracellular signal-related kinase-2 (P-ERK1/2). Multivariate survival models were created from the immunohistochemical data. These models were found to fit well with these data with very high statistical confidence. Numerous prognostic confounding effects and effect modifications were identified among elements of the ECM and IGF signalling cascade and corroborate the survival models. This finding provides further evidence for the prognostic potential of IGF and ECM induced signalling proteins. In addition, the adjusted measures of associations obtained in this study have strengthened the validity and utility of the resulting models. The findings from this study provide insights into the biological interactions that occur during the development of breast tissue and contribute to disease progression. Importantly, these multivariate survival models could provide important prognostic and predictive indicators that assist the clinical management of breast disease, namely in the early identification of cancers with a propensity to metastasise, and/or recur following adjuvant therapy. The outcomes of this study further inform the development of new therapeutics to aid patient recovery. The findings from this study have widespread clinical application in the diagnosis of disease and prognosis of disease progression, and inform the most appropriate clinical management of individuals with breast cancer.