Pricing American options has always been problematic due to its early exercise characteristic. As no closed-form analytical solution for any of the widely used models exists, many numerical approximation methods have been proposed and studied. In this thesis, we investigate the Least-Square Monte Carlo Simulation (LSMC) method of Longstaff & Schwartz for pricing American options under the two-dimensional Heston model. By conducting extensive numerical experimentation, we put the LSMC to test and investigate four different continuation functions for the LSMC. In addition, we consider investigating seven different combination of Heston model parameters. We analyse the results and select the optimal continuation function according to our criteria. Then we uncover and study the early exercise boundary foran American put option upon changing initial volatility and other parameters of the Heston model.

In this paper, we present empirical results from the Swedish equity market when testingdifferent strategies aiming at enhancing the performance of a momentum strategy, over a timeperiod from 2000 to 2021. Similar to research conducted on other markets, we find theexistence of a momentum premium on the Swedish equity market, but with a return that is fattailed and negatively skewed. We show that forming momentum portfolios by ranking stockson the residual return instead of total return increases the Sharpe ratio and reduces the excesskurtosis and skewness. Furthermore, managing volatility by scaling the exposure to the twomomentum styles increases performance of both, but most notably for the traditionalmomentum factor. Assessing the high average returns in relation to the high turnover of theportfolios, we find it likely for the net return after accounting for transaction costs to bestatistically significant based on research on factor strategies and limits to arbitrage. / Denna uppsats undersöker ett antal momentumstrategier på den svenska aktiemarknaden övertidsperioden åren 2000 till 2021. I linje med tidigare forskning visar vi på enmomentumeffekt, där aktier som presterat bättre (sämre) relativt andra under föregående årtenderar att prestera bättre (sämre) även i kommande månader. Vi visar attmomentumportföljer som rankar aktier utifrån dess idiosynkratiska avkastning underföregående tidsperiod förbättrar den riskjusterade avkastningen i jämförelse med dentraditionella momentumfaktorn. Förbättring visas även i en ökad symmetri med en minskadsannolikhet för extrema negativa utfall, ofta benämnt som ”tail risk” i sammanhanget. Vidareundersöks riskstrategier som låter exponeringen mot faktorportföljerna variera baserat påhistorisk volatilitet och resultatet visar på en förbättring, främst för den traditionellamomentumfaktorn. Baserat på portföljernas höga medelavkastning över tidsperioden och denmånatliga omsättningen finner vi det troligt att den positiva avkastningen förblir statistisktsignifikant efter hänsyn tagits till transaktionskostnader.

This thesis investigates the relationship between implied volatility and dividend yield in the options market, focusing on testing the Bird-in-Hand theory versus the Dividend Irrelevancy theory. Utilizing panel data analysis and regression techniques, with both ordinary and lagged regressions, the study explores how dividend yield impacts European options implied volatility across European markets over ten years from February 2013 to February 2023. Employing the Hausman specification test, Breusch Pagan multiplier test, cluster standard errors, and heteroskedasticity for robustness. The analysis includes both call and put options, incorporating various control variables and market factors. The findings reveal that changes in dividend yield consistently impact call option implied volatility and also exhibit a stronger and more consistent negative relationship with put option implied volatility, overall, supporting the Bird-in-Hand theory. Furthermore, this thesis highlights the importance of considering alternative methodologies, expanding sample sizes, and exploring additional variables to enhance understanding of option pricing dynamics.

