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.

Problems of Proto-Slavic Historical Nominal Morphology : On the Basis of Old Church Slavic

In this study I offer a diachronic solution for a number of difficult inflectional endings in Old Church Slavic nominal declensions. In this context I address the perhaps most disputed and the most important question of the Slavic nominal inflectional morphology: whether there was in Proto-Slavic an Auslautgesetz (ALG), a law of final syllables, that narrowed the Proto-Indo-European vowel */o/ to */u/ in closed word-final syllables. In addition, the work contains an exhaustive morphological classification of the nouns and adjectives that occur in canonical Old Church Slavic. I argue that Proto-Indo-European */o/ became Proto-Slavic */u/ before word-final */s/ and */N/. This conclusion is based on the impossibility of finding credible analogical (as opposed to phonological) explanations for the forms supporting the ALG hypothesis, and on the survival of the neuter gender in Slavic. It is not likely that the */o/-stem nominative singular ending */-u/ was borrowed from the accusative singular, because the latter would have been the only paradigmatic form with the stem vowel */-u-/. It is equally unlikely that the ending */-u/ was borrowed from the */u/-stems, because the latter constituted a moribund class. The usually stated motivation for such an analogical borrowing, i.e. a need to prevent the merger of */o/-stem masculines with neuters of the same class, is not tenable. Extra-Slavic, as well as intra-Slavic evidence suggests that phonologically-triggered mergers between two semantically opaque genders do not tend to be prevented, but rather that such mergers lead to the loss of the gender opposition in question. On the other hand, if */-os/ had not become */-us/, most nouns and, most importantly, all adjectives and pronouns would have lost the formal distinction between masculines and neuters. This would have necessarily resulted in the loss of the neuter gender. A new explanation is given for the most apparent piece of evidence against the ALG hypothesis, the nominative-accusative singular of the */es/-stem neuters, e.g. nebo 'sky'. I argue that it arose in late Proto-Slavic dialects, replacing regular nebe, under the influence of the */o/- and */yo/-stems where a correlation had emerged between a hard root-final consonant and the termination -o, on the one hand, and a soft root-final consonant and the termination -e, on the other.

Questions to Artificial Nature: A Philosophical Study of Interdisciplinary Models and their Functions in Scientific Practice

This thesis presents an interdisciplinary analysis of how models and simulations function in the production of scientific knowledge. The work is informed by three scholarly traditions: studies on models and simulations in philosophy of science, so-called micro-sociological laboratory studies within science and technology studies, and cultural-historical activity theory. Methodologically, I adopt a naturalist epistemology and combine philosophical analysis with a qualitative, empirical case study of infectious-disease modelling. This study has a dual perspective throughout the analysis: it specifies the modelling practices and examines the models as objects of research. The research questions addressed in this study are: 1) How are models constructed and what functions do they have in the production of scientific knowledge? 2) What is interdisciplinarity in model construction? 3) How do models become a general research tool and why is this process problematic? The core argument is that the mediating models as investigative instruments (cf. Morgan and Morrison 1999) take questions as a starting point, and hence their construction is intentionally guided. This argument applies the interrogative model of inquiry (e.g., Sintonen 2005; Hintikka 1981), which conceives of all knowledge acquisition as process of seeking answers to questions. The first question addresses simulation models as Artificial Nature, which is manipulated in order to answer questions that initiated the model building. This account develops further the "epistemology of simulation" (cf. Winsberg 2003) by showing the interrelatedness of researchers and their objects in the process of modelling. The second question clarifies why interdisciplinary research collaboration is demanding and difficult to maintain. The nature of the impediments to disciplinary interaction are examined by introducing the idea of object-oriented interdisciplinarity, which provides an analytical framework to study the changes in the degree of interdisciplinarity, the tools and research practices developed to support the collaboration, and the mode of collaboration in relation to the historically mutable object of research. As my interest is in the models as interdisciplinary objects, the third research problem seeks to answer my question of how we might characterise these objects, what is typical for them, and what kind of changes happen in the process of modelling. Here I examine the tension between specified, question-oriented models and more general models, and suggest that the specified models form a group of their own. I call these Tailor-made models, in opposition to the process of building a simulation platform that aims at generalisability and utility for health-policy. This tension also underlines the challenge of applying research results (or methods and tools) to discuss and solve problems in decision-making processes.

