Cette thèse explore théoriquement et empiriquement les implications de la dynamique jointe action/option sur divers problématiques liées au trading d’options. Dans un premier temps, nous commençons par l’étude de la dynamique jointe entre une option sur un stock et une option sur l’indice de marché. Le modèle CAPM fournit un cadre mathématique adéquat pour cette étude car il permet de modéliser la dynamique jointe d’un stock et son indice de marché. En passant aux prix d’options, nous montrons que le beta et la volatilité idiosyncratique, paramètres du modèle, permettent de caractériser la relation entre les surfaces de volatilité implicite du stock et de l’indice. Nous nous penchons alors sur l’estimation du paramètre beta sous la probabilité risque-neutre en utilisant les prix d’options. Cette mesure, appelée beta implicite, représente l’information contenue dans les prix d’options sur la réalisation du paramètre beta dans le futur.Pour cette raison, nous essayons de voir, si le beta implicite a un pouvoir prédictif du beta futur.En menant une étude empirique, nous concluons que le beta implicite n’améliore pas la capacité de prédiction en comparaison avec le beta historique qui est calculé à travers la régression linéaire des rendements du stock sur ceux de l’indice. Mieux encore, nous remarquons que l’oscillation du beta implicite autour du beta futur peut entraîner des opportunités d’arbitrage, et nous proposons une stratégie d’arbitrage qui permet de monétiser cet écart. D’un autre côté, nous montrons que l’estimateur du beta implicite pourrait être utilisé pour la couverture d’options sur le stock en utilisant des instruments sur l’indice, cette couverture concerne notamment le risque de volatilité et aussi le risque de delta. Dans la deuxième partie de notre travail, nous nous intéressons au problème de market making sur options. Dans cette étude, nous supposons que le modèle de dynamique du sous-jacent sous la probabilité risque-neutre pourrait être mal spécifié ce qui traduit un décalage entre la distribution implicite du sous-jacent et sa distribution historique.Dans un premier temps, nous considérons le cas d’un market maker risque neutre qui vise à maximiser l’espérance de sa richesse future. A travers l’utilisation d’une approche de contrôle optimal stochastique, nous déterminons les prix optimaux d’achat et de vente sur l’option et nous interprétons l’effet de présence d’inefficience de prix sur la stratégie optimale. Dans un deuxième temps, nous considérons que le market maker est averse au risque et essaie donc de réduire l’incertitude liée à son inventaire. En résolvant un problème d’optimisation basé sur un critère moyenne-variance, nous obtenons des approximations analytiques des prix optimaux d’achat et de vente. Nous montrons aussi les effets de l’inventaire et de l’inefficience du prix sur la stratégie optimale. Nous nous intéressons par la suite au market making d’options dans une dimension plus élevée. Ainsi, en suivant le même raisonnement, nous présentons un cadre pour le market making de deux options ayant des sous-jacents différents avec comme contrainte la réduction de variance liée au risque d’inventaire détenu par le market-maker. Nous déterminons dans ce cas la stratégie optimale et nous appuyons les résultats théoriques par des simulations numériques.Dans la dernière partie de notre travail, nous étudions la dynamique jointe entre la volatilité implicite à la monnaie et le sous jacent, et nous essayons d’établir le lien entre cette dynamique jointe et le skew implicite. Nous nous intéressons à un indicateur appelé "Skew Stickiness Ratio"qui a été introduit dans la littérature récente. Cet indicateur mesure la sensibilité de la volatilité implicite à la monnaie face aux mouvements du sous-jacent. Nous proposons une méthode qui permet d’estimer la valeur de cet indicateur sous la probabilité risque-neutre sans avoir besoin d’admettre des hypothèses sur la dynamique du sous-jacent. [...] / This thesis explores theoretically and empirically the implications of the stock/option joint dynamics on applications related to option trading. In the first part of the thesis, we look into the relations between stock options and index options under the risk-neutral measure. The Capital Asset Pricing Model offers an adequate mathematical framework for this study as it provides a modeling approach for the joint dynamics between the stock and the index. As we compute option prices according to this model, we find out that the beta and the idiosyncratic volatility of the stock, which are parameters of the model, characterize the relation between the implied volatility surface of the stock and the one of the index. For this reason, we focus on the estimation of the parameter beta under the risk-neutral measure through the use of option prices.This measure, that we call implied beta, is the information contained in option prices concerning the realization of the parameter beta in the future. Trying to use this additional information, we carry out an empirical study in order to investigate whether the implied beta has a predictive power of the forward realized beta. We conclude that the implied beta doesn’t perform better than the historical beta which is estimated using the linear regression of the stock’s returns onthe index returns. We conclude also that the oscillation of the implied beta around the forward realized beta