Text in English with summaries in English and Afrikaans / The introduction of single stock futures to a market presents the opportunity to assess an individual company's response to futures trading directly, in contrast to the market-wide impact obtained from index futures studies. Thirty-eight South African companies were evaluated in terms of a possible price, volume, and volatility effect due to the initial trading of their respective single stock futures contracts. An event study revealed that SSF trading had little impact on the underlying share prices. A normalised volume comparison pre to post SSF trading showed a general increase in spot market trading volumes. The volatility effect was the main focus of this study with a GARCH(1,1) model establishing a volatility structure (pattern of behaviour) per company. Results showed a reduction in the level and changes in the structure of spot market volatility. In addition, a dummy variable regression could find no evidence of an altered company-market relationship (systematic risk) post futures. / Business Management / M.Com. (Business Management)

本文提出一個動態隱含波動度函數模型，以改善一般隱含波動度函數難以隨時間的經過而調整波動度曲線且無法描述資料的時間序列特性等缺點。本文模型為兩階段隱含波動度函數模型，分別配適隱含波動度函數的時間穩定(time-invariant)部分與時間不穩定(time-variant)部分。 本文模型在波動度的時間不穩定部分配適非對稱GARCH(1,1)過程，以描述隱含波動度的時間序列特性。本文使用的非對稱GARCH(1,1)過程將標的資產的正報酬與負報酬對價平隱含波動度的影響分別估計，並將蘊含於歷史價平隱含波動度中的訊息及標的資產報酬率與波動度之間的關連性藉由價平隱含波動度過程納入隱含波動度函數中，使隱含波動度函數能納入波動度的時間序列特性及資產報酬與波動度的相關性，藉此納入最近期的市場資訊，以增加隱含波動度模型的解釋及預測能力。時間穩定部分則根據Pena et al.(1999)的研究結果，取不對稱二次函數形式以配適實證上發現的笑狀波幅現象。時間穩定部分並導入相對價內外程度做為變數，以之描述價內外程度、距到期時間、及價平隱含波動度三者的交互關係；並以相對隱含波動度作為被解釋變數，使隱含波動度函數模型除理論上包含了比先前文獻提出的模型更多的訊息及彈性外，還能描繪「隱含波動度函數隨波動度的高低水準而變動」、「越接近到期日，隱含波動度對價內外程度的曲線越彎曲」、「隱含波動度函數為非對稱的曲線」、「波動度和資產價格有很高的相關性」等實證上常發現的現象。 本文以統計測度及交易策略之獲利能力檢定模型的解釋能力及預測能力是否具有統計與經濟上的顯著性。本文歸納之前文獻提出的不同隱含波動度函數模型，並以之與本文提出的模型做比較。本文以台指選擇權五分鐘交易頻率的成交價作為實證標的，以2003年1月1日~2006年12月31日作為樣本期間，並將模型解釋力及AIC作為模型樣本內配適能力之比較標準，我們發現本文提出的模型具有最佳的資料解釋能力。本文以2006年7月1日~2006年12月31日作為隱含波動度模型預測期間，以統計誤差及delta投資策略檢定模型的預測能力是否具有統計及經濟上的顯著性。實證結果指出，本文提出的模型對於預測下一期的隱含波動度及下一期的選擇權價格，皆有相當良好的表現。關於統計顯著性方面，我們發現本文提出的動態隱含波動度函數模型對於未來的隱含波動度及選擇權價格的預測偏誤約為其他隱含波動度函數模型的五分之一，而預測方向正確頻率亦高於預測錯誤的頻率且超過50%。關於經濟顯著性方面，本文使用delta投資組合進行經濟顯著性檢定，結果發現在不考慮交易成本下，本文提出的模型具有顯著的獲利能力。顯示去除標的資產價格變動對選擇權造成的影響後，選擇權波動度的預測準確性確實能經由delta投資組合捕捉；在考慮交易成本後，各模型皆無法獲得超額報酬。最後，本文提出的動態隱含波動度函數模型在考量非同步交易問題、30分鐘及60分鐘等不同的資料頻率、不同的投資組合交易策略後，整體的結論依然不變。 / This paper proposes a new implied volatility function to facilitate implied volatility forecasting and option pricing. This function specifically takes the time variation in the option implied volatility into account. Our model considers the time-variant part and fits it with an asymmetric GARCH(1,1) model, so that our model contains the information in the returns of spot asset and contains the relationship of the returns and the volatility of spot asset. This function also takes the time invariant in the option implied volatility into account. Our model fits the time invariant part with an asymmetric quadratic functional form to model the smile on the volatility. Our model describes the phenomena often found in the literature, such as the implied volatility level increases as time to maturity decreases, the curvature of the dependence of implied volatility on moneyness increases as options near maturity, the implied volatility curve changes as the volatility level changes, and the implied volatility function is an asymmetric curve. For the empirical results, we used a sample of 5 minutes transaction prices for Taiwan stock index options. For the in-sample period January 1, 2003–June 30, 2006, our model has the highest adjusted- and lowest AIC. For the out-of-sample period July 1, 2006–December 31, 2006, the statistical significance shows that our model substantially improves the forecasting ability and reduces the out-of-sample valuation errors in comparison with previous implied volatility functions. We conjecture that such good performance may be due to the ability of the GARCH model to simultaneously capture the correlation of volatility with spot returns and the path dependence in volatility. To test the economic significance of our model, we examine the profitability of the delta-hedged trading strategy based on various volatility models. We find that although these strategies are able to generate profits without transaction costs, their profits disappear quickly when the transaction costs are taken into consideration. Our conclusions were unchanged when we considered the non-synchronization problem or when we test various data frequency and different strategies.

