The issue of forecasting the future price of risky financial assets has attracted academia and business practice since the inception of the stock exchange. Also due to the just finished financial crisis, which was the worst crisis since the Great Depression, it is clear that research in this area has not been finished yet. On the contrary, new challenges have been raised. The main goal of the thesis is the demonstration of the significant information potential which is hidden in option market prices. These prices contain informations on probability distribution of the underlying asset returns and the risk connected with these returns. Other objectives of the thesis are the forecast of the underlying asset price distribution using parametric and nonparametric estimates, the improvement of this forecast using the utility function of the representative investor, the description of the current market sentiment and the determination of the risk premium, especially the risk premium on Czech market. The thesis deals with the forecast of the underlying asset price probability distribution implied by the current option market prices using parametric and nonparametric estimates. The resulting distribution is described by the moment characteristics which represent a valuable tool for analyzing the current market sentiment. According to the theory, the probability distribution of the underlying asset price implied by option prices is risk neutral, i.e. it applies only to risk neutral investors. The theory further implies that the distribution of real world can be derived from the risk neutral distribution using utility function of the representative investor. The inclusion of a utility function of representative investor improves the forecast of the underlying asset price distribution. Three different utility functions of traditional risk theory are used in the thesis. These functions range from the simple power function to the general function of hyperbolic absolute risk aversion (HARA). Further, Friedman-Savage utility function is used. This function allows both a risk averse investor and a risk loving investor. The thesis also answers the question: Are the current asset prices at so high level that the purchase of the asset means a gamble? The risk premium associated with investing in the risky asset is derived in the thesis. The risk premium can be understood as the premium demanded by investors for investment in a risky asset against the investment in a riskless asset. All the theoretical methods introduced in the thesis are demonstrated on real data coming from two different markets. Developing market is represented by shares of CEZ and developed market is represented by S&P 500 futures. The thesis deals with demonstrations in single point in time as well as in available history of the data. The forecasts of the underlying asset price distribution and the relating risk premium are constructed in the available data history. The goals and the objectives of the thesis have been achieved. The contribution of the thesis is the development of parametric and nonparametric methodology for estimating the underlying asset price probability distribution implied by the option market prices so that the nature of the particular market and instrument is captured. The further contribution of the thesis is the construction of the forecasts of the underlying asset price distribution and the construction of the market sentiment in the available history of data. The contribution of the thesis is also the construction of the market risk premium in the available history and the establishment of the hypothesis that the markets gamble before the crisis.

隨著經濟發展，國民所得水準提高，國民儲蓄成為資本形成的重要來源，而資本市場之功能便在於匯集民間儲蓄，將其導入國內的各項實質建中，是故一個有效率的、健全的資本市場，不僅能讓資金之供需雙方互蒙其利，更可使整體經濟社會的實質財富與所得，隨著資金供給雙方的交互行為而得以持續成長。 　　在台灣目前資本市場發行及流通之信用工具中，不論是初級市場發行額，抑或是次級市場交易額，股票市場一直佔有最重要的地位，所以股票市場也就成為企業籌措長期資金最為倚重的信用工具。 　　正因為股票市場具有如此之重要性，因此本文先從理論與台灣近幾年來的相關實證，針對台灣股票市場效率性做一番釐清，再從所得出之結論進一步借用Galeotti & Schiantarelli (1994)的研究，將股價區分成基本面與非基本面，以及各自適當的代理變數，推導出投資與這些代理變數之間的關係。 　　最後就民國76年5月至83年11月期間，以台灣所有上市公司為研究對象做實證分析。 　　本研究之主要發現如下： 　　1. 台灣股價波動偏離基本價值具有市場異常現象，不符合效率市場假說。 　　2. 由股票市場價值區分出之基本面與非基本面因素，對投資均會產生影響，其中又以落後兩期之解釋變數最為顯著。此結果介於Bosworth (1975)與Merton & Fischer (1984)兩篇研究之間，非基本面亦會影響投資 決策，但非基本面之效果小於基本面效果。

