Problem statement: Accurate and reliable forecasts of trends in the housing market can be useful information for market participants as well as policy makers. This information may be useful to minimize risk related to market uncertainty. Since the burst of the housing bubble in the early 1990s the price level of single-family houses has risen sharply in Sweden. The Swedish housing market has experienced an unusually long period of high growth rates in transaction prices which has opened up for discussions about the risk of another housing bubble. Business and property cycles have shown to contain asymmetries, which linear models are unable to pick up and therefore inappropriate to analyze cycles. Approach: Therefore, this study uses non-linear models which are able to pick up the asymmetries. The estimated models are variations of the Markov-switching regression model, i.e. the Markov-switching autoregressive (MS-AR) model and the Markov-switching dynamic regression (MS-DR) model. Results: Our ndings show that the MS-AR(4) model allowing for varying variance across regimes estimated using the growth rate of FASTPI produce superior forecasts over other MSAR models as well as variations of the MS-DR model. The average expected duration to remain in a positive growth regime is between 6.3 and 7.3 years and the average expected duration to remain in a negative growth regime is between 1.2 to 2.5 years. Conclusion: The next regime shift in the Swedish housing market is projected to occur between 2018 and 2019, counting the contraction period in 2012 as the most recent negative regime. Our ndings support other studies ndings which indicate that the longer the market has remained in one state, the greater is the risk for a regime shift. / Problemformulering: Noggranna och tillforlitliga prognoser om utvecklingen pa bostadsmarknaden kan vara anvandbar information for marknadsaktorer samt beslutsfattare. Denna information kan vara anvandbar for att minimera risken relaterad till osakerheten pa marknaden. Sen bostadsbubblan sprack i borjan av 1990-talet har prisnivan for smahus okat kraftigt i Sverige. Den svenska bostadsmarknaden har upplevt en ovanligt lang period av hog tillvaxt i transaktionspriser som har oppnat upp for diskussioner om risken for en ny bostadsbubbla. Konjunkturoch fastighetscykler har visat sig innehalla asymmetrier som linjara modeller inte kan uppfanga och darfor visat sig vara olampliga for att analysera cykler. Tillvagagangssatt: Darfor anvander den har studien icke-linjara modeller som kan uppfanga dessa asymmetrier. De skattade modellerna ar variationer av Hamiltons Markov-switchingmodell, dvs. en autoregressiv Markov-switchingmodell (MS-AR) och en dynamisk Markov-switchingmodell (MS-DR). Resultat: Resultatet visar att MS-AR(4)-modellen som tar hansyn till varierande varians over regimerna estimerad med tillvaxten av FASTPI producerar overlagsna prognoser jamfort med andra MS-AR-modeller samt variationer av MS-DR-modellen. Den genomsnittliga forvantade varaktigheten att benna sig i en positiv regim ar mellan 6,3 och 7,3 ar och den  genomsnittliga forvantade varaktigheten att benna sig i en negativ regim ar mellan 1,2 till 2,5 ar. Slutsats: Nasta regimskifte pa den svenska bostadsmarknaden beraknas ske mellan 2018 och 2019, antaget att nedgangen under 2012 ar den senaste negativa regimen. Resultatet stodjer tidigare studier, som tyder pa att ju langre marknaden har varit i ett tillstand, desto storre ar risken for ett regimskifte.

