American option valuation: implied calibration of GARCH pricing models

This study analyzes the issue of American option valuation when the underlying exhibits a GARCH-type volatility process. We propose the usage of Rubinstein's Edgeworth binomial tree (EBT) in contrast to simulation-based methods being considered in previous studies. The EBT-based valuation approach makes an implied calibration of the pricing model feasible. By empirically analyzing the pricing performance of American index and equity options, we illustrate the superiority of the proposed approach.

The use of Meteosat satellite data for spatial rainfall estimations and hydrological simulations

Satellite information, in combination with conventional point source measurements, can be a valuable source of information. This thesis is devoted to the spatial estimation of areal rainfall over a region using both the measurements from a dense and sparse network of rain-gauges and images from the meteorological satellites. A primary concern is to study the effects of such satellite assisted rainfall estimates on the performance of rainfall-runoff models. Low-cost image processing systems and peripherals are used to process and manipulate the data. Both secondary as well as primary satellite images were used for analysis. The secondary data was obtained from the in-house satellite receiver and the primary data was obtained from an outside source. Ground truth data was obtained from the local Water Authority. A number of algorithms are presented that combine the satellite and conventional data sources to produce areal rainfall estimates and the results are compared with some of the more traditional methodologies. The results indicate that the satellite cloud information is valuable in the assessment of the spatial distribution of areal rainfall, for both half-hourly as well as daily estimates of rainfall. It is also demonstrated how the performance of the simple multiple regression rainfall-runoff model is improved when satellite cloud information is used as a separate input in addition to rainfall estimates from conventional means. The use of low-cost equipment, from image processing systems to satellite imagery, makes it possible for developing countries to introduce such systems in areas where the benefits are greatest.

Stima dei parametri di modelli idrologici mediante ottimizzazione dell’utilità

Tradizionalmente, l'obiettivo della calibrazione di un modello afflussi-deflussi è sempre stato quello di ottenere un set di parametri (o una distribuzione di probabilità dei parametri) che massimizzasse l'adattamento dei dati simulati alla realtà osservata, trattando parzialmente le finalità applicative del modello. Nel lavoro di tesi viene proposta una metodologia di calibrazione che trae spunto dell'evidenza che non sempre la corrispondenza tra dati osservati e simulati rappresenti il criterio più appropriato per calibrare un modello idrologico. Ai fini applicativi infatti, può risultare maggiormente utile una miglior rappresentazione di un determinato aspetto dell'idrogramma piuttosto che un altro. Il metodo di calibrazione che viene proposto mira a valutare le prestazioni del modello stimandone l'utilità nell'applicazione prevista. Tramite l'utilizzo di opportune funzioni, ad ogni passo temporale viene valutata l'utilità della simulazione ottenuta. La calibrazione viene quindi eseguita attraverso la massimizzazione di una funzione obiettivo costituita dalla somma delle utilità stimate nei singoli passi temporali. Le analisi mostrano come attraverso l'impiego di tali funzioni obiettivo sia possibile migliorare le prestazioni del modello laddove ritenute di maggior interesse per per le finalità applicative previste.

(Figure 2) Mean discharge per day (total and baseflow part) of the San Francisco River and daily precipitation at station ECPL (Planta), in 2007

We investigated controls on the water chemistry of a South Ecuadorian cloud forest catchment which is partly pristine, and partly converted to extensive pasture. From April 2007 to May 2008 water samples were taken weekly to biweekly at nine different subcatchments, and were screened for differences in electric conductivity, pH, anion, as well as element composition. A principal component analysis was conducted to reduce dimensionality of the data set and define major factors explaining variation in the data. Three main factors were isolated by a subset of 10 elements (Ca2+, Ce, Gd, K+, Mg2+, Na+, Nd, Rb, Sr, Y), explaining around 90% of the data variation. Land-use was the major factor controlling and changing water chemistry of the subcatchments. A second factor was associated with the concentration of rare earth elements in water, presumably highlighting other anthropogenic influences such as gravel excavation or road construction. Around 12% of the variation was explained by the third component, which was defined by the occurrence of Rb and K and represents the influence of vegetation dynamics on element accumulation and wash-out. Comparison of base- and fast flow concentrations led to the assumption that a significant portion of soil water from around 30 cm depth contributes to storm flow, as revealed by increased rare earth element concentrations in fast flow samples. Our findings demonstrate the utility of multi-tracer principal component analysis to study tropical headwater streams, and emphasize the need for effective land management in cloud forest catchments.