can engender arbitrage opportunities, and we propose an arbitrage strategy which enables to monetize this difference. In addition, we show that the implied beta is useful to hedge stock options using instruments on the index. In the second part of our work, we consider the problem of option market making. We suppose that the model used to describe the dynamics of the underlying under the risk-neutral probability measure can be misspecified which means thatthe implied distribution of the underlying may be different from its historical one. We consider first the case of a risk neutral market maker who aims to maximize the expectation of her final wealth. Using a stochastic control approach, we determine the optimal bid and ask prices on the option and we interpret the effect of price inefficiency on the optimal strategy. Next to that, we suppose that the market maker is risk averse as she tries to minimize the variance of her finalwealth. We solve a mean-variance optimization problem and we provide analytic approximations for the optimal bid and ask prices. We show the effects of option inventory and price inefficiency on the optimal strategy. We try then to extrapolate the study to a higher dimension in order to see the effect of joint dynamics of the different underlyings on the optimal strategy. Thus, we study market making strategies on a pair of options having different underlyings with the aim to reduce the risk due to accumulated inventories in these two options. Through the resolution of the HJB equation associated to the new optimization problem, we determine the optimal strategy and we support our theoretical finding with numerical simulations. In the final part of the thesis, we study the joint dynamics of the at-the-money implied volatility and the spot process. We try to establish a relation between this joint dynamics and the implied skew through the use of a quantity called the Skew Stickiness Ratio which was introduced in the recent literature. The Skew Stickiness Ratio quantifies the effect of the log-return of the spot on the increment of theat-the-money volatility. We suggest a model-free approach for the estimation of the SSR (Skew Stickiness Ratio) under the risk-neutral measure, this approach doesn’t depend on hypothesis on the dynamics of the underlying. [...]

This dissertation consists of two parts. In the first chapter, we examine the relative performance of four options-based investment strategies versus a buy-and-hold strategy in the underlying stock. Specifically, using ten stocks widely held in 401(k) plans, we examine monthly returns from strategies that include a long stock position as one component. These strategies are long stock, covered call, protective put, collar, and covered combination. Ignoring early exercise for simplicity, we find that the covered combination and covered call strategies generally outperform the long stock strategy, which in turn generally outperforms the collar and protective put strategies regardless of the performance measure considered. Clearly, from the first chapter, strategies that involve writing options, in general, outperform the ones buying options. The second chapter provides a detailed study of the conditions where option writers can maximize returns while minimizing risk. The nonlinear nature of time value decay in options suggests that, theoretically, holding short positions only when the speed of time decay is high might improve the performance of option writing strategies. We examine monthly returns from five option strategies without a position in the underlying asset. These strategies are: short straddle, short strangle, short guts, “crash-neutral” short straddle, and long iron butterfly. The results from two portfolios are compared: a “benchmark” portfolio using standard SPX options that expire the following month and a weekly portfolio using SPXW options that expire at the end of the weekly holding period. The short strangle strategy with weekly options consistently outperforms the other strategies with both standard and weekly options, even after accounting for transaction costs. This finding suggests that short-dated out-of-the-money options can be useful in improving the risk-return characteristics of an option writing strategy. In an effort to improve the performance of the short straddle strategy, this chapter introduces an extremely short holding period portfolio, by stitching together three weekly option expirations into one week. Although the straddle still underperforms relative to the short strangle, the performance of the short straddle is improved by entering the market 15 minutes before the close and by using the extremely short holding period portfolios.

The aim of this diploma thesis is to analyze and implement selected option pricing models using statistical software. The first chapter introduces theoretical basics of options as financial instruments ideal for hedging and speculation. The second chapter constitutes the core part of this thesis since it unveils theoretical concepts of risk-neutral pricing and at the same time analyze some basic, as well as highly sophisticated option pricing models. In addition, each model is accompanied by a practical example of their effective implementation. The final chapter characterize the most widely used option trading strategies and defines the ideal expected market development linked to each strategy.

