In this paper, we study the asset pricing implication of imprecise knowledge about rare events. Modeling rare events as jumps in the aggregate endowment, we explicitly solve the equilibrium asset prices in a pure-exchange economy with a representative agent who is averse not only to risk but also to model uncertainty with respect to rare events. Our results show that there are three components in the equity premium: the diffusive-risk premium, the jump-risk premium, and the "rare event premium." While the first two premia are generated by risk aversion, the last one is driven exclusively by uncertainty aversion. To dis-entangle the "rare event premium" from the standard risk-based premia, we examine the equilibrium prices of options with varying degree of moneyness. We consider models with different levels of uncertainty aversion -- including the one with zero uncertainty aversion, and calibrate all models to the same level of equity premium. Although observationally equivalent with respect to the equity market, these models provide distinctly different predictions on the option market. Without incorporating uncertainty aversion, the standard model cannot explain the extent of the premia implicit in options, particularly the prevalent "smirk" patterns documented in the index options market. In contrast, the models incorporating uncertainty aversion can generate significant premia for at-the-money option prices, as well as pronounced "smirk" patterns for options with different degrees of moneyness.

Estimating risk premia has been at the forefront of the financial economics' literature due to their informational content. Risk premia are of particular interest to academics, policymakers and practitioners given the information they disclose on expected asset returns for a given level of risk, their contribution in asset pricing and their ability to disentangle the different sources of risk. However, risk premia are unobserved and their estimates strongly differ from one study to another, as they are highly sensitive to the specification of the underlying model, sparking hence a strong interest in their analysis. The aim of the thesis is to estimate risk premia in a dynamic term structure model setting. The first part of the thesis comprises of an overview of a particular class of dynamic term structure models, namely affine term structure models. The overview will include important concepts and definitions. The second part of the thesis uses a risk-averse formulation of the uncovered interest rate parity to determine exchange rates through interest rate differentials, and ultimately extract currency risk premia. The method proposed consists of developing an affine Arbitrage-Free class of dynamic Nelson-Siegel term structure models (AFNS) with stochastic volatility to obtain the domestic and foreign discount rate variations, which in turn are used to derive a representation of exchange rate depreciations and risk premia. The third part of the thesis studies both the nominal and real UK term structure of interest rates using a Gaussian dynamic term structure model, which imposes the non-negativity of nominal short maturity rates. Estimates of the term premia, inflation risk premia and market-implied inflation expectations are provided.

The work presented in this dissertation can be grouped around two major themes. The first theme relates to the asset allocation and the second theme relates to risk management. In Chapter Three, we investigate the dynamics of foreign exchange and stock returns based on an extended version of Sentana and Wadhwani (1992) model. This study is mainly driven by the wish to explain two major stylized facts that puzzled the older models. We find evidence to support that only intertemporal variation in the foreign exchange risk premium can be explained by time¡Vvarying covariance priced risk factors. Furthermore, we also find that the first order autocorrelation of both foreign exchange and stock market returns in Taiwan is negatively related to the level of conditional volatility and covariance. This time-varying nature of the serial correlation pattern is consistent with our model where some traders follow feedback strategies. The three nested asset pricing models with four models of conditional second moments are strongly rejected. We conclude that our extended Sentana and Wadhwani model is more adequate in explaining the dynamics of foreign exchange and stock markets. In Chapter Four, we investigate the risk management of futures market and spot market returns. There is widespread evidence that the volatility of stock returns display an asymmetric response to good and bad news. This paper attempted and found the asymmetric behavior co-existence in spot as well as future markets. By using the Asymmetric Dynamic Model (ADC) proposed by Kroner and Ng (1998), we estimated the conditional covariance matrix asymmetric and calculated dynamic optimal hedge ratios. With the help of that asymmetric model, our ¡§out of sample¡¨ dynamic hedging strategy out-performed that of normally dynamic hedging strategies. However, while taking the transaction costs into consideration, the performance was even worse than that of the static strategy.

Purpose: The purpose of this study is to examine the bi-directional causality between political uncertainty and the market risk premium in the US. Design/methodology/approach: I use a theoretical model to motivate signs and then check signs based on a vector autoregression. Findings: I find that political uncertainty has a small positive, delayed effect on the market risk premium. The market risk premium, on the other hand, has a large permanent, negative effect on political uncertainty. Originality/value: This is the first research paper to consider the bi-directional effects of political uncertainty on the market risk premium and vice versa. It also finds interesting empirical results.

