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.

The structure of Norway spruce (Picea abies [L.] Karst.) stems in relation to wood properties of sawn timber

An important challenge in forest industry is to get the appropriate raw material out from the forests to the wood processing industry. Growth and stem reconstruction simulators are therefore increasingly integrated in industrial conversion simulators, for linking the properties of wooden products to the three-dimensional structure of stems and their growing conditions. Static simulators predict the wood properties from stem dimensions at the end of a growth simulation period, whereas in dynamic approaches, the structural components, e.g. branches, are incremented along with the growth processes. The dynamic approach can be applied to stem reconstruction by predicting the three-dimensional stem structure from external tree variables (i.e. age, height) as a result of growth to the current state. In this study, a dynamic growth simulator, PipeQual, and a stem reconstruction simulator, RetroSTEM, are adapted to Norway spruce (Picea abies [L.] Karst.) to predict the three-dimensional structure of stems (tapers, branchiness, wood basic density) over time such that both simulators can be integrated in a sawing simulator. The parameterisation of the PipeQual and RetroSTEM simulators for Norway spruce relied on the theoretically based description of tree structure developing in the growth process and following certain conservative structural regularities while allowing for plasticity in the crown development. The crown expressed both regularity and plasticity in its development, as the vertical foliage density peaked regularly at about 5 m from the stem apex, varying below that with tree age and dominance position (Study I). Conservative stem structure was characterized in terms of (1) the pipe ratios between foliage mass and branch and stem cross-sectional areas at crown base, (2) the allometric relationship between foliage mass and crown length, (3) mean branch length relative to crown length and (4) form coefficients in branches and stem (Study II). The pipe ratio between branch and stem cross-sectional area at crown base, and mean branch length relative to the crown length may differ in trees before and after canopy closure, but the variation should be further analysed in stands of different ages and densities with varying site fertilities and climates. The predictions of the PipeQual and RetroSTEM simulators were evaluated by comparing the simulated values to measured ones (Study III, IV). Both simulators predicted stem taper and branch diameter at the individual tree level with a small bias. RetroSTEM predictions of wood density were accurate. For focusing on even more accurate predictions of stem diameters and branchiness along the stem, both simulators should be further improved by revising the following aspects in the simulators: the relationship between foliage and stem sapwood area in the upper stem, the error source in branch sizes, the crown base development and the height growth models in RetroSTEM. In Study V, the RetroSTEM simulator was integrated in the InnoSIM sawing simulator, and according to the pilot simulations, this turned out to be an efficient tool for readily producing stand scale information about stem sizes and structure when approximating the available assortments of wood products.

N-syndecan and HB-GAM in neural migration and differentiation : Modulation of growth factor activity in brain