Silvicultural decisions based on simulation-optimization systems

Forest management is facing new challenges under climate change. By adjusting thinning regimes, conventional forest management can be adapted to various objectives of utilization of forest resources, such as wood quality, forest bioenergy, and carbon sequestration. This thesis aims to develop and apply a simulation-optimization system as a tool for an interdisciplinary understanding of the interactions between wood science, forest ecology, and forest economics. In this thesis, the OptiFor software was developed for forest resources management. The OptiFor simulation-optimization system integrated the process-based growth model PipeQual, wood quality models, biomass production and carbon emission models, as well as energy wood and commercial logging models into a single optimization model. Osyczka s direct and random search algorithm was employed to identify optimal values for a set of decision variables. The numerical studies in this thesis broadened our current knowledge and understanding of the relationships between wood science, forest ecology, and forest economics. The results for timber production show that optimal thinning regimes depend on site quality and initial stand characteristics. Taking wood properties into account, our results show that increasing the intensity of thinning resulted in lower wood density and shorter fibers. The addition of nutrients accelerated volume growth, but lowered wood quality for Norway spruce. Integrating energy wood harvesting into conventional forest management showed that conventional forest management without energy wood harvesting was still superior in sparse stands of Scots pine. Energy wood from pre-commercial thinning turned out to be optimal for dense stands. When carbon balance is taken into account, our results show that changing carbon assessment methods leads to very different optimal thinning regimes and average carbon stocks. Raising the carbon price resulted in longer rotations and a higher mean annual increment, as well as a significantly higher average carbon stock over the rotation.

Design and testing of stand-specific bucking instructions for use on modern cut-to-length harvesters

This study addresses three important issues in tree bucking optimization in the context of cut-to-length harvesting. (1) Would the fit between the log demand and log output distributions be better if the price and/or demand matrices controlling the bucking decisions on modern cut-to-length harvesters were adjusted to the unique conditions of each individual stand? (2) In what ways can we generate stand and product specific price and demand matrices? (3) What alternatives do we have to measure the fit between the log demand and log output distributions, and what would be an ideal goodness-of-fit measure? Three iterative search systems were developed for seeking stand-specific price and demand matrix sets: (1) A fuzzy logic control system for calibrating the price matrix of one log product for one stand at a time (the stand-level one-product approach); (2) a genetic algorithm system for adjusting the price matrices of one log product in parallel for several stands (the forest-level one-product approach); and (3) a genetic algorithm system for dividing the overall demand matrix of each of the several log products into stand-specific sub-demands simultaneously for several stands and products (the forest-level multi-product approach). The stem material used for testing the performance of the stand-specific price and demand matrices against that of the reference matrices was comprised of 9 155 Norway spruce (Picea abies (L.) Karst.) sawlog stems gathered by harvesters from 15 mature spruce-dominated stands in southern Finland. The reference price and demand matrices were either direct copies or slightly modified versions of those used by two Finnish sawmilling companies. Two types of stand-specific bucking matrices were compiled for each log product. One was from the harvester-collected stem profiles and the other was from the pre-harvest inventory data. Four goodness-of-fit measures were analyzed for their appropriateness in determining the similarity between the log demand and log output distributions: (1) the apportionment degree (index), (2) the chi-square statistic, (3) Laspeyres quantity index, and (4) the price-weighted apportionment degree. The study confirmed that any improvement in the fit between the log demand and log output distributions can only be realized at the expense of log volumes produced. Stand-level pre-control of price matrices was found to be advantageous, provided the control is done with perfect stem data. Forest-level pre-control of price matrices resulted in no improvement in the cumulative apportionment degree. Cutting stands under the control of stand-specific demand matrices yielded a better total fit between the demand and output matrices at the forest level than was obtained by cutting each stand with non-stand-specific reference matrices. The theoretical and experimental analyses suggest that none of the three alternative goodness-of-fit measures clearly outperforms the traditional apportionment degree measure. Keywords: harvesting, tree bucking optimization, simulation, fuzzy control, genetic algorithms, goodness-of-fit

