Access to abstract permanently restricted to Ball State community only. / Estimation and forecasting of time series data -- Fitting of Saudi stock price by deterministic models -- Determination and fitting of the ARIMA models for Saudi stock price data -- Evaluation of forecasts by cross validation. / Access to thesis permanently restricted to Ball State community only. / Department of Mathematical Sciences

Pricing decision support systems have been developed in order to help retail companies optimise the prices they set when selling their goods and services. This research aims to enhance the essential forecasting and optimisation techniques that underlie these systems. This is first done by applying the method of Dynamic Linear Models in order to provide sales forecasts of a higher accuracy compared with current methods. Secondly, the method of Support Vector Regression is used to forecast future competitor prices. This new technique aims to produce forecasts of greater accuracy compared with the assumption currentlyused in pricing decision support systems that each competitor's price will simply remain unchanged. Thirdly, when competitor prices aren't forecasted, a new pricing optimisation technique is presented which provides the highest guaranteed profit. Existing pricing decision support systems optimise price assuming that competitor prices will remain unchanged but this optimisation can't be trusted since competitor prices are never actually forecasted. Finally, when competitor prices are forecasted, an exhaustive search of a game-tree is presented as a new way to optimise a retailer's price. This optimisation incorporates future competitor price moves, something which is vital when analysing the success of a pricing strategy but is absent from current pricing decision support systems. Each approach is applied to the forecasting and optimisation of daily retail vehicle fuel pricing using real commercial data, showing the improved results in each case.

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2016-04-12T13:46:00Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) TESE (2015-08-18) - ABDINARDO MOREIRA BARRETO DE OLIVEIRA.pdf: 3951622 bytes, checksum: d0cb6e21050967dd0af31e235ae9d711 (MD5) / Made available in DSpace on 2016-04-12T13:46:00Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) TESE (2015-08-18) - ABDINARDO MOREIRA BARRETO DE OLIVEIRA.pdf: 3951622 bytes, checksum: d0cb6e21050967dd0af31e235ae9d711 (MD5) Previous issue date: 2015-08-15 / FACEPE / O objetivo deste estudo foi verificar as configurações nas quais as estratégias de hedging são efetivas na diminuição do risco de preço da fruticultura exportadora brasileira. Tal pesquisa é justificada pela seguinte problema: caso fosse possível os fruticultores serem usuários do mercado de derivativos, não se sabe como as estratégias de hedging seriam configuradas para melhor lhes atenderem. Assim, foram calculados os preços médios mensais US$ FOB/kg entre 1989 e 2013, a partir dos dados fornecidos pelo site AliceWeb2, para as seguintes frutas: manga, melão e uva. Elas foram escolhidas por representarem 62% do valor recebido em dólares e 48% do volume exportado das frutas brasileiras. Foram usados os modelos ARIMA/GARCH para obter os preços futuros e estimar o hedge próprio, e adotados os preços futuros WTI do petróleo para estimar o cross-hedge. Realizaram-se previsões para cada abordagem de hedging empregada no estudo: Variância Mínima, Média-Variância, BEKKGARCH, Dominância Estocástica e VaR/CVaR. Em relação ao hedge próprio, o contrato com vencimento em 07 meses e em posição vendida, pela abordagem BEKK-GARCH, foi o mais efetivo para a manga (H = -0,725; HE = 35,8%); em 06 meses e em posição comprada, pela abordagem U-MEG (n = 300), foi o mais efetivo para o melão (H = 0,557; HE = 17,9%); e em 06 meses e em posição vendida, pela abordagem U-MEG (n = 300), foi o mais efetivo para a uva (H = -0,272; HE = 34,8%). Considerando o cross-hedge, o contrato com vencimento em 11 meses e em posição comprada, pela abordagem BEKK-GARCH, foi o mais efetivo, para a manga (H = 0,018; HE = 22%); o contrato com vencimento em 12 meses e em posição vendida, pela abordagem da Variância Mínima, foi o mais efetivo para o melão (H = -0,003; HE = 8,7%); e o contrato com vencimento em 11 meses e em posição vendida, pela abordagem BEKK-GARCH, foi o mais efetivo, para a uva (H = -0,022; HE = 22,1%). Vale ressaltar a dificuldade do cross-hedge a ser feito para o melão, dado os diminutos valores de H a serem realizados em termos práticos, demandando a realização de investigações futuras para melhorar este resultado em particular. / The objective of this study was to verify the settings in which the hedging strategies are effective in reducing the price risk in the Brazilian export fruits. Such research is justified by the following problem: if it were possible fruit growers are users of the derivatives market, it is not known how hedging strategies would be configured to best meet them. Thus, they were calculated the monthly average prices FOB US$/kg between 1989 and 2013, based on data provided by