PERSiST: a flexible rainfall-runoff modelling toolkit for use with the INCA family of models

Runoff generation processes and pathways vary widely between catchments. Credible simulations of solute and pollutant transport in surface waters are dependent on models which facilitate appropriate, catchment-specific representations of perceptual models of the runoff generation process. Here, we present a flexible, semi-distributed landscape-scale rainfall-runoff modelling toolkit suitable for simulating a broad range of user-specified perceptual models of runoff generation and stream flow occurring in different climatic regions and landscape types. PERSiST (the Precipitation, Evapotranspiration and Runoff Simulator for Solute Transport) is designed for simulating present-day hydrology; projecting possible future effects of climate or land use change on runoff and catchment water storage; and generating hydrologic inputs for the Integrated Catchments (INCA) family of models. PERSiST has limited data requirements and is calibrated using observed time series of precipitation, air temperature and runoff at one or more points in a river network. Here, we apply PERSiST to the river Thames in the UK and describe a Monte Carlo tool for model calibration, sensitivity and uncertainty analysis

Coupling model uncertainty for coupled rainfall/runoff and surface water quality models in river problems

Coupled hydrology and water quality models are an important tool today, used in the understanding and management of surface water and watershed areas. Such problems are generally subject to substantial uncertainty in parameters, process understanding, and data. Component models, drawing on different data, concepts, and structures, are affected differently by each of these uncertain elements. This paper proposes a framework wherein the response of component models to their respective uncertain elements can be quantified and assessed, using a hydrological model and water quality model as two exemplars. The resulting assessments can be used to identify model coupling strategies that permit more appropriate use and calibration of individual models, and a better overall coupled model response. One key finding was that an approximate balance of water quality and hydrological model responses can be obtained using both the QUAL2E and Mike11 water quality models. The balance point, however, does not support a particularly narrow surface response (or stringent calibration criteria) with respect to the water quality calibration data, at least in the case examined here. Additionally, it is clear from the results presented that the structural source of uncertainty is at least as significant as parameter-based uncertainties in areal models. © 2012 John Wiley & Sons, Ltd.

Stochastic modelling of rainfall from satellite data

Satellite-based rainfall monitoring is widely used for climatological studies because of its full global coverage but it is also of great importance for operational purposes especially in areas such as Africa where there is a lack of ground-based rainfall data. Satellite rainfall estimates have enormous potential benefits as input to hydrological and agricultural models because of their real time availability, low cost and full spatial coverage. One issue that needs to be addressed is the uncertainty on these estimates. This is particularly important in assessing the likely errors on the output from non-linear models (rainfall-runoff or crop yield) which make use of the rainfall estimates, aggregated over an area, as input. Correct assessment of the uncertainty on the rainfall is non-trivial as it must take account of • the difference in spatial support of the satellite information and independent data used for calibration • uncertainties on the independent calibration data • the non-Gaussian distribution of rainfall amount • the spatial intermittency of rainfall • the spatial correlation of the rainfall field This paper describes a method for estimating the uncertainty on satellite-based rainfall values taking account of these factors. The method involves firstly a stochastic calibration which completely describes the probability of rainfall occurrence and the pdf of rainfall amount for a given satellite value, and secondly the generation of ensemble of rainfall fields based on the stochastic calibration but with the correct spatial correlation structure within each ensemble member. This is achieved by the use of geostatistical sequential simulation. The ensemble generated in this way may be used to estimate uncertainty at larger spatial scales. A case study of daily rainfall monitoring in the Gambia, west Africa for the purpose of crop yield forecasting is presented to illustrate the method.