[pt] Esta dissertação é composta por três capítulos que abordam questões relacionadas à política monetária. O Capítulo 1 avalia o problema de conduzir política monetária com ativos arriscados em um simples modelo neo-Wickselliano. Eu mostro que a potência da política monetária com relação a preços e inflação se reduz uma vez que ela só pode ser condicionalmente ativa na presença de risco subjacente ao ativo de política monetária. Além disso, prêmio de risco não compensado induz viés inflacionário, e há correlação positiva entre probabilidade de calote e inflação, do mesmo sinal que se costuma encontrar em dados empíricos. Esses resultados constituem um argumento novo em favor de uma política monetária mais vigilante em caso de crise fiscal ou política, o que ajuda a explicar o conservadorismo da política monetária em economias arriscadas. O capítulo 2 endogeniza risco no ativo de política monetária como risco fiscal e estuda sua transmissão. Eu desenvolvo um modelo novo-Keynesiano de dois agentes (TANK) com limites fiscais endógenos no qual o banco central opera através de títulos com risco de calote, e calibro para uma grande economia emergente, Brasil. Eu encontro que, ao ignorar o risco subjacente ao ativo de política monetária, o banco central reforça a coincidência desagradável de taxas mais altas de juros real, nominal e inflação na distribuição de equilíbrio do modelo, o que surge como o resultado de expectativas endógenas de recessões severas em caso de calote. Outrossim, acomodar risco de ativo de política induz correlação positiva entre risco de calote e inflação. Do ponto de vista de política, esses resultados lançam dúvidas quanto à correta avaliação da rigidez da política monetária em economias com risco de calote soberano, enquanto também lançam nova luz sobre a antiga discussão de por que a taxa básica de juros foi excepcionalmente alta no Brasil após o Plano Real. Finalmente, o Capítulo 3 responde à controvérsia recente sobre a presença, de fato, de um canal de transmissão de taxa de juros real nos modelos novo-Keynesianos, uma vez que adição de capital endógeno é consistente com a taxa real se movendo em qualquer direção após um choque monetário positivo. Eu mostro que esse problema de identificação pode ser contornado pela inclusão de outro ingrediente tão comum em modelos de tamanho médio quanto o próprio capital: suavização de taxa de juros. / [en] This dissertation presents three chapters addressing issues pertaining to monetary policy. Chapter 1 evaluates the problem of conducting monetary policy with risky assets in a simple neo-Wicksellian monetary model. I show that monetary policy s power w.r.t prices and inflation reduces as it can only be conditionally active in the presence of policy-asset risk. Moreover, uncompensated risk premium induces an inflationary bias, as well as default probability and inflation are positively correlated, the same sign of empirical correlations usually found. These results constitute a novel argument in favor of a more hawkish stance in case of a fiscal or political crisis, which helps to explain monetary policy conservatism in risky economies. Chapter 2 endogenizes policy-asset risk as a fiscal risk and studies its transmission. I lay out a two-agent New-Keynesian (TANK) model with endogenous fiscal limits in which the central bank operates through defaultable bonds, and then calibrate it to a large emerging economy, Brazil. I find that by ignoring policy-asset risk the central bank reinforces the unpleasant coincidence of higher inflation, real, and nominal interest rates in the equilibrium distribution of the model, what emerges as the result of endogenous expectations of a severe recession in case of default. Additionally, accommodating policy-asset risk induces positive correlation between default risk and inflation. From a policy perspective, these results raise serious concerns about the evaluation of monetary policy stance in default-risky economies, while shed new light on the long-standing discussion about why policy rates have been exceptionally high in Brazil after the Real Plan. Finally, Chapter 3 responds to a recent controversy on the actual presence of a real interest rate transmission channel in New-Keynesian models, as the addition of endogenous capital is consistent with real rates moving in any direction after a monetary shock. I show that this identification problem can be circumvented by the inclusion of another ingredient as prevalent as capital itself in middle-scale models: interest-rate smoothing.

