In this paper we present a finite volume method for a two-dimensional Black-Scholes equation with stochastic volatility governing European option pricing. In this work, we first formulate the Black-Scholes equation with a tensor (or matrix) diffusion coefficient into a conversative form. We then present a finite volume method for the resulting equation, based on a fitting technique proposed for a one-dimensional Black-Scholes equation. We show that the method is monotone by proving that the system matrix of the discretized equation is an M-matrix. Numerical experiments, performed to demonstrate the usefulness of the method, will be presented.

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Usually, consumers will collect market information about the product before they decide to buy it or not. In other words, the market information is a critical factor to affect consumers¡¦ purchasing intensions and behavior. Previous research points out that when consumers encounter a wider dispersion of price, they will expect to find cheaper stores. Besides, future price is often considered by consumers too. Kauffman et al. (2002) mentioned that the market price information might affect the recruiting of group buying. In a competitive market, if consumers are unable to perceive the utility of discounts provided by group-buying mechanism, they may shop at other retailers¡¦ stores. Further, because the final price of group buying will not be known until the transaction is closed, consumers¡¦ decisions might be up to their prediction about the final price. This study explores how price dispersion and price volatility affect consumers¡¦ internal reference price and expectation of final price of group buying. The difference between the internal reference and expectation of final price of group-buying indicates the consumers¡¦ transaction utility. How transaction utility affects consumers¡¦ intentions to join group buying is another issue being studied. In addition, if there is interference effect of consumers¡¦ risk attitude on final price forecast of group-buying, it¡¦s investigated, too. The result indicates that price dispersion has significant effects on consumers¡¦ all kinds of internal reference prices and predictions about the final price of group buying. However, the price volatility only has significant effects on consumers¡¦ perceived fair price, aspiration price, and reservation price. Neither significant effect of price volatility on consumers¡¦ price prediction of group buying nor interference effect of risk attitude is found. As expected, there is a significant positive causal relationship between transaction utility and intention to join group-buying. It shows that the transaction utility resulting from the comparison between the lowest market price and the most possible final price of group buying has the most explanatory power to predict consumers¡¦ participating intension to join group-buying.

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In the early stage, the fixed exchange rate policy was established in Taiwan, with focus on the exchange of NT Dollar to US dollar. After undergoing the changes of flexible exchange rate system, the regulation of exchange rate gradually renovates. On January 30, 1991, the exchange rate system changed to a managed floating system that allows the exchange rate to be more liberal. The spot USD trading price is no longer restricted by the upper or lower limit among banks, and the negotiation of trading price is completely free. As the exchange for NTD to USD becomes more liberal, the issue of the factors behind the price fluctuation on NTD to USD has become an interesting subject to study. This paper investigates Taiwan¡¦s foreign exchange market in order to discover the factors that cause the price volatility, whether it is private information or macroeconomic news announcement of public information. This study examines the exchange rate occurred every 15 minutes during January 5, 1992 to November 27, 2001. Given the result that the increase of macroeconomic news announcement does not increase the volatility, the volatility in Taiwan¡¦s foreign exchange market is mainly caused by private information, not public information. Although the return variance is comparatively higher than the return variance in other normal time period during the macroeconomic news announcement, the highest return variance before the trade close does not occur at the time of public news announcement. It represents that the occurrence of volatility is not affected by the macroeconomic news announcement. If foreign exchange volatility is not affected by macroeconomic news announcement of public information, then private information might be the major factor affecting the price volatility. The findings are as follows: 1. The volatility in trading period is much higher than the volatility in non-trading period, demonstrating the existence of ¡§exchange message effectiveness¡¨. Meanwhile, it also states that public information is not the only information existing in the market. Even at the most efficient market, the informative pricing has reflected all the public information. The macroeconomic news announcement of public information would not affect the price volatility, the asset pricing volatility is affected by the private information. 2. Trading time become longer which makes the informed trader not necessary to trade in a hurry, diverging the volatility of transaction. 3. The volatility at closing period increases because of the occurrence of private information. It may downgrade to public information during non-trading period. People holding valuable private information would trade before the market is close. Concluded from above, it can be discovered that the private information has played an important role incurring the large volatility in Taiwan¡¦s foreign exchange market.

