An Empirical Investigation of Value-at-Risk in Long and Short Trading Positions

This paper uses the Value-at-Risk approach to define the risk in both long and short trading positions. The investigation is done on some major market indices(Japanese, UK, German and US). The performance of models that takes into account skewness and fat-tails are compared to symmetric models in relation to both the specific model for estimating the variance, and the distribution of the variance estimate used as input in the VaR estimation. The results indicate that more flexible models not necessarily perform better in predicting the VaR forecast; the reason for this is most probably the complexity of these models. A general result is that different methods for estimating the variance are needed for different confidence levels of the VaR, and for the different indices. Also, different models are to be used for the left respectively the right tail of the distribution.

Modeling and Forecasting Implied Volatility: Implications for Trading, Pricing, and Risk Management

Modeling and forecasting of implied volatility (IV) is important to both practitioners and academics, especially in trading, pricing, hedging, and risk management activities, all of which require an accurate volatility. However, it has become challenging since the 1987 stock market crash, as implied volatilities (IVs) recovered from stock index options present two patterns: volatility smirk(skew) and volatility term-structure, if the two are examined at the same time, presents a rich implied volatility surface (IVS). This implies that the assumptions behind the Black-Scholes (1973) model do not hold empirically, as asset prices are mostly influenced by many underlying risk factors. This thesis, consists of four essays, is modeling and forecasting implied volatility in the presence of options markets’ empirical regularities. The first essay is modeling the dynamics IVS, it extends the Dumas, Fleming and Whaley (DFW) (1998) framework; for instance, using moneyness in the implied forward price and OTM put-call options on the FTSE100 index, a nonlinear optimization is used to estimate different models and thereby produce rich, smooth IVSs. Here, the constant-volatility model fails to explain the variations in the rich IVS. Next, it is found that three factors can explain about 69-88% of the variance in the IVS. Of this, on average, 56% is explained by the level factor, 15% by the term-structure factor, and the additional 7% by the jump-fear factor. The second essay proposes a quantile regression model for modeling contemporaneous asymmetric return-volatility relationship, which is the generalization of Hibbert et al. (2008) model. The results show strong negative asymmetric return-volatility relationship at various quantiles of IV distributions, it is monotonically increasing when moving from the median quantile to the uppermost quantile (i.e., 95%); therefore, OLS underestimates this relationship at upper quantiles. Additionally, the asymmetric relationship is more pronounced with the smirk (skew) adjusted volatility index measure in comparison to the old volatility index measure. Nonetheless, the volatility indices are ranked in terms of asymmetric volatility as follows: VIX, VSTOXX, VDAX, and VXN. The third essay examines the information content of the new-VDAX volatility index to forecast daily Value-at-Risk (VaR) estimates and compares its VaR forecasts with the forecasts of the Filtered Historical Simulation and RiskMetrics. All daily VaR models are then backtested from 1992-2009 using unconditional, independence, conditional coverage, and quadratic-score tests. It is found that the VDAX subsumes almost all information required for the volatility of daily VaR forecasts for a portfolio of the DAX30 index; implied-VaR models outperform all other VaR models. The fourth essay models the risk factors driving the swaption IVs. It is found that three factors can explain 94-97% of the variation in each of the EUR, USD, and GBP swaption IVs. There are significant linkages across factors, and bi-directional causality is at work between the factors implied by EUR and USD swaption IVs. Furthermore, the factors implied by EUR and USD IVs respond to each others’ shocks; however, surprisingly, GBP does not affect them. Second, the string market model calibration results show it can efficiently reproduce (or forecast) the volatility surface for each of the swaptions markets.

Maximum Loss Calculation using Scenario Analysis, Heavy Tails and Implied Volatility Patterns

The objective of this paper is to improve option risk monitoring by examining the information content of implied volatility and by introducing the calculation of a single-sum expected risk exposure similar to the Value-at-Risk. The figure is calculated in two steps. First, there is a need to estimate the value of a portfolio of options for a number of different market scenarios, while the second step is to summarize the information content of the estimated scenarios into a single-sum risk measure. This involves the use of probability theory and return distributions, which confronts the user with the problems of non-normality in the return distribution of the underlying asset. Here the hyperbolic distribution is used to describe one alternative for dealing with heavy tails. Results indicate that the information content of implied volatility is useful when predicting future large returns in the underlying asset. Further, the hyperbolic distribution provides a good fit to historical returns enabling a more accurate definition of statistical intervals and extreme events.