本研究目的在於探討Put-Call Parity（PCP）所隱含的買權、賣權與標的資產間的價格變動關係。藉由探討PCP偏差程度的動態行為，推論若PCP的偏差為隨機漫步過程，則無法達到長期穩定，隱含PCP的廣義關係無法成立；反之，若PCP的偏差具有回歸平均特性，表示長期會達到穩定狀態，則PCP的廣義關係成立。 在研究方法上本文以變異數比率法檢定指數選擇權的PCP偏差是否為隨機漫步過程，採用隱含利率和實際無風險利率的差代表PCP的偏差程度，利用馬可夫轉換模型描繪PCP偏差的動態行為，並使用Gibbs Sampling演算法說明參數的不確定性。 本文以S&P500和DAX為研究標的，並探討股利不確定性是否影響PCP廣義關係，得到下列結論： 1、 對於S&P 500指數選擇權而言，不論是以日資料或週資料估計VR，S&P 500的PCP偏差都無法提供回歸平均的證據，隱含S&P 500的PCP廣義關係無法成立。 2、 對於DAX指數選擇權而言，檢定日資料的結果發現，DAX之PCP偏差在長期時（40~50日）有明顯的回歸平均的證據；而在檢定週資料時，使用原始資料法在90%信心水準下，不論取任何lag都可拒絕虛無假設，使用標準化資料則無法提供明顯的回歸平均證據。 3、 比較S&P 500和DAX，檢定日資料與週資料的結果都發現，DAX的p-value都比S&P 500小，並且S&P 500的PCP偏差都無法提供回歸平均的證據，而DAX有明顯回歸平均現象，隱含在消除股利的不確定性後，指數選擇權PCP的廣義關係式成立之證據較強烈。

Le modèle GARCH à changement de régimes est le fondement de cette thèse. Ce modèle offre de riches dynamiques pour modéliser les données financières en combinant une structure GARCH avec des paramètres qui varient dans le temps. Cette flexibilité donne malheureusement lieu à un problème de path dependence, qui a empêché l'estimation du modèle par le maximum de vraisemblance depuis son introduction, il y a déjà près de 20 ans. La première moitié de cette thèse procure une solution à ce problème en développant deux méthodologies permettant de calculer l'estimateur du maximum de vraisemblance du modèle GARCH à changement de régimes. La première technique d'estimation proposée est basée sur l'algorithme Monte Carlo EM et sur l'échantillonnage préférentiel, tandis que la deuxième consiste en la généralisation des approximations du modèle introduites dans les deux dernières décennies, connues sous le nom de collapsing procedures. Cette généralisation permet d'établir un lien méthodologique entre ces approximations et le filtre particulaire. La découverte de cette relation est importante, car elle permet de justifier la validité de l'approche dite par collapsing pour estimer le modèle GARCH à changement de régimes. La deuxième moitié de cette thèse tire sa motivation de la crise financière de la fin des années 2000 pendant laquelle une mauvaise évaluation des risques au sein de plusieurs compagnies financières a entraîné de nombreux échecs institutionnels. À l'aide d'un large éventail de 78 modèles économétriques, dont plusieurs généralisations du modèle GARCH à changement de régimes, il est démontré que le risque de modèle joue un rôle très important dans l'évaluation et la gestion du risque d'investissement à long terme dans le cadre des fonds distincts. Bien que la littérature financière a dévoué beaucoup de recherche pour faire progresser les modèles économétriques dans le but d'améliorer la tarification et la couverture des produits financiers, les approches permettant de mesurer l'efficacité d'une stratégie de couverture dynamique ont peu évolué. Cette thèse offre une contribution méthodologique dans ce domaine en proposant un cadre statistique, basé sur la régression, permettant de mieux mesurer cette efficacité. / The Markov-switching GARCH model is the foundation of this thesis. This model offers rich dynamics to model financial data by allowing for a GARCH structure with time-varying parameters. This flexibility is unfortunately undermined by a path dependence problem which has prevented maximum likelihood estimation of this model since its introduction, almost 20 years ago. The first half of this thesis provides a solution to this problem by developing two original estimation approaches allowing us to calculate the maximum likelihood estimator of the Markov-switching GARCH model. The first method is based on both the Monte Carlo expectation-maximization algorithm and importance sampling, while the second consists of a generalization of previously proposed approximations of the model, known as collapsing procedures. This generalization establishes a novel relationship in the econometric literature between particle filtering and collapsing procedures. The discovery of this relationship is important because it provides the missing link needed to justify the validity of the collapsing approach for estimating the Markov-switching GARCH model. The second half of this thesis is motivated by the events of the financial crisis of the late 2000s during which numerous institutional failures occurred because risk exposures were inappropriately measured. Using 78 different econometric models, including many generalizations of the Markov-switching GARCH model, it is shown that model risk plays an important role in the measurement and management of long-term investment risk in the context of variable annuities. Although the finance literature has devoted a lot of research into the development of advanced models for improving pricing and hedging performance, the approaches for measuring dynamic hedging effectiveness have evolved little. This thesis offers a methodological contribution in this area by proposing a statistical framework, based on regression analysis, for measuring the effectiveness of dynamic hedges for long-term investment guarantees.