The goal of this thesis in finance is to combine the use of advanced mathematical methods with a return to foundational economic issues. In that perspective, I study generalized rational expectations and asset pricing in Chapter 2, and a converse comparison principle for backward stochastic differential equations with jumps in Chapter 3. Since the use of stochastic methods in finance is an interesting and complex issue in itself - if only to clarify the difference between the use of mathematical models in finance and in physics or biology - I also present a philosophical reflection on the interpretation of mathematical models in finance (Chapter 4). In Chapter 5, I conclude the thesis with an essay on the history and interpretation of mathematical probability - to be read while keeping in mind the fundamental role of mathematical probability in financial models.

One could argue that the most discussed topic in finance is whether or not it is possible to “beat the market”. Even though many people claim to do this, there is little evidence to support the idea that one can consistently beat the market over a long period of time. There are indeed several examples of investors who have managed to outperform the market consistently for a long time, but the efforts of these individuals or institutions could by many be considered to be pure luck. One of the many strategies that have been evaluated by several researchers and is said to generate a risk adjusted return greater than that of the market, is one based on the P/E-effect. This strategy is based on the financial ratio P/E – price divided by earnings – and used by constructing portfolios consisting of stocks with low P/E ratios. Several studies have confirmed the existence of the P/E-effect on various stock markets around the world and over different time periods. On the Swedish market, however, few studies have generated the same results. Most of these studies can be considered to be insufficient with regards to sample sizes and methods, spawning a need for more extensive studies. We have examined the P/E strategy on the Swedish Stock Exchange (SSE) between 2004 and 2012. The sample included 358 companies (excluding financial companies) with available necessary data. The stocks were divided into five portfolios based on their yearly P/E ratios (low to high), upon which the monthly returns of the individual stocks were calculated using a logarithmic formula. The returns were also risk adjusted using the Capital Asset Pricing Model (CAPM), followed by a regression analysis to see if possible abnormal returns could be considered to be statistically significant for the examined time period. The results of our study indicate that the P/E effect is not present on the Swedish Stock Exchange during the examined time period, and we therefore conclude that it was not possible to utilize a strategy based on the P/E effect between 2004 and 2012 in order to achieve an abnormal return. The results can be used to argue that the Swedish stock market is more efficient than for example the U.S. stock market where the P/E effect has been found to exist.

Previous research has confirmed the existence of a value premium in a wide array of markets and using this value stock anomaly has yielded superior performance. This thesis investigates if one could take advantage of the existence of a value premium to deploy a dynamic investment strategy on the Swedish stock market (OMXS30) with focus on minimizing risk to achieve higher risk adjusted performance than the stock market index. The investment strategy implemented use Market-to-Book-Value to screen for both entry and exit signals and Modern Portfolio Theory, using the minimum-variance portfolio with short-selling constraints, to allocate assets within the portfolio. The investment strategy is evaluated using the Modigliani-Modigliani Risk Adjusted Performance measure. Conclusions from the thesis are that the strategy does outperform the Swedish stock market index, both in terms of nominal return and risk-adjusted performance. The suboptimal behaviour of investors where they overreact  to signals and unconsciously rely on heuristics is used to explain why this is possible. Market-to-Book-Value, using the first quartile as entry signal and third quartile as exit signal, is considered to be a successful key ratio to screen for value stocks.