<p>The purpose of this thesis is to examine whether the exchange rate volatility has an impact on Swedish exports. This relationship has been tested in several studies but no consistent result has been found. It is therefore an interesting subject to investigate further and it has not been thoroughly tested for Sweden using aggregated data. Since the exchange rate vola-tility may have an effect on exports, and therefore on the whole economy, the effect can support a certain exchange rate regime. All the data used in this thesis is based on the ag-gregated data for Sweden and the Euro zone between the years 1993 and 2006. The method chosen is a statistical analysis using regressions. Three variables other than ex-change rate volatility were included when conducting the regressions explaining Swedish exports and these are: the real effective exchange rate index, the industrial production in Sweden (“push” factor) and the import from the Euro Zone (“pull” factor). The overall conclusion found was that the industrial production in Sweden, the real effective exchange rate index, the time and lagged values of the export influence the export. There was no evi-dence found that the exchange rate volatility influences the exports for Sweden.</p>

<p>I denna uppsats diskuteras sambandet mellan risk, marknadseffektivitet och volatilitet. En studie görs för att se om volatiliteten (kursrörligheten) har ökat i enskilda aktier under tidsperioden 1988-1999. Vidare behandlas vilka faktorer som kan ge upphov till volatilitetsförändringar, vilka konsekvenser en förändrad volatilitet får för olika typer av investerare samt om utvecklingen är förenlig med EMH (den effektiva marknadshypotesen).Studier av volatilitet är intressanta p g a den risk som uppstår för olika marknadsaktörer vid en ökad volatilitet. Uppstår felvärderingar på aktiemarknaden finns även risk för att kapital fördelas på ett sätt som inte är optimalt. I stora drag kan man definiera begreppet volatilitet som ett mått på hur stor osäkerheten är inför den framtida kursutvecklingen för en aktie. Volatilitet är att betrakta som kortsiktiga rörelser i finansiella priser under loppet av en dag eller från en dag till en annan, men begreppet används också</p> / <p>In this paper the relation between risk, market efficiency and volatility is being discussed. A study has been made to see if there has been any change in the volatility for individual stocks during the time period 1988-1999. Further, the factors that contribute to changes in the volatility have been examined and also which the consequences are for various types of investors and whether the developement is consistent with the efficient market hypothesis. The study of volatility is interesting because of the risk that an increased volatility entails for the investors. When mispricing occurs in the stockmarket there is also a risk for a non-optimal allocation of capital. Roughly speaking the definition of volatility is how large the uncertainty is about the future return from an individual stock. Volatility is considered to be short time period movements in financial prices within a day or from one day to another but is also used as a mesaure to describe price</p>

<p>In recent years, the field of Fractional Brownian motion, Fractional Gaussian noise and long-range dependent processes has gained growing interest. Fractional Brownian motion is of great interest for example in telecommunications, hydrology and the generation of artificial landscapes. In fact, Fractional Brownian motion is a basic continuous process through which we show that it is neither a semimartingale nor a Markov process. In this work, we will focus on the path properties of Fractional Brownian motion and will try to check the absence of the property of a semimartingale. The concept of volatility will be dealt with in this work as a phenomenon in finance. Moreover, some statistical method like R/S analysis will be presented. By using these statistical tools we examine the volatility of shares and we demonstrate empirically that there are in fact shares which exhibit a fractal structure different from that of Brownian motion.</p>

Improvement of biodiesel’s cold flow properties still remains one of the major challenges for using it as an alternative fuel in diesel engines. Therefore, the main objective of the present research was to use newly developed liquid biofuels, 3-hydroxyl fatty acid esters and ethers, as an additive for improving biodiesel cold weather properties. Test results revealed that blending with 10% 3-hydroxyl fatty acid esters (C4, C6, C8 and C12) improved biodiesel volatility, cloud point, flash point and kinematic viscosity without a significant loss in LHV. However, blending biodiesel with 3-hydroxyl fatty acid esters negatively affected the oxidation stability which was then found to improve by blending with 3-hydroxyl fatty acid ethers (1,3-DMO and 1,3-DMD). The latter novel fuel substance (1,3-DMO and 1,3-DMD) exhibited much higher evaporation rate compared to biodiesel and only slightly lower than that of decane, gasoline or ethanol. Moreover, the LHV of 1,3-DMO and 1,3-DMD was found to be almost equal to that of canola biodiesel, and higher than that of methanol and ethanol. These findings suggest that 1,3-DMO and 1,3-DMD have the potential to be used as additive to improve biodiesel cold weather combustion performance or as standalone fuels. / February 2016

This thesis investigates how CEO risk taking incentives related to compensation in the form of executive stock options affect the decision to engage in merger and acquisition (M&A) activities with particular attention to same-industry versus cross-industry acquisitions. Risk taking incentives increase the propensity of M&As, especially for same-industry M&As. Furthermore, risk taking incentives increase the likelihood of cash payment for both same and cross-industry acquisitions. We do not find a significant direct stock price response difference between same-industry and cross-industry acquiring firms. The market responds favorably when risk taking incentives are higher for both same-industry acquisitions and cross-industry takeovers. We further find that the acquiring firm’s post-acquisition cash flow volatility is also positively related to risk taking incentives for both same- and cross-industry M&As.