The juvenile sea squirt wanders through the sea searching for a suitable rock or hunk of coral to cling to and make its home for life. For this task it has a rudimentary nervous system. When it finds its spot and takes root, it doesn't need its brain any more so it eats it. It's rather like getting tenure. Daniel C. Dennett (from Consciousness Explained, 1991) The little sea squirt needs its brain for a task that is very simple and short. When the task is completed, the sea squirt starts a new life in a vegetative state, after having a nourishing meal. The little brain is more tightly structured than our massive primate brains. The number of neurons is exact, no leeway in neural proliferation is tolerated. Each neuroblast migrates exactly to the correct position, and only a certain number of connections with the right companions is allowed. In comparison, growth of a mammalian brain is a merry mess. The reason is obvious: Squirt brain needs to perform only a few, predictable functions, before becoming waste. The more mobile and complex mammals engage their brains in tasks requiring quick adaptation and plasticity in a constantly changing environment. Although the regulation of nervous system development varies between species, many regulatory elements remain the same. For example, all multicellular animals possess a collection of proteoglycans (PG); proteins with attached, complex sugar chains called glycosaminoglycans (GAG). In development, PGs participate in the organization of the animal body, like in the construction of parts of the nervous system. The PGs capture water with their GAG chains, forming a biochemically active gel at the surface of the cell, and in the extracellular matrix (ECM). In the nervous system, this gel traps inside it different molecules: growth factors and ECM-associated proteins. They regulate the proliferation of neural stem cells (NSC), guide the migration of neurons, and coordinate the formation of neuronal connections. In this work I have followed the role of two molecules contributing to the complexity of mammalian brain development. N-syndecan is a transmembrane heparan sulfate proteoglycan (HSPG) with cell signaling functions. Heparin-binding growth-associated molecule (HB-GAM) is an ECM-associated protein with high expression in the perinatal nervous system, and high affinity to HS and heparin. N-syndecan is a receptor for several growth factors and for HB-GAM. HB-GAM induces specific signaling via N-syndecan, activating c-Src, calcium/calmodulin-dependent serine protein kinase (CASK) and cortactin. By studying the gene knockouts of HB-GAM and N-syndecan in mice, I have found that HB-GAM and N-syndecan are involved as a receptor-ligand-pair in neural migration and differentiation. HB-GAM competes with the growth factors fibriblast growth factor (FGF)-2 and heparin-binding epidermal growth factor (HB-EGF) in HS-binding, causing NSCs to stop proliferation and to differentiate, and affects HB-EGF-induced EGF receptor (EGFR) signaling in neural cells during migration. N-syndecan signaling affects the motility of young neurons, by boosting EGFR-mediated cell migration. In addition, these two receptors form a complex at the surface of the neurons, probably creating a motility-regulating structure.

Structure-Function Studies of GDNF Family Ligand-RET signalling

Glial cell line-derived neurotrophic factor (GDNF) and its family members neurturin (NRTN), artemin (ARTN) and persephin (PSPN) are growth factors, which are involved in the development, differentiation and maintenance of many neuron types. In addition, they function outside of the nervous system, e.g. in the development of kidney, testis and liver. GDNF family ligand (GFL) signalling happens through a tetrameric receptor complex, which includes two glycosylphosphatidylinositol (GPI)-anchored GDNF family receptor (GFRα) molecules and two RET (rearranged during transfection) receptor tyrosine kinases. Each of the ligands binds preferentially one of the four GFRα receptors: GDNF binds to GFRα1, NRTN to GFRα2, ARTN to GFRα3 and PSPN to GFRα4. The signal is then delivered by RET, which cannot bind the GFLs on its own, but can bind the GFL-GFRα complex. Under normal cellular conditions, RET is only phosphorylated on the cell surface after ligand binding. At least the GDNF-GFRα1 complex is believed to recruit RET to lipid rafts, where downstream signalling occurs. In general, GFRαs consist of three cysteine-rich domains, but all GFRα4s except for chicken GFRα4 lack domain 1 (D1). We characterised the biochemical and cell biological properties of mouse PSPN receptor GFRα4 and showed that it has a significantly weaker capacity than GFRα1 to recruit RET to the lipid rafts. In spite of that, it can phosphorylate RET in the presence of PSPN and contribute to neuronal differentiation and survival. Therefore, the recruitment of RET to the lipid rafts does not seem to be crucial for the biological activity of all GFRα receptors. Secondly, we demonstrated that GFRα1 D1 stabilises the GDNF-GFRα1 complex and thus affects the phosphorylation of RET and contributes to the biological activity. This may be important in physiological conditions, where the concentration of the ligand or the soluble GFRα1 receptor is low. Our results also suggest a role for D1 in heparin binding and, consequently, in the biodistribution of released GFRα1 or in the formation of the GFL-GFRα-RET complex. We also presented the crystallographic structure of GDNF in the complex with GFRα1 domains 2 and 3. The structure differs from the previously published ARTN-GFRα3 structure in three significant ways. The biochemical data verify the structure and reveal residues participating in the interactions between GFRα1 and GDNF, and preliminarily also between GFRα1 and RET and heparin. Finally, we showed that, the precursor of the oncogenic MEN 2B (multiple endocrine neoplasia type 2) form of RET gets phosphorylated already during its synthesis in the endoplasmic reticulum (ER). We also demonstrated that it associates with Src homology 2 domain-containing protein (SHC) and growth factor receptor-bound protein (GRB2) in the ER, and has the capacity to activate several downstream signalling molecules.