Les titres financiers sont souvent modélisés par des équations différentielles stochastiques (ÉDS). Ces équations peuvent décrire le comportement de l'actif, et aussi parfois certains paramètres du modèle. Par exemple, le modèle de Heston (1993), qui s'inscrit dans la catégorie des modèles à volatilité stochastique, décrit le comportement de l'actif et de la variance de ce dernier. Le modèle de Heston est très intéressant puisqu'il admet des formules semi-analytiques pour certains produits dérivés, ainsi qu'un certain réalisme. Cependant, la plupart des algorithmes de simulation pour ce modèle font face à quelques problèmes lorsque la condition de Feller (1951) n'est pas respectée. Dans ce mémoire, nous introduisons trois nouveaux algorithmes de simulation pour le modèle de Heston. Ces nouveaux algorithmes visent à accélérer le célèbre algorithme de Broadie et Kaya (2006); pour ce faire, nous utiliserons, entre autres, des méthodes de Monte Carlo par chaînes de Markov (MCMC) et des approximations. Dans le premier algorithme, nous modifions la seconde étape de la méthode de Broadie et Kaya afin de l'accélérer. Alors, au lieu d'utiliser la méthode de Newton du second ordre et l'approche d'inversion, nous utilisons l'algorithme de Metropolis-Hastings (voir Hastings (1970)). Le second algorithme est une amélioration du premier. Au lieu d'utiliser la vraie densité de la variance intégrée, nous utilisons l'approximation de Smith (2007). Cette amélioration diminue la dimension de l'équation caractéristique et accélère l'algorithme. Notre dernier algorithme n'est pas basé sur une méthode MCMC. Cependant, nous essayons toujours d'accélérer la seconde étape de la méthode de Broadie et Kaya (2006). Afin de réussir ceci, nous utilisons une variable aléatoire gamma dont les moments sont appariés à la vraie variable aléatoire de la variance intégrée par rapport au temps. Selon Stewart et al. (2007), il est possible d'approximer une convolution de variables aléatoires gamma (qui ressemble beaucoup à la représentation donnée par Glasserman et Kim (2008) si le pas de temps est petit) par une simple variable aléatoire gamma. / Financial stocks are often modeled by stochastic differential equations (SDEs). These equations could describe the behavior of the underlying asset as well as some of the model's parameters. For example, the Heston (1993) model, which is a stochastic volatility model, describes the behavior of the stock and the variance of the latter. The Heston model is very interesting since it has semi-closed formulas for some derivatives, and it is quite realistic. However, many simulation schemes for this model have problems when the Feller (1951) condition is violated. In this thesis, we introduce new simulation schemes to simulate price paths using the Heston model. These new algorithms are based on Broadie and Kaya's (2006) method. In order to increase the speed of the exact scheme of Broadie and Kaya, we use, among other things, Markov chains Monte Carlo (MCMC) algorithms and some well-chosen approximations. In our first algorithm, we modify the second step of the Broadie and Kaya's method in order to get faster schemes. Instead of using the second-order Newton method coupled with the inversion approach, we use a Metropolis-Hastings algorithm. The second algorithm is a small improvement of our latter scheme. Instead of using the real integrated variance over time p.d.f., we use Smith's (2007) approximation. This helps us decrease the dimension of our problem (from three to two). Our last algorithm is not based on MCMC methods. However, we still try to speed up the second step of Broadie and Kaya. In order to achieve this, we use a moment-matched gamma random variable. According to Stewart et al. (2007), it is possible to approximate a complex gamma convolution (somewhat near the representation given by Glasserman and Kim (2008) when T-t is close to zero) by a gamma distribution.

異質信念(Heterogeneous beliefs)修正傳統資產定價理論中同質信念(Homogeneous beliefs)的基本假設，探討投資者間所持有的不同資訊，以及對於資訊的不同參考程度，如何影響資產定價。 本文試圖以Banerjee(2008)的模型，估計出臺灣投資者對於台灣各家公司股票的價格參考密度；並且透過外部研究者的預測作為市場不同信念的代理變數，探討異質信念對於臺灣股市交易的價量影響。 經由實證結果發現，在台灣的股市交易市場上，當市場的資訊流通速度愈快，投資者對公開資訊的參考密度愈低，投資者愈易依賴自己所持有的私人資訊。當投資者的行為決策將愈顯紛歧時，對交易量和報酬率的影響皆為正。 / Heterogeneous beliefs, which revise the basic assumption of traditional asset pricing theory- Homogeneous beliefs, study the impact on asset pricing by different information owned and referred by investors. I use the model derived from Banerjee(2008)to estimate the degree how Taiwan investors will take into account stock prices when they make investment decisions. Also, I study how heterogeneous beliefs of investors influence stock prices and trading volume in Taiwan stock market, using predictions of external researchers as a proxy variable of dispersion in beliefs. The empirical results show that the degree which investors take into account prices will be lower when a faster information flowing speed exists in Taiwan stock market. When investors rely more on their private information, their investment decision will become much diversified. Dispersion in beliefs has a positive influence on stock trading volume and return.