Individualized immunosuppression after renal transplantation in childhood

Pediatric renal transplantation (TX) has evolved greatly during the past few decades, and today TX is considered the standard care for children with end-stage renal disease. In Finland, 191 children had received renal transplants by October 2007, and 42% of them have already reached adulthood. Improvements in treatment of end-stage renal disease, surgical techniques, intensive care medicine, and in immunosuppressive therapy have paved the way to the current highly successful outcomes of pediatric transplantation. In children, the transplanted graft should last for decades, and normal growth and development should be guaranteed. These objectives set considerable requirements in optimizing and fine-tuning the post-operative therapy. Careful optimization of immunosuppressive therapy is crucial in protecting the graft against rejection, but also in protecting the patient against adverse effects of the medication. In the present study, the results of a retrospective investigation into individualized dosing of immunosuppresive medication, based on pharmacokinetic profiles, therapeutic drug monitoring, graft function and histology studies, and glucocorticoid biological activity determinations, are reported. Subgroups of a total of 178 patients, who received renal transplants in 1988 2006 were included in the study. The mean age at TX was 6.5 years, and approximately 26% of the patients were <2 years of age. The most common diagnosis leading to renal TX was congenital nephrosis of the Finnish type (NPHS1). Pediatric patients in Finland receive standard triple immunosuppression consisting of cyclosporine A (CsA), methylprednisolone (MP) and azathioprine (AZA) after renal TX. Optimal dosing of these agents is important to prevent rejections and preserve graft function in one hand, and to avoid the potentially serious adverse effects on the other hand. CsA has a narrow therapeutic window and individually variable pharmacokinetics. Therapeutic monitoring of CsA is, therefore, mandatory. Traditionally, CsA monitoring has been based on pre-dose trough levels (C0), but recent pharmacokinetic and clinical studies have revealed that the immunosuppressive effect may be related to diurnal CsA exposure and blood CsA concentration 0-4 hours after dosing. The two-hour post-dose concentration (C2) has proved a reliable surrogate marker of CsA exposure. Individual starting doses of CsA were analyzed in 65 patients. A recommended dose based on a pre-TX pharmacokinetic study was calculated for each patient by the pre-TX protocol. The predicted dose was clearly higher in the youngest children than in the older ones (22.9±10.4 and 10.5±5.1 mg/kg/d in patients <2 and >8 years of age, respectively). The actually administered oral doses of CsA were collected for three weeks after TX and compared to the pharmacokinetically predicted dose. After the TX, dosing of CsA was adjusted according to clinical parameters and blood CsA trough concentration. The pharmacokinetically predicted dose and patient age were the two significant parameters explaining post-TX doses of CsA. Accordingly, young children received significantly higher oral doses of CsA than the older ones. The correlation to the actually administered doses after TX was best in those patients, who had a predicted dose clearly higher or lower (> ±25%) than the average in their age-group. Due to the great individual variation in pharmacokinetics standardized dosing of CsA (based on body mass or surface area) may not be adequate. Pre-Tx profiles are helpful in determining suitable initial CsA doses. CsA monitoring based on trough and C2 concentrations was analyzed in 47 patients, who received renal transplants in 2001 2006. C0, C2 and experienced acute rejections were collected during the post-TX hospitalization, and also three months after TX when the first protocol core biopsy was obtained. The patients who remained rejection free had slightly higher C2 concentrations, especially very early after TX. However, after the first two weeks also the trough level was higher in the rejection-free patients than in those with acute rejections. Three months after TX the trough level was higher in patients with normal histology than in those with rejection changes in the routine biopsy. Monitoring of both the trough level and C2 may thus be warranted to guarantee sufficient peak concentration and baseline immunosuppression on one hand and to avoid over-exposure on the other hand. Controlling of rejection in the early months after transplantation is crucial as it may contribute to the development of long-term allograft nephropathy. Recently, it has become evident that immunoactivation fulfilling the histological criteria of acute rejection is possible in a well functioning graft with no clinical sings or laboratory perturbations. The influence of treatment of subclinical rejection, diagnosed in 3-month protocol biopsy, to graft function and histology 18 months after TX was analyzed in 22 patients and compared to 35 historical control patients. The incidence of subclinical rejection at three months was 43%, and the patients received a standard rejection treatment (a course of increased MP) and/or increased baseline immunosuppression, depending on the severity of rejection and graft function. Glomerular filtration rate (GFR) at 18 months was significantly better in the patients who were screened and treated for subclinical rejection in comparison to the historical patients (86.7±22.5 vs. 67.9±31.9 ml/min/1.73m2, respectively). The improvement was most remarkable in the youngest (<2 years) age group (94.1±11.0 vs. 67.9±26.8 ml/min/1.73m2). Histological findings of chronic allograft nephropathy were also more common in the historical patients in the 18-month protocol biopsy. All pediatric renal TX patients receive MP as a part of the baseline immunosuppression. Although the maintenance dose of MP is very low in the majority of the patients, the well-known steroid-related adverse affects are not uncommon. It has been shown in a previous study in Finnish pediatric TX patients that steroid exposure, measured as area under concentration-time curve (AUC), rather than the dose correlates with the adverse effects. In the present study, MP AUC was measured in sixteen stable maintenance patients, and a correlation with excess weight gain during 12 months after TX as well as with height deficit was found. A novel bioassay measuring the activation of glucocorticoid receptor dependent transcription cascade was also employed to assess the biological effect of MP. Glucocorticoid bioactivity was found to be related to the adverse effects, although the relationship was not as apparent as that with serum MP concentration. The findings in this study support individualized monitoring and adjustment of immunosuppression based on pharmacokinetics, graft function and histology. Pharmacokinetic profiles are helpful in estimating drug exposure and thus identifying the patients who might be at risk for excessive or insufficient immunosuppression. Individualized doses and monitoring of blood concentrations should definitely be employed with CsA, but possibly also with steroids. As an alternative to complete steroid withdrawal, individualized dosing based on drug exposure monitoring might help in avoiding the adverse effects. Early screening and treatment of subclinical immunoactivation is beneficial as it improves the prospects of good long-term graft function.