Text in English with summaries in English and Afrikaans / The introduction of single stock futures to a market presents the opportunity to assess an individual company's response to futures trading directly, in contrast to the market-wide impact obtained from index futures studies. Thirty-eight South African companies were evaluated in terms of a possible price, volume, and volatility effect due to the initial trading of their respective single stock futures contracts. An event study revealed that SSF trading had little impact on the underlying share prices. A normalised volume comparison pre to post SSF trading showed a general increase in spot market trading volumes. The volatility effect was the main focus of this study with a GARCH(1,1) model establishing a volatility structure (pattern of behaviour) per company. Results showed a reduction in the level and changes in the structure of spot market volatility. In addition, a dummy variable regression could find no evidence of an altered company-market relationship (systematic risk) post futures. / Business Management / M.Com. (Business Management)

The financial crisisand the European debt crisis wreaked havoc on many European economies and stock markets. Previous studies have shown that crises are associated with high debt and linked with lower growth. Studies also suggest that politicians underestimate the risks associated with high debt during economic upturn and that economic crises are usually connected with high volatility. Volatility is used as a measurement of risk since high volatility indicates larger market uncertainty of the valuation of the underlying asset. Previous studies have shown that volatility can be a good indication of a firm’s riskiness. As volatility and capital structure both relate to risk and are influenced by market reactions, investigating the impact that capital structure has on volatility during times of global financial market distress could provide insight and be an important tool for investors. This thesis will investigate firms listed on the Stockholm stock exchange, divided into seven industries, in order to find the impact capital structure may have on volatility, before, during and in the aftermath of the recent European debt crisis (2006-2016). The study will use a quantitative research method, with an objectivistic and positivistic research philosophy as well as a deductive research approach. By using multiple regression models, theoretical relations surrounding volatility and capital structure will be contrasted to the results of the study.The results of the study finds that capital structure does not play a significant part inchanges in volatility for firms during any investigated period when testing for all firms simultaneously. However, the same claim cannot be made for when each industry is tested individually. Empirical evidence showed that capital structure is a influencer for changes in volatility for the consumer goods industry prior to and after the debt crisis and in the consumer goods service industry after the debt crisis. Investors are urged to not be concerned by large debt levels, as long as they invest in largefirms and choose the right sectors. The financial sector is seen as the least risky, with low volatility levels. Furthermore, the basic material sector, despite outward appearances, should be avoided as it presents recent periods of unusually large volatility levels.