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I propose a global risk factor – Currency Traded Risk (CTR). This risk factor is the first to identify the directional link between currencies and equities. CTR captures the genesis of financial globalization, and contains the greatest predictive ability to date for monthly returns on a global stock portfolio. Theoretically, return expectation is intimately linked to time-varying risk premia. Due to the intrinsic scope of currency values in integrating the world’s financial markets, information on time-varying risk premia prices into currencies at greater speed, scale, and global consensus, relative other asset classes. High interest rate currencies proxy as a risk-on asset class. Low interest rate currencies proxy as a risk-off asset class. Innovations in these currencies’ values summarize global risk premia and forecast equity market returns. CTR measures two sources of global risk premia; the difference between averaged spot returns of high interest rate currencies and low interest rate currencies, and the difference between implied and realized volatility of high interest rate currencies. Using recursive regressions, CTR predicts monthly MSCI World Index© returns out of sample, with R2’s consistent at 10% from 2008 to 2017. Currencies track global risk premia, whereas equities respond to it.

The estimation results of Brazilian risk premia are not robust in the literature. For instance, among the 133 market risk premium estimates reported on the literature, 41 are positives, 18 are negatives and the remainder are not significant. In this study, we investigate the grounds for this lack of consensus. First of all, we analyze the sensitivity of the US risk premia estimation to two relevant constraints present in the Brazilian market: the small number of assets (137 eligible stocks) and the short time-series sample available for estimation (14 years). We conclude that the second constrain, small T, has greater impact on the results. Following, we evaluate the two potential causes of problems for the risk premia estimation with small T: i) small sample bias on betas; ii) divergence between ex-post and ex-ante risk premia. Through Monte Carlo simulations, we conclude that for the T available for Brazil, the betas estimates are no longer a problem. However, it is necessary to wait until 2041 to be able to estimate ex-ante risk premia with Brazilian data. / Os resultados das estimações de prêmios de risco brasileiros não são robustos na literatura. Por exemplo, dentre 133 estimativas de prêmio de risco de mercado documentadas, 41 são positivas, 18 negativas e o restante não é significante. No presente trabalho, investigamos os motivos da falta de consenso. Primeiramente, analisamos a sensibilidade da estimação dos prêmios de risco norte-americanos a duas restrições presentes no mercado brasileiro: o baixo número de ativos (137 ações elegíveis) e a pequena quantidade de meses disponíveis para estimação (14 anos). Concluímos que a segunda restrição, T pequeno, tem maior impacto sobre os resultados. Em seguida, avaliamos as duas potenciais causas de problemas para a estimação de prêmios de risco em amostras com T pequeno: i) viés de pequenas amostras nas estimativas dos betas; e ii) divergência entre prêmio de risco ex-post e ex-ante. Através de exercícios de Monte Carlo, concluímos que para o T disponível no Brasil, a estimativa dos betas já não é mais um problema. No entanto, ainda precisamos esperar até 2041 para conseguirmos estimar corretamente os prêmios ex-ante com os dados brasileiros.

The purpose of this thesis is to examine the nonlinear relationships between financial (and economic) variables within the field of financial econometrics. The thesis comprises two reviews of literatures, one on nonlinear time series models andthe other one on term structure of interest rates, and four empirical essays on financialapplications using nonlinear modelling techniques. The first empirical essay compares different model specifications of a Markov switching CIR model on the term structure of UK interest rates. We find the least restricted model provides the best in-sample estimation results. Although models with restrictive specifications may provide slightly better out-of-sample forecasts in directional movements of the yields, the economic gains seem to be small. In the second essay, we jointly model the nominal and real term structure of the UK interest rates using a three-factor essentially affine no-arbitrage term structure model. The model-implied expected inflation rates are then used in the subsequent analysis on its nonlinear relationship with the FTSE 100 index return premiums, utilizing a smooth transition vector autoregressive model. We find the model implied expected inflation rates remain below the actual inflation rates after the independence of the Bank of England in 1997, and the recent sharp decline of the expected inflation rates may lend support to the standing ground of the central bank for keeping interest rates low. The nonlinearity test on the relationship between the FTSE 100 index return premiums and the expected inflation rates shows that there exists a nonlinear adjustment on the impact from lagged expected inflation rates to current return premiums. The third essay provides us additional insight into the nature of the aggregate stock market volatilities and its relationship to the expected returns, in a Markov switching model framework, using centuries-long aggregate stock market data from six countries (Australia, Canada, Sweden, Switzerland, UK and US). We find that the Markov switching model assuming both regime dependent mean and volatility with a 3-regime specification is capable to captures the extreme movements of the stock market which are short-lived. The volatility feedback effect that we studied on each of these six countries shows a positive sign on anticipating a high volatility regime of the current trading month. The investigation on the coherence in regimes over time for the six countries shows different results for different pairs of countries. In the last essay, we decompose the term premium of the North American CDX investment grade index into a permanent and a stationary component using a Markov switching unobserved component model. We explain the evolution of the two components in relating them to monetary policy and stock market variables. We establish that the inversion of the CDX index term premium is induced by sudden changes in the unobserved stationary component, which represents the evolution of the fundamentals underpinning the risk neutral probability of default in the economy. We find strong evidence that the unprecedented monetary policy response from the Fed during the crisis period was effective in reducing market uncertainty and helped to steepen the term structure of the CDX index, thereby mitigating systemic risk concerns. The impact of stock market volatility on flattening the term premium was substantially more robust in the crisis period. We also show that equity returns make a significant contribution to the CDX term premium over the entire sample period.