投資者面對到期日相同的ㄧ序列不同履約價格的選擇權，已有許多文獻提出如何建立選擇權最佳投資組合，但模型中均未考慮交易成本。選擇權在實際市場的交易過程中，投資者所支付的手續費與賦稅即為選擇權的交易成本。本論文針對買賣到期日相同但不同履約價格的買權與賣權如何組合，提出考慮交易成本的整數線性規劃模型，建立選擇權最佳交易策略。我們不考慮股價變動的機率分配型態，延伸楊靜宜 (2004)所建立之整數線性規劃模型和Liu與Liu (2006)的大中取小模型，建構考慮比例制、固定制與混合制交易成本之整數線性規劃模型。最後，我們以台指選擇權(TXO)為例，驗證模型的效能。 關鍵字：交易成本，選擇權交易策略，整數線性規劃，選擇權套利機會。 / There are many researchers focus on constructing the optimal strategies and propose integer linear programming (ILP) for a series of options which are on the same maturity date with different strike price, but they neglect transaction costs in their models. The transaction costs of options are the handling charge and taxes which investors should pay for trading in the market. The thesis proposes an ILP with transaction costs to construct the optimal strategy for an option portfolio of call- and put- options on the same maturity date with different strike price. We leave the distribution of the variety of stock price out of consideration and extend Yang’s (2004) model and Liu & Liu’s (2006) min-max regret model to construct ILP with proportional, fixed, and mixed transaction costs. Finally, we take the trading data of TXO as an empirical study to test and verify the efficiency of our models. Key words: transaction costs, option trading strategies, integer linear programming, option arbitrage opportunities.

Since the introduction of derivatives to the financial markets, volatility trading has emerged as a method for investors to make money in every market condition. In parallel with introducing derivatives to the financial markets, hedging methods have emerged and are today essential instruments for the liquidity providers active in the markets. The most commonly used hedging method is delta hedging which cancels out the directional risk in the option. Hedging the vega risk with dispersion trading seems to be both a profitable and accurate hedging method. This thesis examines the effectiveness of dispersion trading for reducing the vega risk in OMXS30 options. This is investigated by backtesting a strategy based on going short OMXS30 index volatility and long volatility on a tracking portfolio with a zero net vega. This investigation aims to determine if the dispersion trading strategy can be a reliable risk management tool. It was found that vega could accurately be hedged using dispersion trading. However, when considering the bid-ask spread, the strategy did not show profitability over the simulated period. Weighting the portfolio more in favour of companies with smaller bid-ask spreads did not show improved profitability. / Sedan introduktionen av derivat på de finansiella marknaderna har volatilitetshandel dykt upp som en metod för investerare att tjäna pengar i alla marknadsförhållanden. Parallellt med introduktionen av derivat på de finansiella marknaderna har säkringsmetoder vuxit fram och är idag väsentliga instrument för de likviditetsgivare som är verksamma på marknaderna. Den vanligaste säkringsmetoden är delta säkring som tar bort den riktade risken i optionen. Att säkra vegarisken med spridningshandel tycks vara både en lönsam och pålitlig säkringsmetod. Detta examensarbete syftar till att undersöka effektiviteten av att använda en spridningshandel för att minska vegarisken i OMXS30-optioner. Metoden involverar att simulera en strategi baserad på att vara kort volatilitet i OMXS30 och lång volatilitet på en spårningsportfölj på historisk data. Genom denna undersökning strävas det efter att avgöra om strategin för spridningshandel kan vara ett tillförlitligt verktyg för riskhantering. Det visade sig att vega kunde säkras med hjälp av spridningshandel. Strategin visade sig vara lönsam under den simulerade perioden men när köp- och sälj-spreadarna i de enskilda aktieoptioner inkluderades var det inte längre lönsamt att utföra metoden. Att vikta portföljen mer till förmån för företag med mindre köp- och sälj-spread visade inte på förbättrad lönsamhet.