The research presented in this thesis addresses different aspects of dynamic portfolio construction and portfolio risk measurement. It brings the research on dynamic portfolio optimization, replicating portfolio construction, dynamic portfolio risk measurement and volatility forecast together. The overall aim of this research is threefold. First, it is aimed to examine the portfolio construction and risk measurement performance of a broad set of volatility forecast and portfolio optimization model. Second, in an effort to improve their forecast accuracy and portfolio construction performance, it is aimed to propose new models or new formulations to the available models. Third, in order to enhance the replication performance of hedge fund returns, it is aimed to introduce a replication approach that has the potential to be used in numerous applications, in investment management. In order to achieve these aims, Chapter 2 addresses risk measurement in dynamic portfolio construction. In this chapter, further evidence on the use of multivariate conditional volatility models in hedge fund risk measurement and portfolio allocation is provided by using monthly returns of hedge fund strategy indices for the period 1990 to 2009. Building on Giamouridis and Vrontos (2007), a broad set of multivariate GARCH models, as well as, the simpler exponentially weighted moving average (EWMA) estimator of RiskMetrics (1996) are considered. It is found that, while multivariate GARCH models provide some improvements in portfolio performance over static models, they are generally dominated by the EWMA model. In particular, in addition to providing a better risk-adjusted performance, the EWMA model leads to dynamic allocation strategies that have a substantially lower turnover and could therefore be expected to involve lower transaction costs. Moreover, it is shown that these results are robust across the low - volatility and high-volatility sub-periods. Chapter 3 addresses optimization in dynamic portfolio construction. In this chapter, the advantages of introducing alternative optimization frameworks over the mean-variance framework in constructing hedge fund portfolios for a fund of funds. Using monthly return data of hedge fund strategy indices for the period 1990 to 2011, the standard mean-variance approach is compared with approaches based on CVaR, CDaR and Omega, for both conservative and aggressive hedge fund investors. In order to estimate portfolio CVaR, CDaR and Omega, a semi-parametric approach is proposed, in which first the marginal density of each hedge fund index is modelled using extreme value theory and the joint density of hedge fund index returns is constructed using a copula-based approach. Then hedge fund returns from this joint density are simulated in order to compute CVaR, CDaR and Omega. The semi-parametric approach is compared with the standard, non-parametric approach, in which the quantiles of the marginal density of portfolio returns are estimated empirically and used to compute CVaR, CDaR and Omega. Two main findings are reported. The first is that CVaR-, CDaR- and Omega-based optimization offers a significant improvement in terms of risk-adjusted portfolio performance over mean-variance optimization. The second is that, for all three risk measures, semi-parametric estimation of the optimal portfolio offers a very significant improvement over non-parametric estimation. The results are robust to as the choice of target return and the estimation period. Chapter 4 searches for improvements in portfolio risk measurement by addressing volatility forecast. In this chapter, two new univariate Markov regime switching models based on intraday range are introduced. A regime switching conditional volatility model is combined with a robust measure of volatility based on intraday range, in a framework for volatility forecasting. This chapter proposes a one-factor and a two-factor model that combine useful properties of range, regime switching, nonlinear filtration, and GARCH frameworks. Any incremental improvement in the performance of volatility forecasting is searched for by employing regime switching in a conditional volatility setting with enhanced information content on true volatility. Weekly S&P500 index data for 1982-2010 is used. Models are evaluated by using a number of volatility proxies, which approximate true integrated volatility. Forecast performance of the proposed models is compared to renowned return-based and range-based models, namely EWMA of Riskmetrics, hybrid EWMA of Harris and Yilmaz (2009), GARCH of Bollerslev (1988), CARR of Chou (2005), FIGARCH of Baillie et al. (1996) and MRSGARCH of Klaassen (2002). It is found that the proposed models produce more accurate out of sample forecasts, contain more information about true volatility and exhibit similar or better performance when used for value at risk comparison. Chapter 5 searches for improvements in risk measurement for a better dynamic portfolio construction. This chapter proposes multivariate versions of one and two factor MRSACR models introduced in the fourth chapter. In these models, useful properties of regime switching models, nonlinear filtration and range-based estimator are combined with a multivariate setting, based on static and dynamic correlation estimates. In comparing the out-of-sample forecast performance of these models, eminent return and range-based volatility models are employed as benchmark models. A hedge fund portfolio construction is conducted in order to investigate the out-of-sample portfolio performance of the proposed models. Also, the out-of-sample performance of each model is tested by using a number of statistical tests. In particular, a broad range of statistical tests and loss functions are utilized in