Modeling Asymmetries in Financial Data with Multiplicative Error Models

This thesis addresses modeling of financial time series, especially stock market returns and daily price ranges. Modeling data of this kind can be approached with so-called multiplicative error models (MEM). These models nest several well known time series models such as GARCH, ACD and CARR models. They are able to capture many well established features of financial time series including volatility clustering and leptokurtosis. In contrast to these phenomena, different kinds of asymmetries have received relatively little attention in the existing literature. In this thesis asymmetries arise from various sources. They are observed in both conditional and unconditional distributions, for variables with non-negative values and for variables that have values on the real line. In the multivariate context asymmetries can be observed in the marginal distributions as well as in the relationships of the variables modeled. New methods for all these cases are proposed. Chapter 2 considers GARCH models and modeling of returns of two stock market indices. The chapter introduces the so-called generalized hyperbolic (GH) GARCH model to account for asymmetries in both conditional and unconditional distribution. In particular, two special cases of the GARCH-GH model which describe the data most accurately are proposed. They are found to improve the fit of the model when compared to symmetric GARCH models. The advantages of accounting for asymmetries are also observed through Value-at-Risk applications. Both theoretical and empirical contributions are provided in Chapter 3 of the thesis. In this chapter the so-called mixture conditional autoregressive range (MCARR) model is introduced, examined and applied to daily price ranges of the Hang Seng Index. The conditions for the strict and weak stationarity of the model as well as an expression for the autocorrelation function are obtained by writing the MCARR model as a first order autoregressive process with random coefficients. The chapter also introduces inverse gamma (IG) distribution to CARR models. The advantages of CARR-IG and MCARR-IG specifications over conventional CARR models are found in the empirical application both in- and out-of-sample. Chapter 4 discusses the simultaneous modeling of absolute returns and daily price ranges. In this part of the thesis a vector multiplicative error model (VMEM) with asymmetric Gumbel copula is found to provide substantial benefits over the existing VMEM models based on elliptical copulas. The proposed specification is able to capture the highly asymmetric dependence of the modeled variables thereby improving the performance of the model considerably. The economic significance of the results obtained is established when the information content of the volatility forecasts derived is examined.

Essays on the Modeling and Prediction of Volatility and Higher Moments of Stock Returns (summary section only)

One of the most fundamental and widely accepted ideas in finance is that investors are compensated through higher returns for taking on non-diversifiable risk. Hence the quantification, modeling and prediction of risk have been, and still are one of the most prolific research areas in financial economics. It was recognized early on that there are predictable patterns in the variance of speculative prices. Later research has shown that there may also be systematic variation in the skewness and kurtosis of financial returns. Lacking in the literature so far, is an out-of-sample forecast evaluation of the potential benefits of these new more complicated models with time-varying higher moments. Such an evaluation is the topic of this dissertation. Essay 1 investigates the forecast performance of the GARCH (1,1) model when estimated with 9 different error distributions on Standard and Poor’s 500 Index Future returns. By utilizing the theory of realized variance to construct an appropriate ex post measure of variance from intra-day data it is shown that allowing for a leptokurtic error distribution leads to significant improvements in variance forecasts compared to using the normal distribution. This result holds for daily, weekly as well as monthly forecast horizons. It is also found that allowing for skewness and time variation in the higher moments of the distribution does not further improve forecasts. In Essay 2, by using 20 years of daily Standard and Poor 500 index returns, it is found that density forecasts are much improved by allowing for constant excess kurtosis but not improved by allowing for skewness. By allowing the kurtosis and skewness to be time varying the density forecasts are not further improved but on the contrary made slightly worse. In Essay 3 a new model incorporating conditional variance, skewness and kurtosis based on the Normal Inverse Gaussian (NIG) distribution is proposed. The new model and two previously used NIG models are evaluated by their Value at Risk (VaR) forecasts on a long series of daily Standard and Poor’s 500 returns. The results show that only the new model produces satisfactory VaR forecasts for both 1% and 5% VaR Taken together the results of the thesis show that kurtosis appears not to exhibit predictable time variation, whereas there is found some predictability in the skewness. However, the dynamic properties of the skewness are not completely captured by any of the models.