Uncertainty Characterization Of A Conceptual Rainfall-Runoff Model By Using Grey Numbers

A procedure for characterizing global uncertainty of a rainfall-runoff simulation model based on using grey numbers is presented. By using the grey numbers technique the uncertainty is characterized by an interval; once the parameters of the rainfall-runoff model have been properly defined as grey numbers, by using the grey mathematics and functions it is possible to obtain simulated discharges in the form of grey numbers whose envelope defines a band which represents the vagueness/uncertainty associated with the simulated variable. The grey numbers representing the model parameters are estimated in such a way that the band obtained from the envelope of simulated grey discharges includes an assigned percentage of observed discharge values and is at the same time as narrow as possible. The approach is applied to a real case study highlighting that a rigorous application of the procedure for direct simulation through the rainfall-runoff model with grey parameters involves long computational times. However, these times can be significantly reduced using a simplified computing procedure with minimal approximations in the quantification of the grey numbers representing the simulated discharges. Relying on this simplified procedure, the conceptual rainfall-runoff grey model is thus calibrated and the uncertainty bands obtained both downstream of the calibration process and downstream of the validation process are compared with those obtained by using a well-established approach, like the GLUE approach, for characterizing uncertainty. The results of the comparison show that the proposed approach may represent a valid tool for characterizing the global uncertainty associable with the output of a rainfall-runoff simulation model.

Extension And Testing Of A 2D Hydrodynamic Model For Direct Rainfall Runoff Simulation

While the simulation of flood risks originating from the overtopping of river banks is well covered within continuously evaluated programs to improve flood protection measures, flash flooding is not. Flash floods are triggered by short, local thunderstorm cells with high precipitation intensities. Small catchments have short response times and flow paths and convective thunder cells may result in potential flooding of endangered settlements. Assessing local flooding and pathways of flood requires a detailed hydraulic simulation of the surface runoff. Hydrological models usually do not incorporate surface runoff at this detailedness but rather empirical equations are applied for runoff detention. In return 2D hydrodynamic models usually do not allow distributed rainfall as input nor are any types of soil/surface interaction implemented as in hydrological models. Considering several cases of local flash flooding during the last years the issue emerged for practical reasons but as well as research topics to closing the model gap between distributed rainfall and distributed runoff formation. Therefore, a 2D hydrodynamic model, depth-averaged flow equations using the finite volume discretization, was extended to accept direct rainfall enabling to simulate the associated runoff formation. The model itself is used as numerical engine, rainfall is introduced via the modification of waterlevels at fixed time intervals. The paper not only deals with the general application of the software, but intends to test the numerical stability and reliability of simulation results. The performed tests are made using different artificial as well as measured rainfall series as input. Key parameters of the simulation such as losses, roughness or time intervals for water level manipulations are tested regarding their impact on the stability.