Novel CDNF/MANF protein family : Molecular structure, expression and neurotrophic activity

Neurotrophic factors (NTFs) are secreted proteins which promote the survival of neurons, formation and maintenance of neuronal contacts and regulate synaptic plasticity. NTFs are also potential drug candidates for the treatment of neurodegenerative diseases. Parkinson’s disease (PD) is mainly caused by the degeneration of midbrain dopaminergic neurons. Current therapies for PD do not stop the neurodegeneration or repair the affected neurons. Thus, search of novel neurotrophic factors for midbrain dopaminergic neurons, which could also be used as therapeutic proteins, is highly warranted. In the present study, we identified and characterized a novel protein named conserved dopamine neurotrophic factor (CDNF), a homologous protein to mesencephalic astrocyte-derived neurotrophic factor (MANF). Others have shown that MANF supports the survival of embryonic midbrain dopaminergic neurons in vitro, and protects cultured cells against endoplasmic reticulum (ER) stress. CDNF and MANF form a novel evolutionary conserved protein family with characteristic eight conserved cysteine residues in their primary structure. The vertebrates have CDNF and MANF encoding genes, whereas the invertebrates, including Drosophila and Caenorhabditis have a single homologous CDNF/MANF gene. In this study we show that CDNF and MANF are secreted proteins. They are widely expressed in the mammalian brain, including the midbrain and striatum, and in several non-neuronal tissues. We expressed and purified recombinant human CDNF and MANF proteins, and tested the neurotrophic activity of CDNF on midbrain dopaminergic neurons using a 6-hydroxydopamine (6-OHDA) rat model of PD. In this model, a single intrastriatal injection of CDNF protected midbrain dopaminergic neurons and striatal dopaminergic fibers from the 6-OHDA toxicity. Importantly, an intrastriatal injection of CDNF also restored the functional activity of the nigrostriatal dopaminergic system when given after the striatal 6-OHDA lesion. Thus, our study shows that CDNF is a potential novel therapeutic protein for the treatment of PD. In order to elucidate the molecular mechanisms of CDNF and MANF activity, we resolved their crystal structure. CDNF and MANF proteins have two domains; an amino (N)-terminal saposin-like domain and a presumably unfolded carboxy (C)-terminal domain. The saposin-like domain, which is formed by five α-helices and stabilized by three intradomain disulphide bridges, may bind to lipids or membranes. The C-terminal domain contains an internal cysteine bridge in a CXXC motif similar to that of thiol/disulphide oxidoreductases and isomerases, and may thus facilitate protein folding in the ER. Our studies suggest that CDNF and MANF are novel potential therapeutic proteins for the treatment of neurodegenerative diseases. Future studies will reveal the neurotrophic and cytoprotective mechanisms of CDNF and MANF in more detail.