Modeling Nonlinearities and Asymmetries in Asset Pricing

Financial time series tend to behave in a manner that is not directly drawn from a normal distribution. Asymmetries and nonlinearities are usually seen and these characteristics need to be taken into account. To make forecasts and predictions of future return and risk is rather complicated. The existing models for predicting risk are of help to a certain degree, but the complexity in financial time series data makes it difficult. The introduction of nonlinearities and asymmetries for the purpose of better models and forecasts regarding both mean and variance is supported by the essays in this dissertation. Linear and nonlinear models are consequently introduced in this dissertation. The advantages of nonlinear models are that they can take into account asymmetries. Asymmetric patterns usually mean that large negative returns appear more often than positive returns of the same magnitude. This goes hand in hand with the fact that negative returns are associated with higher risk than in the case where positive returns of the same magnitude are observed. The reason why these models are of high importance lies in the ability to make the best possible estimations and predictions of future returns and for predicting risk.

Optimal Risk Adoption: A Real Options Approach

This study develops a real options approach for analyzing the optimal risk adoption policy in an environment where the adoption means a switch from one stochastic flow representation into another. We establish that increased volatility needs not decelerate investment, as predicted by the standard literature on real options, once the underlying volatility of the state is made endogenous. We prove that for a decision maker with a convex (concave) objective function, increased post-adoption volatility increases (decreases) the expected cumulative present value of the post-adoption profit flow, which consequently decreases (increases) the option value of waiting and, therefore, accelerates (decelerates) current investment.

Prevention of type 2 diabetes with lifestyle intervention - emphasis on dietary composition and identification of high-risk individuals

Type 2 diabetes is an increasing, serious, and costly public health problem. The increase in the prevalence of the disease can mainly be attributed to changing lifestyles leading to physical inactivity, overweight, and obesity. These lifestyle-related risk factors offer also a possibility for preventive interventions. Until recently, proper evidence regarding the prevention of type 2 diabetes has been virtually missing. To be cost-effective, intensive interventions to prevent type 2 diabetes should be directed to people at an increased risk of the disease. The aim of this series of studies was to investigate whether type 2 diabetes can be prevented by lifestyle intervention in high-risk individuals, and to develop a practical method to identify individuals who are at high risk of type 2 diabetes and would benefit from such an intervention. To study the effect of lifestyle intervention on diabetes risk, we recruited 522 volunteer, middle-aged (aged 40 - 64 at baseline), overweight (body mass index > 25 kg/m2) men (n = 172) and women (n = 350) with impaired glucose tolerance to the Diabetes Prevention Study (DPS). The participants were randomly allocated either to the intensive lifestyle intervention group or the control group. The control group received general dietary and exercise advice at baseline, and had annual physician's examination. The participants in the intervention group received, in addition, individualised dietary counselling by a nutritionist. They were also offered circuit-type resistance training sessions and were advised to increase overall physical activity. The intervention goals were to reduce body weight (5% or more reduction from baseline weight), limit dietary fat (< 30% of total energy consumed) and saturated fat (< 10% of total energy consumed), and to increase dietary fibre intake (15 g / 1000 kcal or more) and physical activity (≥ 30 minutes/day). Diabetes status was assessed annually by a repeated 75 g oral glucose tolerance testing. First analysis on end-points was completed after a mean follow-up of 3.2 years, and the intervention phase was terminated after a mean duration of 3.9 years. After that, the study participants continued to visit the study clinics for the annual examinations, for a mean of 3 years. The intervention group showed significantly greater improvement in each intervention goal. After 1 and 3 years, mean weight reductions were 4.5 and 3.5 kg in the intervention group and 1.0 kg and 0.9 kg in the control group. Cardiovascular risk factors improved more in the intervention group. After a mean follow-up of 3.2 years, the risk of diabetes was reduced by 58% in the intervention group compared with the control group. The reduction in the incidence of diabetes was directly associated with achieved lifestyle goals. Furthermore, those who consumed moderate-fat, high-fibre diet achieved the largest weight reduction and, even after adjustment for weight reduction, the lowest diabetes risk during the intervention period. After discontinuation of the counselling, the differences in lifestyle variables between the groups still remained favourable for the intervention group. During the post-intervention follow-up period of 3 years, the risk of diabetes was still 36% lower among the former intervention group participants, compared with the former control group participants. To develop a simple screening tool to identify individuals who are at high risk of type 2 diabetes, follow-up data of two population-based cohorts of 35-64 year old men and women was used. The National FINRISK Study 1987 cohort (model development data) included 4435 subjects, with 182 new drug-treated cases of diabetes identified during ten years, and the FINRISK Study 1992 cohort (model validation data) included 4615 subjects, with 67 new cases of drug-treated diabetes during five years, ascertained using the Social Insurance Institution's Drug register. Baseline age, body mass index, waist circumference, history of antihypertensive drug treatment and high blood glucose, physical activity and daily consumption of fruits, berries or vegetables were selected into the risk score as categorical variables. In the 1987 cohort the optimal cut-off point of the risk score identified 78% of those who got diabetes during the follow-up (= sensitivity of the test) and 77% of those who remained free of diabetes (= specificity of the test). In the 1992 cohort the risk score performed equally well. The final Finnish Diabetes Risk Score (FINDRISC) form includes, in addition to the predictors of the model, a question about family history of diabetes and the age category of over 64 years. When applied to the DPS population, the baseline FINDRISC value was associated with diabetes risk among the control group participants only, indicating that the intensive lifestyle intervention given to the intervention group participants abolished the diabetes risk associated with baseline risk factors. In conclusion, the intensive lifestyle intervention produced long-term beneficial changes in diet, physical activity, body weight, and cardiovascular risk factors, and reduced diabetes risk. Furthermore, the effects of the intervention were sustained after the intervention was discontinued. The FINDRISC proved to be a simple, fast, inexpensive, non-invasive, and reliable tool to identify individuals at high risk of type 2 diabetes. The use of FINDRISC to identify high-risk subjects, followed by lifestyle intervention, provides a feasible scheme in preventing type 2 diabetes, which could be implemented in the primary health care system.