AliceWeb2 site for the following fruits: mango, melon and grape. They were chosen because they represent 62% of the amount received in dollars and 48% of the exported volume of Brazilian fruits. They were used the ARIMA / GARCH models to get the future prices and estimate the own hedge, and adopted the WTI future price of oil to estimate the cross-hedge. It was conducted estimations for each hedging approach used in the study: Minimum Variance, Mean-Variance, BEKK-GARCH, Stochastic Dominance and VaR/CVaR. Regarding to own hedge, the contract maturing in 07 months and short position by BEKK-GARCH approach was the most effective for mango (H = -0.725; HE = 35.8%); in 06 months and long position, the U-MEG approach (n = 300), was the most effective for melon (H = 0.557; HE = 17.9%); and 06 months and short position for the U-MEG approach (n = 300), was the most effective for grape (H = -0.272; HE = 34.8%). Considering the crosshedge, the contract maturing in 11 months and long position, by BEKK-GARCH approach was the most effective for mango (H = 0.018; HE = 22%); the contract maturing in 12 months and short position, the approach of the Minimum Variance was the most effective for melon (H = -0.003; HE = 8.7%); and the contract maturing in 11 months and short position by BEKK-GARCH approach was the most effective for grape (H = -0.022; HE = 22.1%). It is worth mentioning the difficulty of cross-hedge to be made to the melon, given the tiny H values to be realized in practical terms, which demands the realization of further investigations to improve this particular result.

Commodities primárias, tais como metais, petróleo e agricultura, constituem matérias-primas fundamentais para a economia mundial. Dentre os metais, destaca-se o alumínio, usado em uma ampla gama de indústrias, e que detém o maior volume de contratos na London Metal Exchange (LME). Como o preço não está diretamente relacionado aos custos de produção, em momentos de volatilidade ou choques econômicos, o impacto financeiro na indústria global de alumínio é significativo. Previsão de preços do alumínio é fundamental, portanto, para definição de política industrial, bem como para produtores e consumidores. Este trabalho propõe um modelo ótimo de previsões para preços de alumínio, por meio de combinações de previsões e de seleção de modelos através do Model Confidence Set (MCS), capaz de aumentar o poder preditivo em relação a métodos tradicionais. A abordagem adotada preenche uma lacuna na literatura para previsão de preços de alumínio. Foram ajustados 5 modelos individuais: AR(1), como benchmarking, ARIMA, dois modelos ARIMAX e um modelo estrutural, utilizando a base de dados mensais de janeiro de 1999 a setembro de 2014. Para cada modelo individual, foram geradas 142 previsões fora da amostra, 12 meses à frente, por meio de uma janela móvel de 36 meses. Nove combinações de modelos foram desenvolvidas para cada ajuste dos modelos individuais, resultando em 60 previsões fora da amostra, 12 meses à frente. A avaliação de desempenho preditivo dos modelos foi realizada por meio do MCS para os últimos 60, 48 e 36 meses. Um total de 1.250 estimações foram realizadas e 1.140 variáveis independentes e suas transformadas foram avaliadas. A combinação de previsões usando ARIMA e um ARMAX foi o único modelo que permaneceu no conjunto de modelos com melhor acuracidade de previsão para 36, 48 e 60 meses a um nível descritivo do MCS de 0,10. Para os últimos 36 meses, o modelo combinado proposto apresentou resultados superiores em relação a todos os demais modelos. Duas co-variáveis identificadas no modelo ARMAX, preço futuro de três meses e estoques mundiais, aumentaram a acuracidade de previsão. A combinação ótima apresentou um intervalo de confiança pequeno, equivalente a 5% da média global da amostra completa analisada, fornecendo subsídio importante para tomada de decisão na indústria global de alumínio. iii / Primary commodities, including metals, oil and agricultural products are key raw materials for the global economy. Among metals, aluminum stands out for its large use in several industrial applications and for holding the largest contract volume on the London Metal Exchange (LME). As the price is not directly related to production costs, during volatility periods or economic shocks, the financial impact on the global aluminum industry is significant. Aluminum price forecasting, therefore, is critical for industrial policy as well as for producers and consumers. This work has proposed an optimal forecast model for aluminum prices by using forecast combination and the Model Confidence Set for model selection, resulting in superior performance compared to tradicional methods. The proposed approach was not found in the literature for aluminum price forecasting. Five individual models were developed: AR(1) for benchmarking, ARIMA, two ARIMAX models and a structural model, using monthly data from January 1999 to September 2014. For each individual model, 142 out-of-sample, 12 month ahead, forecasts were generated through a 36 month rolling window. Nine foreast combinations were deveoped for each