Volatility is an important measure of stock market performance. Competing securities market makers keep abreast of the pace of volatility change by adjusting the bid-ask spreads and bid/ask quotes properly and efficiently. For intradaily high frequency transaction data, the observed volatility of stock returns can be decomposed into the sum of the two components - the realized volatility and the volatility due to microstructure noise. The quote adjustments of the market makers comprise part of the microstructure noise. In this study, we define the ratio of the realized integrated volatility to the observed squared returns as the proportion of realized integrated volatility (PIV). Time series models with generalized error distributed innovations are fitted to the PIV data based on 70-minute returns of NYSE tick-to-tick transaction data. Both retrospective and dynamic online control charts of the PIV data are established based on the fitted time series models. The McNemar test supports that the dynamic online control charts have the same power of detecting out of control events as the retrospective control charts. The Wilcoxon signedrank test is adopted to test the differences between the changes of the market maker volatility and the realized volatility for in-control and out-of-control periods, respectively. The results reveals that the points above the upper control limit are related to the situation when the market makers can not keep up with the realized integrated volatility, whereas the points below the lower control limit indicate excessive reaction of the the market makers.

We quantify the effects on contingent claim valuation of using an estimator for the volatility of a geometric Brownian motion (GBM) process. That is, we show what difficulties can arise when failing to account for estimation risk. Our working problem uses a direct estimator of volatility based on the sample standard deviation of increments from the underlying Brownian motion. After substituting into the GBM the direct volatility estimator for the true, but unknown, value of the parameter sigma, we derive the resulting marginal distribution of the approximated GBM. This allows us to derive post-estimation distributions and valuation formulae for an assortment of European contingent claims that are in accord with the basic properties of the underlying risk-neutral process. Next we extend our work to the contingent claim sensitivities associated with an assortment of European option portfolios that are based on the direct estimator of the volatility of the GBM process. Our approach to the option sensitivities - the Greeks - uses the likelihood function technique. This allows us to obtain computable results for the technically more-complicated formulae associated with our post-estimation process. We discuss an assortment of difficulties that can ensue when failing to account for estimation risk in valuation and hedging formulae.

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<p>Trying to find explanations to movements in the exchange rate is something that econo-mists have been dealing with to a great extend lately. Especially since the break down of the Bretton Wood system in the early 1970’s, when many countries introduced a floating sys-tem instead. One of the most famous and often tested models is Jeffery A. Frankel’s Real Interest Differential (RID) model from 1979.</p><p>This paper investigates which of the variables included in the model are affecting move-ments in the exchange rate for Sweden, the UK and Japan against the US dollar between January 1995 and December 2004. The variables in question are money supply, industrial production, interest rate and inflation differential. The model has purchasing power parity and uncovered interest parity as underlying theoretical assumptions, two main building blocks of open macro economics, and when combined, they can offer a relationship be-tween changes in the exchange rate and the interest rate differential.</p><p>The results show that the variable interest rate differential constitutes a significant explana-tory variable for exchange rate movements regarding all three countries included in the model. Both Sweden and the UK have also, in accordance with the RID model, the ex-pected negative sign on the coefficient. The results regarding the other variables are mixed between the countries, but it can in general be said that the model seems to be able to ex-plain movements in the exchange rate to a certain degree.</p>

<p>Value-at-Risk (VaR) is among financial institutions a commonly used tool for measuring market risk. Several methods to calculate VaR exists and different implementations often results in different VaR forecasts. An interesting implementation is historical simulation, and the purpose of this thesis is to examine whether historical simulation with dynamic volatility updating is useful as a model to calculate VaR and how this differs in regard to type of asset or instrument. To carry out the investigation six different models are implemented, which then are tested for statistical accuracy through Christoffersens test. We find that incorporation of volatility updating into the historical simulation method in many cases improves the model. The model also generates good results compared to other commonly used models, especially if the volatility is predicted through a GARCH(1,1) updating scheme.</p> / <p>Value-at-Risk (VaR) är ett bland finansiella institutioner vanligt mått för att mäta marknadsrisk. Det finns ett flertal olika sätt att beräkna VaR, vilka ofta ger olika resultat beroende på förutsättningar. Ett av dessa är historisk simulering, och syftet med denna uppsats är att undersöka huruvida historisk simulering med dynamiskt uppdaterande volatilitet är en användbar modell för beräkning av VaR och hur dess lämplighet beror på valt tillgångsslag eller instrument. För att besvara detta implementeras sex olika modeller för beräkning av VaR, vilka sedan testas med hjälp av Christoffersens test. Vi finner att inkorporering av dynamisk volatilitet i historisk simulering i många fall medför en förbättring av modellen ifråga om statistisk riktighet. Vidare kan historisk simulering med dynamiskt uppdaterande volatilitet anses vara konkurrenskraftig i jämförelse med andra vanligt använda modeller, framförallt då volatiliteten skattas genom GARCH(1,1).</p>