Options are an important part in today's financial market. It's therefore of high importance to be able to understand when options are overvalued and undervalued to get a lead on the market. To determine this, the relation between the volatility of the underlying asset, called realized volatility, and the market's expected volatility, called implied volatility, can be analyzed. In this thesis five models were investigated for modeling the relation between implied and realized volatility. The five models consisted of one Ornstein–Uhlenbeck model, two autoregressive models and two artificial neural networks. To analyze the performance of the models, different accuracy measures were calculated for out-of-sample forecasts. Signals from the models were also calculated and used in a simulated options trading environment to get a better understanding of how well they perform in trading applications. The results suggest that artificial neural networks are able to model the relation more accurately compared to more traditional time series models. It was also shown that a trading strategy based on forecasting the relation was able to generate significant profits. Furthermore, it was shown that profits could be increased by combining a forecasting model with a signal classification model. / Optioner är en viktig del i dagens finansiella marknad. Det är därför viktigt att kunna förstå när optioner är över- och undervärderade för att vara i framkant av marknaden. För att bestämma detta kan relationen mellan den underliggande tillgångens volatilitet, kallad realiserad volatilitet, och marknadens förväntade volatilitet, kallad implicit volatilitet, analyseras. I den här avhandlingen undersöktes fem modeller för att modellera relationen mellan implicit och realiserad volatilitet. De fem modellerna var en Ornstein–Uhlenbeck modell, två autoregressiva modeller samt två artificiella neurala nätverk. För att analysera modellernas prestanda undersöktes olika nogrannhetsmått för prognoser från modellerna. Signaler från modellerna beräknades även och användes i en simulerad optionshandelsmiljö för att få en bättre förståelse för hur väl de presterar i en handelstillämpning. Resultaten tyder på att artificiella neurala nätverk kan modellera relationen bättre än mer traditionella tidsseriemodellerna. Det visades även att en handelsstrategi baserad på prognoser av relationen kunde generera en signifikant vinst. Det visades dessutom att vinster kunde ökas genom att kombinera en prognosmodell med en modell som klassificerar signaler.

Seit der Nahrungsmittelpreiskrise 2007/08 ist die Volatilität von Nahrungsmittelpreisen wieder als wichtiges Thema in der politischen Diskussion aufgetaucht. Nicht nur die Beobachtung eines steigenden Preisniveaus, sondern auch der scheinbare Anstieg der Volatilität auf Schlüsselmärkten (vor allem Getreide) hat viele Studien sowohl auf konzeptioneller als auch auf empirischer Ebene ausgelöst. Da Menschen, insbesondere in Entwicklungsländern, unter hohen und instabilen Preisen leiden, ist diese Entwicklung als globales Problem und ein Haupthindernis zur Bekämpfung von Hunger und Mangelernährung erkannt worden. Diese Doktorarbeit hat das Ziel, zu der Debatte beizutragen, wie am besten mit Preisvolatilität auf Agrarmärkten umzugehen ist. Um einen umfassenden Überblick über Agrarpreisvolatilität, ihre Ursachen und die Möglichkeiten, betroffenen Marktteilnehmern sinnvoll zu helfen, zu geben, konzentriert sich diese Arbeit auf drei bedeutende Aspekte, welche die drei Hauptkapitel dieser kumulativen Dissertation bilden: Kapitel 2 hat das Ziel, die Frage, wie sich Volatilität seit der Nahrungsmittelpreiskrise 2007/08 entwickelt hat, robust zu beantworten. Generelle Unterschiede im Volatilitätslevel, der Volatilität der Volatilität und der Persistenz der Volatilität werden für ein Set von realisierten, GARCH-Modell basierten und impliziten Volatilitäten auf drei Agrarmärkten – Weizen, Mais und Sojabohnen – betrachtet. Darüber hinaus werden verbreitete Aussagen bezüglich des Anstiegs der Volatilität seit der Nahrungsmittelpreiskrise 2007/08 und weitere relevante Aspekte wie die Veränderung der Persistenz der Volatilität und die Quantifizierung des Anstiegs hinsichtlich einer robusten Schlussfolgerung geprüft. Kapitel 3 identifiziert die Treiber von Volatilität für verschiedene Ölsaaten und pflanzliche Ölmärkte. Das Kapitel liefert eine Untersuchung der gemeinsamen Effekte von fundamentalen Volatilitätstreibern und der Übertragungseffekte zwischen verwandten Märkten. Kapitel 4 stellt ein Set von verwandten Risikomaßen vor, um die detaillierte Struktur der Volatilität in Agrarmärkten zu charakterisieren. Diese Maße erlauben die Zerlegung einer allgemeinen Preisbewegung in „große“ Veränderungen mit möglicherweise schwerwiegenden ökonomischen Konsequenzen und „normale“ Veränderungen. Es werden zukunftsgerichtete Schätzer der Risikomaße abgeleitet, die die Erwartungen des Marktes über zukünftige Bewegungen der Rohwarenpreise aus aktuellen Optionspreisen extrahieren. Eine empirische Studie für wichtige Getreidemärkte demonstriert die Vorhersagekraft der impliziten Schätzer. Insgesamt zeigt die Doktorarbeit, dass Risikomanagement und die Abmilderung der Effekte erhöhter Preisvolatilität nur dann wirkungsvoll ist, wenn man sich bewusst ist, welche Agrarmärkte betroffen sind, mit welcher genauen Art von Preisrisiko man konfrontiert ist und somit welche Gruppe von Marktteilnehmern Schutz benötigt und wenn das Risiko frühzeitig erkannt wird, um hilfreiche Maßnahmen zu unternehmen.