individual model estimation, resulting in 60 out-of-sample, 12 month ahead forecasts. Model predictive performace was assessed through the Model Confidence Set for the latest 36, 48, and 60 months, through 12-month ahead out-of-sample forecasts. A total of 1,250 estimations were performed and 1,140 independent variables and their transformations were assessed. The forecast combination using ARMA and ARIMAX was the only model among the best set of models presenting equivalent performance at 0.10 MCS p-value in all three periods. For the latest 36 months, the proposed combination was the best model at 0.1 MCS p-value. Two co-variantes, identified for the ARMAX model, namely, 3-month forward price and global inventories increased forecast accuracy. The optimal forecast combination has generated a small confidence interval, equivalent to 5% of average aluminum price for the entire sample, proving relevant support for global industry decision makers.

Dans le contexte de l’augmentation de la part de la production énergétique provenant de sources renouvelables imprévisibles, les prix de l’électricité sont plus volatiles que jamais. Cette volatilité rend la prévision des prix plus difficile mais en même temps de plus grande valeur. Dans cette recherche, une analyse comparative de 8 modèles de prévision est effectuée sur la tâche de prédire les prix de gros de l’électricité du lendemain en France, en Allemagne, en Belgique et aux Pays-Bas. La méthodologie utilisée pour produire les prévisions est expliquée en détail. Les différences de précision des prévisions entre les modèles sont testées pour leur signification statistique. La méthode de gradient boosting a produit les prévisions les plus précises, suivi de près par une méthode d’ensemble. / In the context of the increase in the fraction of power generation coming from unpredictable renewable sources, electricity prices are as volatile as ever. This volatility makes forecasting future prices more difficult yet more valuable. In this research, a benchmark of 8 forecasting models is conducted on the task of predicting day-ahead wholesale electricity prices in France, Germany, Belgium and the Netherlands. The methodology used to produce the forecasts is explained in detail. The differences in forecast accuracy between the models are tested for statistical significance. Gradient boosting produced the most accurate forecasts, closely followed by an ensemble method.

The pulp and paper industry has a significant role in Europe’s economy and society, and its significance is still growing. The pulp market and the customers’ requirements are highly affected by the pulp market prices and the requested kind of pulp, i.e., Elementary Chlorine Free (ECF) or Total Chlorine Free (TCF). There is a need to predict different market aspects, where the market price is one, to gain a better understanding of a business situation. Understanding market dynamics can support organizations to optimize their processes and production. Forecasting future pulp prices has not recently been done, but it would help businesses to make decisions that are more informed about where to sell their product. The studies existing about the pulp industry and forecast of market prices were completed over 20 years ago, and the market has changed since then in terms of, e.g., demand and production volume. There is a research gap within the pulp industry from a market price perspective. The pulp market is similar to, e.g., the energy industry in some aspects, and time-series analysis has been used to forecast electricity prices to support decision making by electricity producers and retailers. Autoregressive Integrated Moving Average (ARIMA) is one time-series analysis method that is used when data are collected with a constant frequency and when the average is not constant. Holt-Winters model is a well-known and simple time-series analysis. In this thesis, time-series analysis is used to predict the weekly market price for pulp the three upcoming months, with the research question “With what accuracy can time-series analysis be used to forecast the European PIX price on pulp on a week-ahead basis?”. The research method in this thesis is a case study where data are collected through the data collection method documents. First, articles are studied to gain understanding within the problem area leading to the use of the artefact time-series analyses and a case study. Then, historical data are collected from the organization FOEX Fastmarkets, where a new market price of pulp has been released every Tuesday since September 1996. The dataset has a total of 1200 data points. After data cleaning, it is merged to 1196 data points that are used for the analysis. To evaluate the results from the time-series analysis models ARIMA and Holt-Winter, Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE) are used. The software RStudio is used for programming. The results shows that the ARIMA model provides the most accurate results. The mean value for MAE is 16,59 for ARIMA and 44,61 for Holt-Winters. The mean value for MAPE is 1,99% for ARIMA and 5,37% for Holt-Winters.

