Imaginable surprise in global change science

Decisionmakers at all scales (individuals, firms, and local, national, and international governmental organizations) are concerned about reducing their vulnerability to (or the likelihood of) unexpected events, 'surprises.' After briefly and selectively reviewing the literature on uncertainty and surprise, we adopt a definition of 'surprise' that does not include the strict requirement that it apply to a wholly unexpected outcome, but rather recognizes that many events are often anticipated by some, even if not most observers. Thus, we define 'imaginable surprise' as events or processes that depart from the expectations of some definable community. Therefore, what gets labelled as 'surprise' depends on the extent to which what happens departs from community expectations and on the salience of the problem. We offer a typology of surprise that distinguishes imaginable surprises from risk and uncertainty, and develops several kinds of impediments to overcoming ignorances. These range from the need for more 'normal science' to phenomenological impediments (e.g., inherentunpredictability in some chaotic systems) to epistemological ignorance (e.g., ideological blocks to reducing ignorance). Based on the input of some two dozen scholars at an Aspen Global Change Institute Summer Workshop in 1994 *, we construct two tables in which participants offer many possible 'imaginable surprises' in the global change context, as well as their potential salience for creating unexpectedly high or low carbon dioxide emissions. Improving the anticipation of surprises is an interdisciplinary enterprise that should offer a sceptical welcoming of outlier ideas and methods.     

Modelling bonds and credit default swaps using a structural model with contagion

This paper develops a two-dimensional structural framework for valuing credit default swaps and corporate bonds in the presence of default contagion. Modelling the values of related firms as correlated geometric Brownian motions with exponential default barriers, analytical formulae are obtained for both credit default swap spreads and corporate bond yields. The credit dependence structure is influenced by both a longer-term correlation structure as well as by the possibility of default contagion. In this way, the model is able to generate a diverse range of shapes for the term structure of credit spreads using realistic values for input parameters.     

Modeling default risk with support vector machines

Predicting default risk is important for firms and banks to operate successfully. There are many reasons to use nonlinear techniques for predicting bankruptcy from financial ratios. Here we propose the so-called Support Vector Machine (SVM) to predict the default risk of German firms. Our analysis is based on the Creditreform database. In all tests performed in this paper the nonlinear model classified by SVM exceeds the benchmark logit model, based on the same predictors, in terms of the performance metric, AR. The empirical evidence is in favor of the SVM for classification, especially in the linear non-separable case. The sensitivity investigation and a corresponding visualization tool reveal that the classifying ability of SVM appears to be superior over a wide range of SVM parameters. In terms of the empirical results obtained by SVM, the eight most important predictors related to bankruptcy for these German firms belong to the ratios of activity, profitability, liquidity, leverage and the percentage of incremental inventories. Some of the financial ratios selected by the SVM model are new because they have a strong nonlinear dependence on the default risk but a weak linear dependence that therefore cannot be captured by the usual linear models such as the DA and logit models.     

Breast cancer risk perceptions and breast cancer worry: what predicts what?

This longitudinal study explored the relationship between perceived breast cancer risk and worry. We measured both absolute and comparative risk perceptions, and also used the Gail algorithm to assess the accuracy of participants' risk perceptions. Three hundred and one women ages 40–75 participated in a two‐part study assessing how format of breast cancer risk presentation affected perceptions of risk. Relative to their Gail scores, women were biased pessimistically about their own absolute breast cancer risk and yet largely accurate about their comparative breast cancer risk. Perceived comparative risk, but not perceived absolute risk or biases in absolute or comparative risk, predicted subsequent worry. Worry predicted subsequent perceived absolute risk and biases in absolute and comparative risk. These results suggest that women's emotional reactions to breast cancer risk are based on accurate (unbiased) perceptions of their comparative risks. In turn, greater worry prompts a re‐evaluation of absolute risk as well as changes in risk biases. Implications for screening are discussed.     

Consistent risk management: Three models outlined

This article introduces three models on how to understand the demand for consistent risk management. The first model, which accords with traditional risk analysis, is called the Standard Model. In this model, the decisive criterion of whether or not to accept a risk is if the total benefit exceeds the total cost. Since this model cannot protect the individual from unfair risk exposure two more models are outlined. The arguments in the Model of Inviolable Rights and in the Model of Procedural Justice evolve around the separateness of individuals, rights and fair risk taking. It is argued that risk management needs to acknowledge a variety of morally salient factors to avoid exposing people unfairly to risks.     

Basket trading under co-integration with the logistic mixture autoregressive model

In this paper, we propose a co-integration model with a logistic mixture auto-regressive equilibrium error (co-integrated LMAR), in which the equilibrium relationship among cumulative returns of different financial assets is modelled by a logistic mixture autoregressive time series model. The traditional autoregression (AR) based unit root test (ADF test), used in testing co-integration, cannot give a sound explanation when a time series passes the ADF test. However, its largest root in the AR polynomial is extremely close to, but less than, one, which is most likely the result of a mixture of random-walk and mean-reverting processes in the time series data. With this background, we put an LMAR model into the co-integration framework to identify baskets that have a large spread but are still well co-integrated. A sufficient condition for the stationarity of the LMAR model is given and proved using a Markovian approach. A two-step estimating procedure, combining least-squares estimation and the Expectation-Maximization (EM) algorithm, is given. The Bayesian information criterion (BIC) is used in model selection. The co-integrated LMAR model is applied to basket trading, which is a widely used tool for arbitrage. We use simulation to assess the model in basket trading strategies with the statistical arbitrage feature in equity markets. Data from several sectors of the Hong Kong Hang Seng Index are used in a simulation study on basket trading. Empirical results show that a portfolio using the co-integrated LMAR model has a higher return than portfolios selected by traditional methods. Although the volatility in the return increases, the Sharpe ratio also increases in most cases. This risk–return profile can be explained by the shorter converging period in the co-integrated LMAR model and the larger volatility in the ‘mean-reverting’ regime.     

The representation of American options prices under stochastic volatility and jump-diffusion dynamics

This paper considers the problem of pricing American options when the dynamics of the underlying are driven by both stochastic volatility following a square-root process as used by Heston [Rev. Financial Stud., 1993, 6, 327–343], and by a Poisson jump process as introduced by Merton [J. Financial Econ., 1976, 3, 125–144]. Probability arguments are invoked to find a representation of the solution in terms of expectations over the joint distribution of the underlying process. A combination of Fourier transform in the log stock price and Laplace transform in the volatility is then applied to find the transition probability density function of the underlying process. It turns out that the price is given by an integral dependent upon the early exercise surface, for which a corresponding integral equation is obtained. The solution generalizes in an intuitive way the structure of the solution to the corresponding European option pricing problem obtained by Scott [Math. Finance, 1997, 7(4), 413–426], but here in the case of a call option and constant interest rates.     

Variance swap dynamics

We compare several parametric and non-parametric approaches for modelling variance swap curves by conducting an in-sample and an out-of-sample analysis using market prices. The forecasted Heston model gives the best overall performance. Moreover, the static Heston model highlights some problems of stochastic volatility models in option pricing of forward starting products.