本文考量波動度不對稱效果(Volatility Asymmetric Effect)與均數回歸(Mean Reverting)兩個特性，並考量台股市場特性，嘗試建立一個適合台灣市場的波動度交易策略。利用GARCH(1,1)波動度與VIX指標建構第一個交易訊號，並建立當日沖銷部位。以賺取日內行情為出發點，利用時間序列模型捕捉波動度的高估或低估且搭配純跨式(Pure Straddle)策略或根據Delta調整後的跨式(Adjusted Straddle)策略。第二個交易訊號則是利用市場敏感指標，觀察外資與自營商在交易部位與未平倉部位的變化，找出對於波動度的影響。建立由選擇權與期貨組成的Delta-Hedged部位，藉由觀察市場上主力籌碼的變化，動態調整部位契約，尋找波段之間的獲利機會。 實証部分以期交所公布的每日交易資料與VIX日資料，利用2007至2008兩年的歷史資料，估計參數與測試交易訊號。樣本外期間為2009年1月開始至3月結束共55個交易日。考量交易成本後，兩個不同型態的交易訊號，仍然能夠藉由本研究的策略，獲得正的報酬。本文認為台灣為一個淺碟市場，過度反應資訊的特性，讓波動度策略出現獲利的機會。藉由這個波動度交易系統的研究，除了讓資金豐沛的機構投資人使用外，也能夠讓一般投資大眾建立自己的波動度交易策略 關鍵字:波動度交易，選擇權交易策略，GARCH(1,1)，VIX，市場情緒指標 / Trying to apply a preliminary study of volatility trading strategies in Taiwan derivative market is the topic of this dissertation. Capturing the market movement or even the dynamic of underlying asset is a Pandora’s Box for academic researchers and industry participants. Mean-reverting and asymmetrical effects are the two special characteristics of volatility for us to design our trading system according to the previous empirical studies. In our study, we use different type of volatility signal to capture the trading opportunities. Use the new released information form TAIFEX including VIX and Position Structure of Institutional Traders to design our signal. We apply the idea to use pure option position and delta-hedged position as our trading tools in this volatility trading system and look for the opportunities between realized volatility and implied volatility. An over-reaction may rises the uncertainty and also lead the market volatility change coherently. We use history data from 2007 to 2008 test our trading signal and parameters. The out sample period is from 2009 January to 2009 March which has 55 trading days to simulate our strategies. In the end, we see a positive result in both trading signals which earns positive return after considering the trading cost. Key words: Volatility Trading, Market Sentiment Indices, Option Strategies, VIX, GARCH(1,1)

本論文提出線性規劃的方法以還原隱藏於選擇權市場價格中的風險中立機率測度，並利用該機率測度計算選擇權的合理價格。模型中假設選擇權對應同一標的資產與到期日，資產價格於到期日的狀態為離散點且個數有限，當市場不具任何套利機會時，以極小化市場價格與合理價格之離差總和作為挑選風險中立機率測度的準則。最後，以臺指選擇權(TXO)的交易資料做為實證對象。實證中發現，加入平滑限制式與離差權重之線性規劃模型在評價歐式選擇權合理價格的效能最為優異。 / The thesis proposes a liner programming to recover the risk-neutral probability distribution of an underlying asset price from its associated market option prices, and we evaluate the fair prices of options via the resulting risk-neutral probability distribution. Assume that we face a series of European options with different exercise prices on the same maturity and underlying asset in this linear programming model. The criterion of choosing a risk-neutral probability distribution is minimizing the sum of total deviations subject to requiring that the fair prices of options are consistent with observed market option prices. Finally, we take the trading data of TXO as an empirical study. The empirical study indicates that the model with smooth constraints and weighted deviations has the best performance in pricing the rational price of European options.

Ce travail doctoral étudie l’effet « retour » de l’information financière liée aux prix des actions sur les décisions des dirigeants d’entreprise. Plus précisément, j'étudie si et comment les gestionnaires apprennent effectivement les nouvelles informations contenues dans les prix des actions pour guider leurs décisions d'entreprise. Ma thèse de doctorat est composée de trois essais, chacun abordant un aspect différent de ce même sujet. Le premier essai étudie le lien entre l'efficacité informationnelle du marché d'actions et le niveau d’efficacité économique réelle de l'entreprise. Dans le premier essai, je constate que lorsque les prix de l'action agrègent une plus quantité d'informations utile plus grande, les décisions des entreprises prises par les gestionnaires devraient être encore plus optimales efficaces. Le deuxième essai étudie si les gestionnaires cherchent à apprendre les informations utilisées par les vendeurs à découvert. L’étude des prix des actions en présence de vendeurs à découvert est-il utile pour les décisions de l'entreprise ? Dans le deuxième essai, j'ai surmonté les difficultés empiriques en exploitant une caractéristique institutionnelle unique sur le marché des actions de Hong Kong. Je constate que les gestionnaires des entreprises « non-shortable » peuvent tirer profit des informations des vendeurs à découvert sur les conditions économiques sectorielles par l'intermédiaire des prix des actions d'autres entreprises « shortable » dans la même industrie et les utilisent dans leurs décisions d'entreprise. Le troisième essai étudie les effets réels de la négociation d'options à long terme. Dans le troisième essai, je constate que l’introduction d’une catégorie spécifique d'options à long terme stimule la production d'informations privées à long terme et donc entraîne une augmentation de l'informativité des prix sur les fondamentaux à long terme des entreprises. Par conséquent, les dirigeants peuvent extraire davantage d'informations du prix de l’action pour guider leurs décisions d'investissement à long terme. / In my doctoral thesis, I investigate the information feedback from stock prices to managers’ decisions. More specifically, I study whether and how managers learn new information from stock prices to guide their corporate decisions. My doctoral thesis includes three essays focusing on this topic. The first essay studies the relationship between stock market informational efficiency and real economy efficiency at firm-level. In the first essay, I find that when stock prices reflect greater amount of information that managers care about, corporate decisions made by managers become more efficient. The second essay studies whether managers seek to learn short sellers’ information from stock prices and use it in corporate decisions. In the second essay, I overcome the empirical difficulties by exploiting a unique institutional feature in Hong Kong stock market that only stocks included in an official list are allowed for short sales. I find that that non-shortable firms’ managers can learn short sellers’ information on external conditions from shortable peers’ stock prices and use it in their corporate decisions. The third essay studies the real effects of long-term option trading. I find that long-term option trading stimulates the production of long-term information, which managers can use to guide their long-term investment decisions.