Electricity needs to be consumed when it is produced, making sure that supply closely meets demand at all times. To account for the rapidly changing operational status and the need for increasing the flexibility of power systems, financial instruments have been put in place creating markets where electricity is traded as a commodity across different time frames; from months or days to minutes before, or even after, planned delivery. In this work, the focus is placed on the short-term electricity markets and particularly on forecasting the intraday volume-weighted average price of the last three hours of trading of hourly power products. To this end, two state-of-the-art recurrent neural network architectures, namely the Temporal Fusion Transformer and the DeepAR network, are compared against well-established statistical models, such as the Linear Regression, ARX and SARIMAX models, with respect to their forecast accuracy on each of the 24 hourly delivery products. Two different experimental setups are applied, with one utilizing two input features drawn specifically from the findings of relevant literature and the other blindly exploiting all available streams of information in either their raw or aggregated form. All models are trained individually per hourly product per experimental setup to support a fair and decisive comparison, leading to 240 unique model instances being trained in total. Furthermore, the input feature importance is inferred by exploiting the inbuilt attention mechanism of the Temporal Fusion Transformer architecture. Finally, by using various realworld historical market data originating from the Nord Pool power exchange as well as from the Svenska Kraftnät, available up until the day of delivery, it is shown that the statistical models outperform both contemporary neural network architectures, with the latter suffering from the inability to generalize to elevated price levels—which are absent from the training dataset. / El måste förbrukas när den produceras, och se till att utbudet alltid motsvarar efterfrågan. För att ta hänsyn till den snabbt föränderliga operativa statusen och behovet av att öka flexibiliteten i kraftsystemen har finansiella instrument införts för att skapa marknader där el handlas som en vara över olika tidsramar; från månader eller dagar till minuter före, eller till och med efter, planerad leverans. I detta arbete läggs fokus på de kortsiktiga elmarknaderna och särskilt på att prognostisera det intradagsvolymvägda genomsnittspriset för de senaste tre timmarnas handel med timkraftprodukter. För detta ändamål jämförs två toppmoderna återkommande neurala nätverksarkitekturer, nämligen Temporal Fusion Transformer och DeepAR-nätverket, mot väletablerade statistiska modeller, såsom modellerna Linear Regression, ARX och SARIMAX, med avseende på deras prognosnoggrannhet för var och en av 24-timmarsleveransprodukterna. Två olika experimentella uppsättningar tillämpas, där den ena använder två indatafunktioner som hämtats specifikt från resultaten av relevant litteratur och den andra utnyttjar blint alla tillgängliga informationsströmmar i antingen deras råa eller aggregerade form. Alla modeller tränas individuellt per timprodukt per experimentuppställning för att stödja en rättvis och avgörande jämförelse, vilket leder till att 240 unika modellinstanser tränas totalt. Dessutom härleds ingångsfunktionens betydelse genom att utnyttja den inbyggda uppmärksamhetsmekanismen i Temporal Fusion Transformer-arkitekturen. Slutligen, genom att använda olika verkliga historiska marknadsdata från elbörsen Nord Pool såväl som från Svenska Kraftnät, tillgängliga fram till leveransdagen, visas att de statistiska modellerna överträffar både moderna neurala nätverksarkitekturer, med sistnämnda lider av oförmågan att generalisera till förhöjda prisnivåer — som saknas i utbildningsdataset.

