Risk Analysis of Gold Prices in Pakistan Using Extreme Value Theory

Extreme value theory (EVT) is useful for modeling the impact of crashes or situations of extreme stress on investor portfolios. EVT is mostly utilized in financial modeling, risk management, insurance, and hydrology. The price of gold fluctuates considerably over time, and this introduces a risk on its own. The goal of this study is to analyze the risk of gold investment by applying the EVT to historical daily data for extreme daily losses and gains in the price of gold. We used daily gold prices in the Pakistan Bullion Market from August 1, 2011 to July 30, 2021. This paper covers two methods such as Block Maxima (BM) and Peak Over Threshold (POT) modeling. The risk measures which are adopted in this paper are Value at Risk (VaR) and Expected Shortfall (ES). The point and interval estimates of VaR and ES are obtained by fitting the Generalized Pareto (GPA) distribution. Moreover, in this paper, return-level forecasting is also included for the next 5 and 10 years by analyzing the Generalized Extreme Value (GEV) distribution.

Method of estimating the effective zone induced by rapid impact compaction

This paper proposes a method for estimating the effective zone, including effective depth and effective range of compaction degree, from rapid impact compaction (RIC) on sand layer whose fines content is less than 10%. The proposed method utilizes a string of microelectromechanical system accelerometers to monitor the acceleration at various depths and propagation distances during compaction. To interpret and extract useful information from monitored data, peak-over-threshold (POT) processing and normal distribution function were used to analyze the recorded acceleration. The mean and standard deviation of the threshold peak acceleration were used to evaluate the effective depth and the effective range of compaction degree during RIC compaction. Moreover, spatial contours were used to determine the correlation of the threshold peak acceleration against depth and propagation distance from the RIC impact point. These contours help indicating the distribution of the effect zone after compaction. Lastly, a proposed method is suggested for frequent use in trial tests to quickly determine RIC’s required depth and impact spacing.

Analysis of Rainfall Time Series with Application to Calculation of Return Periods

This paper presents a study of the characteristics of rainfall in a typical Mediterranean climate, characterized by infrequent and irregular rain in the territorial area and its intensity. One of the main components of this type of climate is short-duration and high-intensity rain events that cause a large amount of damage to property and human lives, seriously affecting the operation of infrastructure and the activity of society in general. The objective of this study was to design a methodology based on peak over threshold (POT) analysis. This methodology allows us to establish reference precipitation values and more approximate return periods in the absence of sufficiently extensive historical precipitation series. In addition, the frequency of these extreme events or return periods is established. The characteristics of the precipitation regime make direct analysis difficult. Thus, the functions of the probability distributions underlying the described phenomena are improved.

Mixed POT-BM Approach for Modeling Unhealthy Air Pollution Events

This article proposes a novel data selection technique called the mixed peak-over-threshold–block-maxima (POT-BM) approach for modeling unhealthy air pollution events. The POT technique is employed to obtain a group of blocks containing data points satisfying extreme-event criteria that are greater than a particular threshold u. The selected groups are defined as POT blocks. In parallel with that, a declustering technique is used to overcome the problem of dependency behaviors that occurs among adjacent POT blocks. Finally, the BM concept is integrated to determine the maximum data points for each POT block. Results show that the extreme data points determined by the mixed POT-BM approach satisfy the independent properties of extreme events, with satisfactory fitted model precision results. Overall, this study concludes that the mixed POT-BM approach provides a balanced tradeoff between bias and variance in the statistical modeling of extreme-value events. A case study was conducted by modeling an extreme event based on unhealthy air pollution events with a threshold u > 100 in Klang, Malaysia.

An innovative, timeseries-analysis-based method to extract rainfall-streamflow events from continuous timeseries

<p>A widely accepted objective methodology to select individual rainfall-streamflow events is missing and this makes it difficult to synthesize findings from independent research initiatives. In fact, the selection of individual events is a fundamental step in many hydrological studies, but the importance and impact of the choices made at this stage are largely unrecognised.</p><p>The event selection methods found in the literature start by looking at either the rainfall timeseries or the streamflow timeseries. Moreover, most of the methodologies involve hydrograph separation, which is a highly uncertain step and can be performed using many different algorithms. Further increasing the subjectivity of the procedure, a wide range of ad hoc conditions are usually applied (e.g. peak-over-threshold, minimum duration of rainfall event, minimum duration of dry spell, minimum rainfall intensity…).</p><p>For these reasons, we present a new methodology to extract rainfall-streamflow events which minimizes the conceptual hypotheses and user’s choices, and bases the identification of the events mainly on the joint fluctuations of the two signals. The proposed methodology builds upon a timeseries analysis technique to estimate catchment response time, the Detrending Moving-average Cross-correlation Analysis-based method.</p><p>The proposed method has the advantage of looking simultaneously at the evolution in time of rainfall and streamflow timeseries, providing a more systemic detection of events. Moreover, the presented method can easily be adapted to extract events at different time resolutions (provided the resolution is fine enough to capture the delay between the rainfall and streamflow responses).</p><p>Properties of the events extracted with the proposed method are compared with the ones of the events extracted with the most traditional approach (based on hydrograph separation) to show strengths and weaknesses of the two techniques and suggest in which situations the proposed method can be most useful.</p>

Analysis of diurnal, seasonal, and annual distribution of urban sub-hourly to hourly rainfall extremes in Germany

The timing of short extreme rainstorm, which was usually thought to occur on midsummer afternoons, was investigated to improve future mitigation options for infrastructure and safety from localised flash flooding. Using a peak-over-threshold approach, the timing of 10- and 60-min extreme events was filtered from high-resolution rainfall series assessing diurnal, seasonal, and annual distributions and analysed for spatial variations and prevailing atmospheric circulation types (CTs). The diurnal distribution showed a clear deviation from that of the entire rainfall regime. A complex spatial pattern was identified with distinct timing signatures of storms in the northern (mostly afternoon) and southern regions (a bimodal distribution with a second peak in the early morning) of Germany and a more homogenous diurnal distribution of events across the central regions. Most storms occurred in summer, but 42% of 10-min events occurred outside the summer months (June–July–August). A distinct annual clustering of extremes was identified, which varied distinctly between the 10- and 60-min extremes, indicating that the sub-hourly and hourly events were far from running conterminously. The timing of extreme events on the investigated time scales was not dominated by the occurrence of specific CTs in most cases, suggesting that other factors control these extremes.

Pricing catastrophe reinsurance under the standard deviation premium principle

<abstract><p>Catastrophe reinsurance is an important way to prevent and resolve catastrophe risks. As a consequence, the pricing of catastrophe reinsurance becomes a core problem in catastrophic risk management field. Due to the severity of catastrophe loss, the Peak Over Threshold (POT) model in extreme value theory (EVT) is extensively applied to capture the tail characteristics of catastrophic loss distribution. However, there is little research available on the pricing formula of catastrophe excess of loss (Cat XL) reinsurance when the catastrophe loss is modeled by POT. In the context of POT model, we distinguish three different relations between retention and threshold, and then prove the explicit pricing formula respectively under the standard deviation premium principle. Furthermore, we fit POT model to the earthquake loss data in China during 1990–2016. Finally, we give the prices of earthquake reinsurance for different retention cases. The computational results illustrate that the pricing formulas obtained in this paper are valid and can provide basis for the pricing of Cat XL reinsurance contracts.</p></abstract>