Serum uric acid and metabolic risk factors in three ethnic groups: Asian Indians and Creoles in Mauritius and Chinese in Qingdao, China

In humans with a loss of uricase the final oxidation product of purine catabolism is uric acid (UA). The prevalence of hyperuricemia has been increasing around the world accompanied by a rapid increase in obesity and diabetes. Since hyperuricemia was first described as being associated with hyperglycemia and hypertension by Kylin in 1923, there has been a growing interest in the association between elevated UA and other metabolic abnormalities of hyperglycemia, abdominal obesity, dyslipidemia, and hypertension. The direction of causality between hyperuricemia and metabolic disorders, however, is unceartain. The association of UA with metabolic abnormalities still needs to be delineated in population samples. Our overall aims were to study the prevalence of hyperuricemia and the metabolic factors clustering with hyperuricemia, to explore the dynamical changes in blood UA levels with the deterioration in glucose metabolism and to estimate the predictive capability of UA in the development of diabetes. Four population-based surveys for diabetes and other non-communicable diseases were conducted in 1987, 1992, and 1998 in Mauritius, and in 2001-2002 in Qingdao, China. The Qingdao study comprised 1 288 Chinese men and 2 344 women between 20-74, and the Mauritius study consisted of 3 784 Mauritian Indian and Mauritian Creole men and 4 442 women between 25-74. In Mauritius, re-exams were made in 1992 and/or 1998 for 1 941 men (1 409 Indians and 532 Creoles) and 2 318 non pregnant women (1 645 Indians and 673 Creoles), free of diabetes, cardiovascular diseases, and gout at baseline examinations in 1987 or 1992, using the same study protocol. The questionnaire was designed to collect demographic details, physical examinations and standard 75g oral glucose tolerance tests were performed in all cohorts. Fasting blood UA and lipid profiles were also determined. The age-standardized prevalence in Chinese living in Qingdao was 25.3% for hyperuricemia (defined as fasting serum UA > 420 μmol/l in men and > 360 μmol/l in women) and 0.36% for gout in adults between 20-74. Hyperuricemia was more prevalent in men than in women. One standard deviation increase in UA concentration was associated with the clustering of metabolic risk factors for both men and women in three ethnic groups. Waist circumference, body mass index, and serum triglycerides appeared to be independently associated with hyperuricemia in both sexes and in all ethnic groups except in Chinese women, in whom triglycerides, high-density lipoprotein cholesterol, and total cholesterol were associated with hyperuricemia. Serum UA increased with increasing fasting plasma glucose levels up to a value of 7.0 mmol/l, but significantly decreased thereafter in mainland Chinese. An inverse relationship occurred between 2-h plasma glucose and serum UA when 2-h plasma glucose higher than 8.0 mmol/l. In the prospective study in Mauritius, 337 (17.4%) men and 379 (16.4%) women developed diabetes during the follow-up. Elevated UA levels at baseline increased 1.14-fold in risk of incident diabetes in Indian men and 1.37-fold in Creole men, but no significant risk was observed in women. In conclusion, the prevalence of hyperuricemia was high in Chinese in Qingdao, blood UA was associated with the clustering of metabolic risk factors in Mauritian Indian, Mauritian Creole, and Chinese living in Qingdao, and a high baseline UA level independently predicted the development of diabetes in Mauritian men. The clinical use of UA as a marker of hyperglycemia and other metabolic disorders needs to be further studied. Keywords: Uric acid, Hyperuricemia, Risk factors, Type 2 Diabetes, Incidence, Mauritius, Chinese