Chung Kwong-leung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 80-84). / Abstracts in English and Chinese. / ACKNOWOLEDGMENTS --- p.iii / LIST OF TABLES --- p.iv / LIST OF ILLUSTRATIONS --- p.vi / CHAPTER / Chapter ONE --- INTORDUCTION --- p.1 / Chapter TWO --- LITERATURE REVIEW --- p.5 / Volatility / ARCH Models / The Accuracy of ARCH Volatility Estimates / Chapter THREE --- METHODOLOGY --- p.11 / Testing and Estimation / Simulation / Chapter FOUR --- DATA DESCRIPTION AND EMPIRICAL RESULTS --- p.29 / Data Description / Testing and Estimation Results / Simulation Results / Chapter FIVE --- CONCLUSION --- p.45 / TABLES --- p.49 / ILLUSTRATIONS --- p.58 / APPENDICES --- p.77 / BIBOGRAPHY --- p.80

Thesis (MBA)--Stellenbosch University, 2000. / ENGLISH ABSTRACT: The price earnings multiple is a ratio of valuation and is published widely in the media as a comparative instrument of investment decisions. It is used to compare company valuation levels and their future growth/franchise opportunities. There have been numerous research studies done on the price earnings multiple, but no study has been able to design or derive a model to successfully predict the future price earnings multiple where the current stock price and following year-end earnings per share is used. The most widely accepted method of share valuation is to discount the future cash flows by an appropriate discount rate. Popular and widely used stock valuation models are the Dividend Discount Model and the Gordon Model. Both these models assume that future dividends are cash flows to the shareholder. Thomas K. Philips, the chief investment officer at Paradigm Asset Management in New York, constructed a valuation model at the end of 1999, which he published in The Journal of Portfolio Management. The model (Philips price earnings multiple model) was derived from the Dividend Discount Model and calculates an implied future price earnings multiple. The Philips price earnings multiple model includes the following independent variables: the cost of equity, the return on equity and the dividend payout ratio. Each variable in the Philips price earnings multiple model is a calculated present year-end point value, which was used to calculate the implied future price earnings multiple (present year stock price divided by following year-end earnings per share). This study used a historical five year (1995-2000) year-end data to calculate the implied and actual future price earnings multiple. Out of 225, Johannesburg Stock Exchange listed companies studied, only 36 were able to meet the criteria of the Philips price earnings multiple model. Correlation and population mean tests were conducted on the implied and constructed data sets. It proved that the Philips price earnings multiple model was unsuccesful in predicting the future price earnings multiple, at a statistical 0,20 level of significance. The Philips price earnings multiple model is substantially more complex than the Discount Dividend Model and includes greater restrictions and more assumptions. The Philips price earnings multiple model is a theoretical instrument which can be used to analyse hypothetical (with all model assumptions and restrictions having been met) companies. The Philips price earnings multiple model thus has little to no applicability in the practical valuation of stock price on Johannesburg Stock Exchange listed companies. / AFRIKAANSE OPSOMMING: Die prysverdienste verhouding is 'n waarde bepalingsverhouding en word geredelik gepubliseer in die media. Hierdie verhouding is 'n maatstaf om maatskappye se waarde vlakke te vergelyk en om toekomstige groei geleenthede te evalueer. Daar was al verskeie navorsingstudies gewy aan die prysverdiensteverhouding, maar nog geen model is ontwikkel wat die toekomstige prysverdiensteverhouding (die teenswoordige aandeelprys en toekomstige jaareind verdienste per aandeel) suksesvol kon modelleer nie. Die mees aanvaarbare metode vir waardebepaling van aandele is om toekomstige kontantvloeie te verdiskonteer teen 'n toepaslike verdiskonteringskoers. Van die vernaamste en mees gebruikte waardeberamings modelle is die Dividend Groei Model en die Gordon Model. Beide modelle gebruik die toekomstige dividendstroom as die toekomstige kontantvloeie wat uitbetaal word aan die aandeelhouers. Thomas K. Philips, die hoof beleggingsbeampte by Paradigm Asset Management in New York, het 'n waardeberamingsmodel ontwerp in 1999. Die model (Philips prysverdienste verhoudingsmodei) was afgelei vanaf die Dividend Groei Model