Idag äger många svenskar andelar i olika fonder. Detta beror delvis på att det allmänna pensionssystemet i Sverige idag består av en premiepensionsdel, där individen kan göra ett individuellt val hur dennes pensionspengar ska investeras. Gemensamt för investerare är att de vill erhålla en god avkastning. Ett vanligt sätt att bedöma förväntad avkastning i en finansiell tillgång kallas Capital Asset Pricing Model, eller CAPM. Detta är en mycket behandlad, debatterad och även kritiserad modell. Förutom CAPM utgår studien från en nyare teori som heter Black Swan theory. År 2007 presenterade Taleb sin teori om Black Swan. Han menar att en Black Swan är en händelse som avviker från det normala, har långtgående effekter och som efteråt får naturliga förklaringar. Ett potentiellt Swan-fenomen är finanskrisen. Om nu finanskrisen kan räknas som ett Swan-fenomen innebär det att den finansiella verkligheten har förändrats. Om nu den finansiella världen har påverkats så finns det anledning att tro att även modeller och deras överensstämmelse med verkligheten har påverkats. Det är detta vi i denna studie ämnar att undersöka och mynnar därför ut i frågeställningen: Var CAPM en fungerande modell gällande Sverigefonder åren 2005-2014? Studiens syfte lyder enligt följande: Att undersöka hur väl CAPM:s prediktion av förväntad avkastning i Sverigefonder stämmer överens med den faktiska avkastningen. Vi vill också genom undersökningen se ifall denna överensstämmelse har förändrats under vår undersökningsperiod och ifall detta i sådana fall kan kopplas till ett potentiellt Swan-fenomen som finanskrisen. Med teoretisk utgångspunkt i modern portföljvalsteori, CAPM och Black Swan theory undersöks sambandet mellan betavärde och avkastning i Sverigefonder. Vi utgår från en positivistisk kunskapssyn och genom en deduktiv ansats genomförs en regressionsanalys för att svara på vår frågeställning. Det empiriska materialet består av månadsavkastning från de valda fonderna, riskfri ränta och marknadsindexets avkastning. I vår studie hade vi endast ett år med signifikant positivt samband mellan beta och avkastning (som försvann i och med heteroskedasticitet i datamaterialet). Vi hade däremot ett år med negativt signifikans (2014) samtidigt som en positiv marknad, vilket inte överensstämmer med tidigare empiriska undersökningar. Vissa år ser det ut som att det finns samband genom att grafiskt titta på våra figurer i resultatdelen, men det är även år där det motsatta förhållandet finns. Med resultaten och analysen i åtanke kan vi inte förkasta nollhypotesen 2005-2013 (det finns inget samband mellan beta och avkastning).