evaluating the forecast performance of the variance covariance matrix of each portfolio. It is found that, in terms statistical test results, proposed models offer significant improvements in forecasting true volatility process, and, in terms of risk and return criteria employed, proposed models perform better than benchmark models. Proposed models construct hedge fund portfolios with higher risk-adjusted returns, lower tail risks, offer superior risk-return tradeoffs and better active management ratios. However, in most cases these improvements come at the expense of higher portfolio turnover and rebalancing expenses. Chapter 6 addresses the dynamic portfolio construction for a better hedge fund return replication and proposes a new approach. In this chapter, a method for hedge fund replication is proposed that uses a factor-based model supplemented with a series of risk and return constraints that implicitly target all the moments of the hedge fund return distribution. The approach is used to replicate the monthly returns of ten broad hedge fund strategy indices, using long-only positions in ten equity, bond, foreign exchange, and commodity indices, all of which can be traded using liquid, investible instruments such as futures, options and exchange traded funds. In out-of-sample tests, proposed approach provides an improvement over the pure factor-based model, offering a closer match to both the return performance and risk characteristics of the hedge fund strategy indices.

Le modèle GARCH à changement de régimes est le fondement de cette thèse. Ce modèle offre de riches dynamiques pour modéliser les données financières en combinant une structure GARCH avec des paramètres qui varient dans le temps. Cette flexibilité donne malheureusement lieu à un problème de path dependence, qui a empêché l'estimation du modèle par le maximum de vraisemblance depuis son introduction, il y a déjà près de 20 ans. La première moitié de cette thèse procure une solution à ce problème en développant deux méthodologies permettant de calculer l'estimateur du maximum de vraisemblance du modèle GARCH à changement de régimes. La première technique d'estimation proposée est basée sur l'algorithme Monte Carlo EM et sur l'échantillonnage préférentiel, tandis que la deuxième consiste en la généralisation des approximations du modèle introduites dans les deux dernières décennies, connues sous le nom de collapsing procedures. Cette généralisation permet d'établir un lien méthodologique entre ces approximations et le filtre particulaire. La découverte de cette relation est importante, car elle permet de justifier la validité de l'approche dite par collapsing pour estimer le modèle GARCH à changement de régimes. La deuxième moitié de cette thèse tire sa motivation de la crise financière de la fin des années 2000 pendant laquelle une mauvaise évaluation des risques au sein de plusieurs compagnies financières a entraîné de nombreux échecs institutionnels. À l'aide d'un large éventail de 78 modèles économétriques, dont plusieurs généralisations du modèle GARCH à changement de régimes, il est démontré que le risque de modèle joue un rôle très important dans l'évaluation et la gestion du risque d'investissement à long terme dans le cadre des fonds distincts. Bien que la littérature financière a dévoué beaucoup de recherche pour faire progresser les modèles économétriques dans le but d'améliorer la tarification et la couverture des produits financiers, les approches permettant de mesurer l'efficacité d'une stratégie de couverture dynamique ont peu évolué. Cette thèse offre une contribution méthodologique dans ce domaine en proposant un cadre statistique, basé sur la régression, permettant de mieux mesurer cette efficacité. / The Markov-switching GARCH model is the foundation of this thesis. This model offers rich dynamics to model financial data by allowing for a GARCH structure with time-varying parameters. This flexibility is unfortunately undermined by a path dependence problem which has prevented maximum likelihood estimation of this model since its introduction, almost 20 years ago. The first half of this thesis provides a solution to this problem by developing two original estimation approaches allowing us to calculate the maximum likelihood estimator of the Markov-switching GARCH model. The first method is based on both the Monte Carlo expectation-maximization algorithm and importance sampling, while the second consists of a generalization of previously proposed approximations of the model, known as collapsing procedures. This generalization establishes a novel relationship in the econometric literature between particle filtering and collapsing procedures. The discovery of this relationship is important because it provides the missing link needed to justify the validity of the collapsing approach for estimating the Markov-switching GARCH model. The second half of this thesis is motivated by the events of the financial crisis of the late 2000s during which numerous institutional failures occurred because risk exposures were inappropriately measured. Using 78 different econometric models, including many generalizations of the Markov-switching GARCH model, it is shown that model risk plays an important role in the measurement and management of long-term investment risk in the context of variable annuities. Although the finance literature has devoted a lot of research into the development of advanced models for improving pricing and hedging performance, the approaches for measuring dynamic hedging effectiveness have evolved little. This thesis offers a methodological contribution in this area by proposing a statistical framework, based on regression analysis, for measuring the effectiveness of dynamic hedges for long-term investment guarantees.