【第一篇論文中文摘要】 本文檢測公司負債合約中的利差是否可被最終的違約後償還率所解釋。透過1962年至2007年間在美國金融市場上發行但最後卻違約的負債合約資料來進行實證，發現違約後償還率的確有反映在發行時的利差上，且此關聯性會隨著美國開放商業銀行進行證券承銷業務後隨之更加顯著。我們並且進一步發現此償還率的資訊能更加有效反映原因與發行公司的資訊不對稱程度降低有關。此外，我們同時又發現此負債合約中的利差與違約後償還率的關聯性對於公司治理較差、以及非投資等級的發行公司會更為顯著。最後，我們的實證結果在考量內生問題、潛在可能遺漏解釋變數、以及其他模型設定後，仍同樣具有堅實性。 【第二篇論文中文摘要】 本文使用臺指選擇權的日內資料來探討選擇權提前交易期間是否具有資訊內涵與價格發現的功能。就作者所知，我們是第一篇透過選擇權資料探討提前交易期間資訊內涵的研究。首先，我們分別透過價、量、與高階動差三類資訊變數指標來衡量提前交易期間的資訊內涵。實證結果顯示：選擇權提前交易期間不只能有效反映隔夜資訊 (公開資訊)，且具有預測當日現貨指數開盤後5分鐘內股價指數移動的能力 (反應私有資訊)，說明提前交易期間的確具有資訊內涵與價格發現的功能。此外，我們進一步發現價平選擇權包含最強的資訊內涵，此應與投資人尋求交易流動性最高的價平選擇權來迅速實現其利潤以反映其資訊有關。最後，本研究亦發現前一日海外市場 (美國) 投資人情緒傳染效果的強度會影響提前交易期間選擇權的資訊內涵，而前一日是否交易 (週末效果與假日效果)則不會影響此資訊內涵。 / 【第一篇論文英文摘要】 We investigate whether the spread of corporate debt contacts can be explained by their ultimate recovery rates. Using the actual realized recovery rates of defaulted debt instruments issued in the U.S. from 1962 to 2007, we find that recovery rate is reflected in the spread at issuance, and that this relationship has become more significant since commercial banks were allowed to underwrite corporate securities. Our further investigation indicates that the enhanced informativeness of recovery rate can be attributed to the lowering of information asymmetry of individual firms. Besides, the relation between the spread at issuance and the recovery rate is stronger for weak corporate governance and non-investment grade issuers. Our conclusions are found to be robust to endogeneity issues, potentially omitted variables and alternative model specifications. 【第二篇論文英文摘要】 This study uses tick-by-tick data to examine the information content and price discovery of TAIEX option trading during the pre-opening period. To the best of our knowledge, this is the first study that focuses on the options market. We construct three groups of information variables to measure the information content of the pre-opening period, including the price, volume, and high moment information variables. We find that option trading during the pre-opening period not only can reflect the overnight information (public information) but also predict the 5-minute intraday returns after the opening of spot market (private information), showing the information content and price discovery of option trading during the pre-opening period. We also find that at-the-money options contain the strongest richness of information content, which may result from its highest liquidity. Finally, we also find that the empirical results would be stronger depending on the intensity of investor sentiment from overseas (U.S. market) of last day but not the length of hours without trading (weekend and holiday effect).