One of the main tenets of finance is diversification. Investors choose their portfolios so as to diversify away their idiosyncratic risk. In four essays included into this dissertation the implications of less than perfect diversification on investors’ performance and asset pricing are investigated. In Essay I we examine one particular instance in which diversification may play a role in a non-portfolio type of investment: the IPO. In an IPO, a set of potentially non-diversified investors – the existing shareholders – reduce their holdings of a company, listing the company and selling part of its shares. Our contribution is to show how portfolio diversification of controlling investors in private companies affects the IPO process. We demonstrate that companies sold by more diversified shareholders are less likely to be taken public, but when doing so they are priced more favourably. In Essays II and III we investigate the impact of incomplete diversification and imperfect risk-sharing on asset returns. Our argument is that the smaller shareholder base a firm has, the larger the fraction of company idiosyncratic risk on average its investors have to carry, and the higher return they would demand for that. We demonstrate that there is a negative and significant relationship between companies’ shareholder base and stock returns as well as between changes in shareholder base and stock returns. This effect is more pronounced for younger companies, but remains significant for seasoned companies as well. Applying our analysis to corporate events we demonstrate that abnormal performance following the repurchase can be partially explained by the reduction in the shareholders base resulting from repurchase. In Essay IV I investigate the motives behind one of the most puzzling examples of investors’ underdiversification – the local bias. Contrary to the predictions of classical financial theories, investors on aggregate overweight stock of proximate companies in their portfolios. I demonstrate that being placed in new community, individual investors not only soon become biased towards companies with establishments in this new locality, but they also obtain superior returns from these investments. Investing into the local stocks, therefore, is to a large degree rational. / Diss. Stockholm : Handelshögskolan, 2005 S. ii-vi: sammanfattning, s. 1-134: 4 uppsatser

Stocks, Bonds, and Long-Run Consumption Risks. Bansal and Yaron (2004) show that long-run consumption risks and time-varying economic uncertainty in conjunction with recursive preferences can account for important features of equity markets. I bring the model to the term structure of interest rates and show that a calibrated version of the model can simultaneously explain properties of bonds and equities. Specifically, the model accounts for deviations from the expectations hypothesis, the upward sloping nominal yield curve, and the predictive power of the nominal yield spread. However, an estimation of the model using Simulated Method of Moments yields less convincing results and illustrates the difficulty of precisely estimating parameters of the model. Real (nominal) interest rates in the model are positively (negatively) correlated with consumption growth and real stock returns move inversely with inflation. The cyclicality of nominal interest rates and yield spreads is shown to depend on the relative values of the elasticity of intertemporal substitution and the correlation between real consumption growth and inflation. The “Fed-model” and the Changing Correlation of Stock and Bond Returns: An Equilibrium Approach. This paper presents an equilibrium model that provides a rational explanation for two features of data that have been considered puzzling: The positive relation between US dividend yields and nominal interest rates, often called the Fed-model, and the time-varying correlation of US stock and bond returns. Key ingredients are time-varying first and second moments of consumption growth, inflation, and dividend growth in conjunction with Epstein-Zin and Weil recursive preferences. Historically in the US, inflation has signaled low future consumption growth. The representative agent therefore dislikes positive inflation shocks and demands a positive risk premium for holding assets that are poor inflation hedges, such as equity and nominal bonds. As a result, risk premiums on equity and nominal bonds comove positively through their exposure to macroeconomic volatility. This generates a positive correlation between dividend yields and nominal yields and between stock and bond returns. High levels of macro volatility in the late 1970s and early 1980s caused stock and bond returns to comove strongly. The subsequent moderation in aggregate economic risk has brought correlations lower. The model is able to produce correlations that can switch sign by including the covariances between consumption growth, inflation, and dividend growth as state variables. International Bond Risk Premia. We extend Cochrane and Piazzesi (2005, CP) to international bond markets by constructing forecasting factors for bond excess returns across different countries. While the international evidence for predictability is weak using Fama and Bliss (1987) regressions, we document that local CP factors have significant predictive power. We also construct a global CP factor and provide evidence that it predicts bond returns with high R2 across countries. The local and global factors are jointly significant when included as regressors, which suggests that variation in bond excess returns are driven by country-specific factors and a common global factor. Shocks to US bond risk premia seem to be particularly important determinants for international bond premia. Motivated by these results, we estimate a parsimonious no-arbitrage affine term structure model in which risk premia are driven by one local and one global CP factor. We find that international bond risk premia are driven by a local slope factor and a world interest rate level factor.