Black and Scholes (1973)對於報酬率提出以B-S模型配適，但B-S模型無法有效解釋報酬率不對稱高狹峰、波動度微笑、波動度叢聚、長記憶性的性質。Merton (1976)認為不尋常的訊息來臨會影響股價不連續跳躍，因此發展B-S模型加入不連續跳躍風險項的跳躍擴散模型，該模型可同時描述報酬率不對稱高狹峰和波動度微笑兩性質。Charles, Fuh and Lin (2011)加以考慮市場狀態提出狀態轉換跳躍模型，除了保留跳躍擴散模型可描述報酬率不對稱高狹峰和波動度微笑，更可以敘述報酬率的波動度叢聚和長記憶性。本文進一步拓展狀態轉換跳躍模型，考慮不連續跳躍風險項的帄均數與市場狀態相關，提出狀態轉換跳躍相關模型。並以道瓊工業指數與S&P 500指數1999年至2010年股價指數資料，採用EM和SEM分別估計參數與估計參數共變異數矩陣。使用概似比檢定結果顯示狀態轉換跳躍相關模型比狀態轉換跳躍獨立模型更適合描述股價指數報酬率。並驗證狀態轉換跳躍相關模型也可同時描述報酬率不對稱高狹峰、波動度微笑、波動度叢聚、長記憶性。最後利用Esscher轉換法計算股價指數選擇權定價公式，以敏感度分析模型參數對於定價結果的影響，並且市場驗證顯示狀態轉換跳躍相關模型會有最小的定價誤差。 / Black and Scholes (1973) proposed B-S model to fit asset return, but B-S model can’t effectively explain some asset return properties, such as leptokurtic, volatility smile, volatility clustering and long memory. Merton (1976) develop jump diffusion model (JDM) that consider abnormal information of market will affect the stock price, and this model can explain leptokurtic and volatility smile of asset return at the same time. Charles, Fuh and Lin (2011) extended the JDM and proposed regime-switching jump independent model (RSJIM) that consider jump rate is related to market states. RSJIM not only retains JDM properties but describes volatility clustering and long memory. In this paper, we extend RSJIM to regime-switching jump dependent model (RSJDM) which consider jump size and jump rate are both related to market states. We use EM and SEM algorithm to estimate parameters and covariance matrix, and use LR test to compare RSJIM and RSJDM. By using 1999 to 2010 Dow-Jones industrial average index and S&P 500 index as empirical evidence, RSJDM can explain index return properties said before. Finally, we calculate index option price formulation by Esscher transformation and do sensitivity analysis and market validation which give the smallest error of option prices by RSJDM.