en word gebruik om 'n geïmpliseerde toekomstige prysverdiensteverhouding te bereken. Die Philips prysverdienste verhoudingsmodel sluit die volgende onafhanklike veranderlikes in: die koste van kapitaal, die opbrengs op aandeelhouding en die uitbetalingsverhouding. Elke veranderlike in hierdie model is 'n berekende teenswoordige jaareinde puntwaarde, wat gebruik was om die toekomstige geïmpliseerde prysverdiensteverhouding (teenswoordige jaar aandeelprys gedeel deur die toekomstige verdienste per aandeel) te bereken. In hierdie studie word vyf jaar historiese jaareind besonderhede gebruik om die geïmpliseerde en werklike toekomstige prysverdiensteverhouding te bereken. Van die 225 Johannesburg Effektebeurs genoteerde maatskappye, is slegs 36 gebruik wat aan die vereistes voldoen om die Philips prysverdienste verhoudingsmodel te toets. Korrelasie en populasie gemiddelde statistiese toetse is op die berekende en geïmpliseerde data stelle uitgevoer en gevind dat die Philips prysverdienste verhoudingsmodel, teen 'n statistiese 0,20 vlak van beduidenheid, onsuksesvol was om die toekomstige prysverdiensteverhouding vooruit te skat. Die Philips prysverdienste verhoudingsmodel is meer kompleks as die Dividend Groei Model met meer aannames en beperkings. Die Philips prysverdienste verhoudingsmodel is 'n teoretiese instrument wat gebruik kan word om hipotetiese (alle model aannames en voorwaardes is nagekom) maatskappye te ontleed. Dus het die Philips prysverdienste verhoudingsmodel min tot geen praktiese toepassingsvermoë in die werkilke waardasie van aandele nie.

Assignment (MComm)--Stellenbosch University, 2005. / ENGLISH ABSTRACT: Volatilty was originally seen to be constant and deterministic, but it was later realised that return series are non-stationary. Owing to this non-stationarity nature of returns, there were no reliable ex-post volatility measurements. Subsequently, researchers focussed on ex-ante volatility models. It was only then realised that before good volatility models can be created, reliable ex-post volatility measuremetns need to be defined. In this study we examine non-parametric ex-post volatility measurements in order to obtain approximations of the variances of non-stationary return series. A detailed mathematical derivation and discussion of the already developed volatility measurements, in particular the realised volatility- and DST measurements, are given In theory, the higher the sample frequency of returns is, the more accurate the measurements are. These volatility measurements referred to above, however, all have short-comings in that the realised volatility fails if the sample frequency becomes to high owing to microstructure effects. On the other hand, the DST measurement cannot handle changing instantaneous volatility. In this study we introduce a new volatility measurement, termed microstructure realised volatility, that overcomes these shortcomings. This measurement, as with realised volatility, is based on quadratic variation theory, but the underlying return model is more realistic. / AFRIKAANSE OPSOMMING: Volatiliteit is oorspronklik as konstant en deterministies beskou, dit was eers later dat besef is dat opbrengste nie-stasionêr is. Betroubare volatiliteits metings was nie beskikbaar nie weens die nie-stasionêre aard van opbrengste. Daarom het navorsers gefokus op vooruitskattingvolatiliteits modelle. Dit was eers op hierdie stadium dat navorsers besef het dat die definieering van betroubare volatiliteit metings 'n voorvereiste is vir die skepping van goeie vooruitskattings modelle. Nie-parametriese volatiliteit metings word in hierdie studie ondersoek om sodoende benaderings van die variansies van die nie-stasionêre opbrengste reeks te beraam. 'n Gedetaileerde wiskundige afleiding en bespreking van bestaande volatiliteits metings, spesifiek gerealiseerde volatiliteit en DST- metings, word gegee. In teorie salopbrengste wat meer dikwels waargeneem word tot beter akkuraatheid lei. Bogenoemde volatilitieits metings het egter tekortkominge aangesien gerealiseerde volatiliteit faal wanneer dit te hoog raak, weens mikrostruktuur effekte. Aan die ander kant kan die DST meting nie veranderlike oombliklike volatilitiet hanteer nie. Ons stel in hierdie studie 'n nuwe volatilitieits meting bekend, naamlik mikro-struktuur gerealiseerde volatiliteit, wat nie hierdie tekortkominge het nie. Net soos met gerealiseerde volatiliteit sal hierdie meting gebaseer wees op kwadratiese variasie teorie, maar die onderliggende opbrengste model is meer realisties.