依據中華民國證券櫃檯買賣中心公佈之新金融商品業務概況，我們可以看出債券選擇權雖然到2004年7月才核准開放，但是從年度成交金額，債券選擇權均居所有債券與利率衍生性商品之冠。由於債券選擇權市場仍處於開放初期，相關資料如債券選擇權隱含波動率取得不易，因此關於台灣債券選擇權市場並未如指數選擇權市場吸引很多學術與實務界之注目。 本研究嘗試對於台灣債券選擇權市場，從評價模型、市場實務概況描述及未來可能之發展，作進一步之研究；此外，本文亦參酌Goodman and Ho（1997）所進行之美國債券選擇權損益之實證研究，來探討賣出債券「買進選擇權」之一方，是否能同樣在台灣債券選擇權市場獲得相對等之報酬。 本實證分析方法基本上是假設，「債券買權」賣方賣出履約殖利率為一個基本點價外之「債券買權」，選擇權存續期間是以兩個星期為一個循環，以中華民國證券櫃檯買賣中心公佈之每日10年期指標公債加權平均殖利率作為相對應部位調整之依據，分別代入實際波動率與期初「債券買權」之隱含波動率，進行Delta Neutral避險，且假設債券拆借與資金融通利率為中華民國證券櫃檯買賣中心公佈之等殖成交行情表（附條件）中所揭露之附條件利率，來探討賣方是否能夠賺取一定合理之報酬率及其可能面對之風險。 從2005年4月至2005年11月底之實證期間，共計13個循環週期，我們發現下列幾個現象： ◆債券買權與賣權之隱含波動率普遍高於實際波動率，賣權隱含波動率又高於買權。 ◆以賣出債券買權為例，在不考慮交易成本下，賣出買權之一方均能獲利，但損益之變異性都相當大。 ◆在避險波動率參數之使用上，代入實際波動率，不論是從損益之絕對數值或每單位風險報酬，均優於代入期初買權隱含波動率。 ◆從等殖成交行情表（附條件）中所揭露之附條件利率，即債券融資與融券利率，其波動性遠大於債券殖利率，因此在進行債券選擇權交易時必需將此列入評價之重要考量因素。 ◆如果考慮權利金收入，由於目前稅法無法與避險損失互抵，必需被課徵25%營利事業所得稅，因此選擇權賣方均無法獲利。 / According to the fact reports of OTC derivatives released by GraTai Securities Market (GTSM) in 2005, trading value of bond option was top of all interest rate derivatives and bond derivatives, though it was opened lately in July 2004. Due to the difficulty to get the market information like implied volatility of options, we haven’t seen considerable studies on Taiwan bond option market. Owing to the writer of this paper serves in this field, we can take advantage of collecting these data from Interdealer brokers and dealers. Accordingly, we have ground to develop this research. In this paper, we begin our discussion by presenting the landscape of Taiwan bond option market and then turn to review the basic models. Lastly, we reference the empirical study of US OTC Treasury option done by Goodman and Ho (1997) to construct the framework for measuring how investors are fairly compensated by selling call in Taiwan bond option market. To evaluate the profit and risk of option writing, we assume writer can sell two-week call options on ten-year Treasury note at market implied volatility, with a strike yield at one basis point out of daily closing yield. Option writer uses daily closing yields to do the delta neutral hedge. Besides, we take overnight call loan rates of Electronic Bond Trading System in GTSM as the borrowing and lending rates of government bond. Over the empirical period of 2005.04.1-2005.11.30, several circumstances can be found from this study. 1.In average, the implied volatilities are higher than actual volatility. This is in agreement with the results of Goodman and Ho (1997). Besides, implied volatility of put option is generally higher than call option. 2.Without considering transaction cost, call option writer can have vulnerable profit from selling volatility. 3.Adoption of actual volatility can bring better absolute profit and risk-adjusted return than implied volatility in the option valuation. 4.In this article, it shows a striking effect of the borrowing and lending rates of government bonds on the movement of implied volatility spread between call and put. 5.Under current Act of Income Tax, the hedging loss of option writer cannot be offset by premium income. Therefore, call writer can not make profit after tax.