Residential property price premia (‘premia’) have long fascinated investors, particularly in times of euphoria, but their social, climatic and urban ramifications are much wider. A proper understanding of premia is hindered by the variety of exogenous influences determining them. They occur within idiosyncratic, complex, and continuously reconfiguring metropoli, conditioned by topography, history, regime, commerce, and culture. Given imperfectly competitive housing markets, conventional explanations for premia are either restricted to their financial dissection, trawl though metrics or cast around for hedonic coefficients. However, premia illuminate affordability and other problems in the broader planning and social debate. With the general significance of premia clarified, the research question of the project becomes: ‘What drives residential property price premium evolution in a metropolis?’ A complete answer involves dissecting the nature and establishing the location of putative premia and disentangling the influence and interactions of their various price drivers. To provide it, the project conducts a property and urban literature review. Based on theory’s insight that higher order contains lower order systems, it develops and investigates a general systems model of residential premia with two modes. The system is conditioned by ideology but forced by population and capital inflows. Within it, premia mutate, influenced by a nested hierarchy of more or less contaminated information. To investigate the model and its different modes, the project employs tests across system pointers, at the macro, meso (all urban) and micro spatial resolutions. First, the turbulence and permeability of residential property markets to exogenous influences is assessed. The project then looks at the urban mosaic in the growing Sunbelt migration city of Brisbane, Australia, over the boom period from 1998-2004. Locally, it conducts a case study and survey in one micro-location, seeking clues in transaction patterns (output), property system agents (components) and the information they use (feedback mechanisms). Finally, the project draws some relevant policy implications. Its key findings are that urban housing markets are open, complex and polarised. In an exuberant economic climate, migration and debt fuel metropolitan price escalation. Public urban initiatives reinforce central incumbent affluence or spark fresh bouts of speculation. Individual premia are heterogeneous but often feed off local construction projects or iconic refurbishment. Reflecting their demographics and motives, agent risk appetites are diverse although investors are usually less averse to renewal. System feedback involves a congruence of media and local activity signals. Neither local conviviality nor Bohemian influences are, by themselves, significant. Rather, buyer rationality is validated by post-purchase infrastructure completions. The thesis of this project is, hence, that in euphoric capital markets, migration and debt accelerates the endogenous mutation of property from homes within a community towards speculative paper assets. The implication is that the excessive proliferation of premia indicates economic imbalance and urban malaise which requires recognition and treatment. While premia are paid for perceived privilege or prospects, cognitive risk representations and expectations evolve. Sometimes judgment is contaminated by media fantasy but often validated by accommodating government policy and central revitalisation projects. Yet, within a wider social and ecological remit, rampant premia suggest flaws in urban strategy, governance and planning practice. In terms of windfall events or unearned rent, the cumulative effects of ill-considered projects and price distortions can be ugly and wasteful. They alienate and accentuate spatial privilege without generating sustainable jobs. The project has procedural and substantive policy implications. The dynamics of residential premia cannot be disentangled from capital market volatility, urban fragmentation and reconstitution. Enlightened property development requires visionary urban planning beyond electoral cycles. Rather than unregulated markets or disjointed incrementalism, the project points to the advantages of cohesive projects and inclusive hubs. It impels ecological and people-focused development to nurture capable, connected and considerate edge communities. Its first steps are theoretical recognition, policy clarification, government reform, market constraints, price and tax rationalisation and spatial transparency.

Economics