Efficient accommodation of local minima in watershed model calibration

The Gauss-Marquardt-Levenberg (GML) method of computer-based parameter estimation, in common with other gradient-based approaches, suffers from the drawback that it may become trapped in local objective function minima, and thus report optimized parameter values that are not, in fact, optimized at all. This can seriously degrade its utility in the calibration of watershed models where local optima abound. Nevertheless, the method also has advantages, chief among these being its model-run efficiency, and its ability to report useful information on parameter sensitivities and covariances as a by-product of its use. It is also easily adapted to maintain this efficiency in the face of potential numerical problems (that adversely affect all parameter estimation methodologies) caused by parameter insensitivity and/or parameter correlation. The present paper presents two algorithmic enhancements to the GML method that retain its strengths, but which overcome its weaknesses in the face of local optima. Using the first of these methods an intelligent search for better parameter sets is conducted in parameter subspaces of decreasing dimensionality when progress of the parameter estimation process is slowed either by numerical instability incurred through problem ill-posedness, or when a local objective function minimum is encountered. The second methodology minimizes the chance of successive GML parameter estimation runs finding the same objective function minimum by starting successive runs at points that are maximally removed from previous parameter trajectories. As well as enhancing the ability of a GML-based method to find the global objective function minimum, the latter technique can also be used to find the locations of many non-global optima (should they exist) in parameter space. This can provide a useful means of inquiring into the well-posedness of a parameter estimation problem, and for detecting the presence of bimodal parameter and predictive probability distributions. The new methodologies are demonstrated by calibrating a Hydrological Simulation Program-FORTRAN (HSPF) model against a time series of daily flows. Comparison with the SCE-UA method in this calibration context demonstrates a high level of comparative model run efficiency for the new method. (c) 2006 Elsevier B.V. All rights reserved.

Role of rainfall and catchment characteristics on urban stormwater quality

Urbanisation significantly changes the characteristics of a catchment as natural areas are transformed to impervious surfaces such as roads, roofs and parking lots. The increased fraction of impervious surfaces leads to changes to the stormwater runoff characteristics, whilst a variety of anthropogenic activities common to urban areas generate a range of pollutants such as nutrients, solids and organic matter. These pollutants accumulate on catchment surfaces and are removed and trans- ported by stormwater runoff and thereby contribute pollutant loads to receiving waters. In summary, urbanisation influences the stormwater characteristics of a catchment, including hydrology and water quality. Due to the growing recognition that stormwater pollution is a significant environmental problem, the implementation of mitigation strategies to improve the quality of stormwater runoff is becoming increasingly common in urban areas. A scientifically robust stormwater quality treatment strategy is an essential requirement for effective urban stormwater management. The efficient design of treatment systems is closely dependent on the state of knowledge in relation to the primary factors influencing stormwater quality. In this regard, stormwater modelling outcomes provide designers with important guidance and datasets which significantly underpin the design of effective stormwater treatment systems. Therefore, the accuracy of modelling approaches and the reliability modelling outcomes are of particular concern. This book discusses the inherent complexity and key characteristics in the areas of urban hydrology and stormwater quality, based on the influence exerted by a range of rainfall and catchment characteristics. A comprehensive field sampling and testing programme in relation to pollutant build-up, an urban catchment monitoring programme in relation to stormwater quality and the outcomes from advanced statistical analyses provided the platform for the knowledge creation. Two case studies and two real-world applications are discussed to illustrate the translation of the knowledge created to practical use in relation to the role of rainfall and catchment characteristics on urban stormwater quality. An innovative rainfall classification based on stormwater quality was developed to support the effective and scientifically robust design of stormwater treatment systems. Underpinned by the rainfall classification methodology, a reliable approach for design rainfall selection is proposed in order to optimise stormwater treatment based on both, stormwater quality and quantity. This is a paradigm shift from the common approach where stormwater treatment systems are designed based solely on stormwater quantity data. Additionally, how pollutant build-up and stormwater runoff quality vary with a range of catchment characteristics was also investigated. Based on the study out- comes, it can be concluded that the use of only a limited number of catchment parameters such as land use and impervious surface percentage, as it is the case in current modelling approaches, could result in appreciable error in water quality estimation. Influential factors which should be incorporated into modelling in relation to catchment characteristics, should also include urban form and impervious surface area distribution. The knowledge created through the research investigations discussed in this monograph is expected to make a significant contribution to engineering practice such as hydrologic and stormwater quality modelling, stormwater treatment design and urban planning, as the study outcomes provide practical approaches and recommendations for urban stormwater quality enhancement. Furthermore, this monograph also demonstrates how fundamental knowledge of stormwater quality processes can be translated to provide guidance on engineering practice, the comprehensive application of multivariate data analyses techniques and a paradigm on integrative use of computer models and mathematical models to derive practical outcomes.