Structure and function of GDNF receptor alpha splice variants

The growth factors of the glial cell line-derived neurotrophic factor (GDNF) family consisting of GDNF, neurturin (NRTN), artemin (ARTN) and persephin (PSPN), are involved in the development, differentiation and maintenance of many types of neurons. They also have important functions outside the nervous system in the development of kidney, testis and thyroid gland. Each of these GFLs preferentially binds to one of the glycosylphosphatidylinositol (GPI)-anchored GDNF family receptors α (GFRα). GDNF binds to GFRα1, NRTN to GFRα2, ARTN to GFRα3 and PSPN to GFRα4. The GFLs in the complex with their cognate GFRα receptors all bind to and signal through the receptor tyrosine kinase RET. Alternative splicing of the mouse GFRα4 gene yields three splice isoforms. These had been described as putative GPI-anchored, transmembrane and soluble forms. My goal was to characterise the function of the different forms of mouse GFRα4. I firstly found that the putative GPI-anchored GFRα4 (GFRα4-GPI) is glycosylated, membrane-bound, GPI-anchored and interacts with PSPN and RET. We also showed that mouse GFRα4-GPI mediates PSPN-induced phosphorylation of RET, promotes PSPN-dependent neuronal differentiation of the rat pheochromocytoma cell line PC6-3 and PSPN-dependent survival of cerebellar granule neurons (CGN). However, although this receptor can mediate PSPN-signalling and activate RET, GFRα4-GPI does not recruit RET into lipid rafts. The recruitment of RET into lipid rafts has previously been thought to be a crucial event for GDNF- and GFL-mediated signalling via RET. I secondly demonstrated that the putative transmembrane GFRα4 (GFRα4-TM) is indeed a real transmembrane GFRα4 protein. Although it has a weak binding capacity for PSPN, it can not mediate PSPN-dependent phosphorylation of RET, neuronal differentiation or survival. These data show that GFRα4-TM is inactive as a receptor for PSPN. Surprisingly, GFRα4-TM can negatively regulate PSPN-mediated signalling via GFRα4-GPI. GFRα4-TM interacts with GFRα4-GPI and blocks PSPN-induced phosphorylation of RET, neuronal differentiation as well as survival. Taken together, our data show that GFRα4-TM may act as a dominant negative inhibitor of PSPN-mediated signaling. The most exciting part of my work was the finding that the putative soluble GFRα4 (GFRα4-sol) can form homodimers and function as an agonist of the RET receptor. In the absence of PSPN, GFRα4-sol can promote the phosphorylation of RET, trigger the activation of the PI-3K/AKT pathway, induce neuronal differentiation and support the survival of CGN. Our findings are in line with a recent publication showing the GFRα4-sol might contribute to the inherited cancer syndrome multiple endocrine neoplasia type 2. Our data provide an explanation to how GFRα4-sol may cause or modify the disease. Mammalian GFRα4 receptors all lack the first Cys-rich domain which is present in other GFRα receptors. In the final part of my work I have studied the function of this particular domain. I created a truncated GFRα1 construct lacking the first Cys-rich domain. Using binding assays in both cellular and cell-free systems, phosphorylation assays with RET, as well as neurite outgrowth assays, we found that the first Cys-rich domain contributes to an optimal function of GFRα1, by stabilizing the interaction between GDNF and GFRα1.

Dynamics of free-running, pump-modulated and coupled semiconductor and solid-state lasers

The output of a laser is a high frequency propagating electromagnetic field with superior coherence and brightness compared to that emitted by thermal sources. A multitude of different types of lasers exist, which also translates into large differences in the properties of their output. Moreover, the characteristics of the electromagnetic field emitted by a laser can be influenced from the outside, e.g., by injecting an external optical field or by optical feedback. In the case of free-running solitary class-B lasers, such as semiconductor and Nd:YVO4 solid-state lasers, the phase space is two-dimensional, the dynamical variables being the population inversion and the amplitude of the electromagnetic field. The two-dimensional structure of the phase space means that no complex dynamics can be found. If a class-B laser is perturbed from its steady state, then the steady state is restored after a short transient. However, as discussed in part (i) of this Thesis, the static properties of class-B lasers, as well as their artificially or noise induced dynamics around the steady state, can be experimentally studied in order to gain insight on laser behaviour, and to determine model parameters that are not known ab initio. In this Thesis particular attention is given to the linewidth enhancement factor, which describes the coupling between the gain and the refractive index in the active material. A highly desirable attribute of an oscillator is stability, both in frequency and amplitude. Nowadays, however, instabilities in coupled lasers have become an active area of research motivated not only by the interesting complex nonlinear dynamics but also by potential applications. In part (ii) of this Thesis the complex dynamics of unidirectionally coupled, i.e., optically injected, class-B lasers is investigated. An injected optical field increases the dimensionality of the phase space to three by turning the phase of the electromagnetic field into an important variable. This has a radical effect on laser behaviour, since very complex dynamics, including chaos, can be found in a nonlinear system with three degrees of freedom. The output of the injected laser can be controlled in experiments by varying the injection rate and the frequency of the injected light. In this Thesis the dynamics of unidirectionally coupled semiconductor and Nd:YVO4 solid-state lasers is studied numerically and experimentally.