SPECT-aided diagnostics and genetic risk factors in Parkinson's disease

Hypokinesia, rigidity, tremor, and postural instability are the cardinal symptoms of Parkinson s disease (PD). Since these symptoms are not specific to PD the diagnosis may be uncertain in early PD. Etiology and pathogenesis of PD remain unclear. There is no neuroprotective therapy. Genetic findings are expected to reveal metabolic routes in PD pathogenesis and thereby eventually lead to therapeutic innovations. In this thesis, we first aimed to study the usefulness and accuracy of 123I-b-CIT SPECT in the diagnosis of PD in a consecutive clinic-based material including various movement disorders. We subsequently a genetic project to identify genetic risk factors for sporadic PD using a candidate gene approach in a case-control setting including 147 sporadic PD patients and 137 spouse controls. Dopamine transporter imaging by 123I-b-CIT SPECT could distinguish PD from essential tremor, drug-induced parkinsonism, dystonia and psychogenic parkinsonism. However, b-CIT uptake in Parkinson plus syndromes (PSP and multiple system atrophy) and dementia with Lewy bodies was not significantly different from PD. 123I-b-CIT SPECT could not reliably differentiate PD from vascular parkinsonism. 123I-b-CIT SPECT was 100% sensitive and specific in the diagnosis of PD in patients younger than 55 years but less specific in older patients, due to differential distribution of the above conditions in the younger and older age groups. 123I-b-CIT SPECT correlated with symptoms and detected bilateral nigrostriatal defect in patients whose PD was still in unilateral stage. Thus, in addition to as a differential diagnostic aid, 123I-b-CIT SPECT may be used to detect PD early, even pre-symptomatically in at-risk individuals. 123I-b-CIT SPECT was used to aid in the collection of patients to the genetic studies. In the genetic part of this thesis we found an association between PD and a polymorphic CAG-repeat in POLG1 gene encoding the catalytic subunit of mitochondrial polymerase gamma. The CAG-repeat encodes a polyglutamine tract (polyQ), the two most common lengths of which are 10Q (86-90%) and 11Q. In our Finnish material, the rarer non-10Q or non-11Q length variants (6Q-9Q, 12Q-14Q, 4R+9Q) were more frequent in patients than in spouse controls (10% vs. 3.5 %, p=0.003), or population controls (p=0.001). Therefore, we performed a replication study in 652 North American PD patients and 292 controls. Non-10/11Q alleles were more common in the US PD patients compared to the controls but the difference did not reach statistical significance (p=0.07). This larger data suggested our original definition of variant length allele might need reconsideration. Most previous studies on phenotypic effects of POLG1 polyQ have defined 10Q as the only normal allele. Non-10Q alleles were significantly more common in patients compared to the controls (17.3% vs. 12.3 %, p= 0.005). This association between non-10Q length variants and PD remained significant when compared to a larger set of 1541 literature controls (p=0.00005). In conclusion, POLG1 polyQ alleles other than 10Q may predispose to PD. We did not find association between PD and parkin or DJ-1, genes underlying autosomal recessive parkinsonism. The functional Val158Met polymorphism, which affects the catalytic effect of COMT enzyme, and another coding polymorphism in COMT were not associated with PD in our patient material. The APOE e2/3/4 polymorphism modifies risk for Alzheimer s disease and prognosis of for example brain trauma. APOE promoter and enhancer polymorphisms 219G/T and +113G/C, and APOE e3 haplotypes, have also been shown to modify the risk of Alzheimer s disease but not reported in PD. No association was found between PD and APOE e2/3/4 polymorphism, the promoter or enhancer polymorphisms, or the e3 haplotypes.