這一篇文章主要的目的在於檢視 Bollen and Whaley (2004) 所提出來的淨買壓假說 (Net Buying Pressure Hypothesis) 在台指選擇權市場上是否一樣有相同的現象。 在本文的研究當中，我們也發現台指選擇權市場，較符合套利限制假說，包括落後一期的隱含波動率的變化和當期的隱含波動率的變化呈現負相關的現象以及價平選擇權的淨買壓對於價外的選擇權隱含波動率影響的程度較價外選擇權的淨買壓來的小。但是從淨買壓來看，其結果和S&P 500指數選擇權不同，因為台指選擇權的淨買壓，除了深度價外賣權以外，全部都是負數。 另外，本研究也將樣本資料區間中，另外分成總統大選前以及總統大選後這兩個階段來分析選擇權的淨買壓是否對於選擇權的隱含波動率變化仍然具有影響力，其結果發現在總統大選前，對買權來說，買權的市場行為符合套利限制假說。另外對賣權而言，在總統大選前，賣權的市場行為符合學習假說。在總統大選後，對買權而言，買權的市場行為改變為符合學習假說。而對賣權而言，在總統大選後，賣權的市場行為並沒有改變，仍然符合學習假說。 / This paper mainly examines that whether the Net Buying Pressure Hypothesis which is issued by Bollen and Whaley (2004) fits the options market in Taiwan? In this paper, we find that the options market in Taiwan supports the limits to arbitrage hypothesis. These phenomena include the changes of implied volatility with lag one is negative with the changes of implied volatility and the net buying pressure of the at-the-money options have less effect on the changes of the implied volatility in comparison with that of out-of-the-money options. But form the prospect of the net buying pressure, the result is different from that of the S&P 500 index options. This is because the net buying pressures in the options markets in Taiwan are all negative besides the deep-out-of-the-money put options. Besides, this paper also analyzes that whether the net buying pressure in the options market will affect the changes of implied volatility of the options before the President election and after the President election. Our research finds that before the election, the market behaviors support the limits to arbitrate hypothesis for call options. But the market behaviors support the learning hypothesis for put options. After the election, the market behaviors support the learning hypothesis for call options. For put options, the results are the same, which support the learning hypothesis.

We investigate the applicability of the method of maximum entropy regularization (MER) including convergence and convergence rates of regularized solutions to the specific inverse problem (SIP) of calibrating a purely time-dependent volatility function. In this context, we extend the results of [16] and [17] in some details. Due to the explicit structure of the forward operator based on a generalized Black-Scholes formula the ill-posedness character of the nonlinear inverse problem (SIP) can be verified. Numerical case studies illustrate the chances and limitations of (MER) versus Tikhonov regularization (TR) for smooth solutions and solutions with a sharp peak.

In this paper, we consider the inverse problem of calibrating a generalization of the bivariate Ornstein-Uhlenbeck model introduced by Lo and Wang. Even though the generalized Black-Scholes option pricing formula still holds, option prices change in comparison to the classical Black-Scholes model. The time-dependent volatility function and the other (real-valued) parameters in the model are calibrated simultaneously from option price data and from some empirical moments of the logarithmic returns. This gives an ill-posed inverse problem, which requires a regularization approach. Applying the theory of Engl, Hanke and Neubauer concerning Tikhonov regularization we show convergence of the regularized solution to the true data and study the form of source conditions which ensure convergence rates.

Syfte: Högfrekvenshandel har på senare år varit ett omdiskuterat och kontroversiellt ämne. Fenomenet har genomgått omfattande granskning och åsikterna kring dess påverkan på marknaden och dess aktörer går isär. Då tidigare forskning främst genomförts på den amerikanska marknaden är syftet med den här studien att bistå med en djupare insikt kring denna typ av handel och dess avtryck på den svenska finansmarknaden. Metod: För att behandla syftet har en kvalitativ studie av högfrekvenshandel med en deduktiv ansats genomförts. Teori: Studien utgår från Rational Choice Theory, Effektiva marknadshypotesen och tidigare forskning inom ämnet. Med hjälp av det teoretiska ramverket har studien analyserat det empiriska underlaget. Relevanta aspekter har identifierats som kan förklara varför studiens respondenter har ett specifikt förhållningssätt gentemot högfrekvenshandel. Empiri: Studien består av en dokumentstudie och fyra semistrukturerade intervjuer med intressenter på den svenska finansmarknaden. Intervjuerna ämnar identifiera de olika intressenternas förhållningssätt gentemot högfrekvenshandel och dess bakomliggande orsaker. Slutsats: Studien har kommit fram till att förhållningssättet gentemot högfrekvenshandel står i relation till vilken typ av verksamhet som intressenten bedriver. Vidare kan det konstateras att tidigare forskning till stor del går att applicera på den svenska marknaden. / Purpose: In recent years, High Frequency Trading has been a widely debated and controversial topic. The phenomenon has been subject to extensive examination and the opinions regarding its effect on the financial markets are inconsistent. Previous research has foremost been conducted on the American financial market. Thus the purpose of this thesis is to contribute with deeper insight regarding this kind of trading and its impact on the Swedish financial market. Method: To address the purpose of this thesis, a qualitative study with a deductive approach has been conducted. Theory: The thesis emanates from Rational Choice Theory, The Efficient Market Hypothesis and previous research within the field. Using the theoretical framework, the thesis has analyzed the empirical data. Relevant aspects has been identified which can explain why the thesis’ respondents has a specific approach towards High Frequency Trading. Empirics: The thesis consists of a document study and four semi structured interviews with stakeholders on the Swedish financial market. Through these interviews, the thesis aims to identify the stakeholders’ different approaches towards High Frequency Trading and what might cause this particular point of view. Conclusion: The thesis can conclude that the approach towards High Frequency Trading is correlated to the type of operation conducted by the respondent. Furthermore, it can be concluded that previous research in general is applicable on the Swedish financial market.