With the surge of Internet-based corporate communication, organization, andinformation management, financial markets have undergone radical transformation. Inthe interconnected economy of today, market participants are forced to acceptcyberattacks, data breaches, system failures, or security flaws as any other (varying)cost of doing business. While cyberspace encompasses practically any firm indeveloped economies and a large portion in developing ones, combatting such risks isdeemed a question of firm-specific responsibility: the situation resembles an ‘every manfor himself’ scenario. Consulting standard financial theory, rational utility-maximizinginvestors assume firm-specific (idiosyncratic) risk under expectations of additionalcompensation for shouldering such risk – they are economically incentivized. The omnipresence of cyberattacks challenges fundamental assumptions of the CapitalAsset Pricing Model, Optimal Portfolio Theory, and the concept of diversifiability. Thethesis problematizes underlying rationality notions by investigating the effect of acyberattack on stock volatility. Explicitly, the use of stock volatility as a proxy for riskallows for linking increased volatility to higher risk premiums and increased cost ofcapital. In essence, we investigate the following research question: What is the effect ofa disclosed cyberattack on stock volatility for firms listed in the USA?. Using event study methodology, we compile a cyberattack database for events between2010 and 2015 involving 115 firms listed on US stock exchanges. The specified timeperiod cover prevailing research gaps; due to literature paucity the focus on volatilityfits well. For a finalized sample of 189 events, stock return data is matched to S&P500index return data within a pre-event estimation window and a post-event window tocalculate abnormal returns using the market model. The outputs are used to estimateabnormal return volatility before and after each event; testing pre and post volatilityagainst each other in significance tests then approximates the event-induced volatility.Identical procedures are performed for all subsamples based on time horizon, industrybelonging, attack type, firm size, and perpetrator motivation. The principal hypothesis, that stock volatility is significantly higher after a cyberattack,is found to hold within both event windows. Evidence on firm-specific characteristics ismore inconclusive. In the long run, inaccessibility and attacks on smaller firms seem torender significantly larger increases in volatility compared to intrusion and attacks onlarger firms; supporting preexisting literature. Contrastingly, perpetrator motive appearsirrelevant. Generally, stocks are more volatile immediately after an attack, attributableto information asymmetry. For most subsamples volatility seem to diminish with time,following the Efficient Market Hypothesis. Summing up, disparate results raisequestions of the relative importance of contingency factors, and also about futuredevelopments within and outside academic research.