波動度對於金融市場影響甚多，同時為金融資產定價的重要參數以及市場穩 定度的衡量指標，尤其在金融危機發生時，波動度指數的驟升反映資產價格震盪。 本篇論文嘗試捕捉S&P500 指數實現波動度與VIX變動率未來之動態，並將VIX、 VIX 選擇權與VVIX 納入預測模型中，探討其資訊內涵。透過研究S&P500 指數 實現波動度，能夠預測S&P500 指數未來之波動度與報酬，除了能夠觀察市場變 動，亦能使未來選擇權定價更為準確；而藉由模型預測VIX，能夠藉由VIX 選 擇權或VIX 期貨，提供避險或投資之依據。文章採用2006 年至2011 年之S&P500 指數、VIX、VIX 選擇權與VVIX 資料。 在 S&P500 指數之實現波動度預測當中，本篇論文的模型改良自先前文獻， 結合實現波動度、隱含波動度與S&P500 指數選擇權之風險中立偏態，所構成之 異質自我回歸模型(HAR-RV-IV-SK model)。論文額外加入VIX 變動率以及VIX指數選擇權之風險中立偏態作為模型因子，預測未來S&P500 指數實現波動度。 研究結果表示，加入VIX 變動率作為S&P500 指數實現波動度預測模型變數後， 可增加S&P500 指數實現波動度預測模型之準確性。 在 VIX 變動率預測模型之中，論文採用動態轉換模型，作為高低波動度之 下，區分預測模型的方法。以VIX 過去的變動率、VIX 選擇權之風險中立動差 以及VIX 之波動度指數(VVIX)作為變數，預測未來VIX 變動率。結果顯示動態 轉換模型能夠提升VIX 預測模型的解釋能力，並且在動態轉換模型下，VVIX 與 VIX 選擇權之風險中立動差，對於VIX 預測具有相當之資訊隱涵於其中。 / This paper tries to capture the future dynamic of S&P 500 index realized volatility and VIX. We add the VIX change rate and the risk neutral skewness of VIX options into the Heterogeneous Autoregressive model of Realized Volatility, Implied Volatility and Skewness (HAR-RV-IV-SK) model to forecast the S&P 500 realized volatility. Also, this paper uses the regime switching model and joins the VIX, risk neutral moments of VIX options and VVIX variables to raise the explanatory ability in the VIX forecasting. The result shows that the VIX change rate has additional information on the S&P 500 realized volatility. By using the regime switching model, the VVIX and the risk neutral moments of VIX options variables have information contents in VIX forecasting. These models can be used for hedging or investment purposes.

本文實證探討黃金期貨報酬率的特性並在標的黃金期貨價格遵循狀態轉換跳躍擴散過程時實現美式選擇權之評價。在這樣的動態過程下，跳躍事件被一個複合普瓦松過程與對數常態跳躍振幅所描述，以及狀態轉換到達強度是由一個其狀態代表經濟狀態的隱藏馬可夫鏈所捕捉。考量不同的跳躍風險假設，我們使用Merton測度與Esscher轉換推導出在一個不完全市場設定下的風險中立黃金期貨價格動態過程。為了達到所需的精確度，最小平方蒙地卡羅法被用來近似美式黃金期貨選擇權的價值。基於實際市場資料，我們提供實證與數值結果來說明這個動態模型的優點。 / This dissertation empirically investigates the characteristics of gold futures returns and achieves the valuation of American-style options when the underlying gold futures price follows a regime-switching jump-diffusion process. Under such dynamics, the jump events are described as a compound Poisson process with a log-normal jump amplitude, and the regime-switching arrival intensity is captured by a hidden Markov chain whose states represent the economic states. Considering the different jump risk assumptions, we use the Merton measure and Esscher transform to derive risk-neutral gold futures price dynamics under an incomplete market setting. To achieve a desired accuracy level, the least-squares Monte Carlo method is used to approximate the values of American gold futures options. Our empirical and numerical results based on actual market data are provided to illustrate the advantages of this dynamic model.

本文使用Esscher轉換法推導狀態轉換模型、跳躍獨立風險下狀狀態轉換模型及跳躍相關風險下狀態轉換模型的選擇權定價公式。藉由1999年至2011年道瓊工業指數真實市場資料使用EM演算法估計模型參數並使用概似比檢定得到跳躍相關風險下狀態轉換模型最適合描述報酬率資料。接著進行敏感度分析得知，高波動狀態的機率、報酬率的整體波動度及跳躍頻率三者與買權呈現正相關。最後由市場驗證可知，跳躍相關風險下狀態轉換模型在價平及價外的定價誤差皆是最小，在價平的定價誤差則略高於跳躍獨立風險下狀態轉換模型。 / In this paper, we derive regime switching model, regime switching model with independent jump and regime switching model with dependent jump by Esscher transformation. We use the data from 1999 to 2011 Dow-Jones industrial average index market price to estimate the parameter by EM algorithm. Then we use likelihood ratio test to obtain that regime switching model with dependent jump is the best model to depict return data. Moreover, we do sensitivity analysis and find the result that the probability of the higher volatility state , the overall volatility of rate of return , and the jump frequency are positively correlated with call option value. Finally, we enhance the empirical value of regime switching model with dependent jump by means of calculating the price error.