This dissertation is centered around two comprehensive themes: the extraction of information embedded in equity index option prices, and how to use this information in order to be able to make optimal decisions in the equity index option markets. These problems are important for decision makers in the equity index options markets, since they are continuously faced with making decisions under uncertainty given observed market prices. The methods developed in this dissertation provide robust tools that can be used by practitioners in order to improve the quality of the decisions that they make. In order to be able to extract information embedded in option prices, the dissertation develops two different methods for estimation of stable option implied surfaces which are consistent with observed market prices. This is a difficult and ill-posed inverse problem which is complicated by the fact that observed option prices contain a large amount of noise stemming from market micro structure effects. Producing estimated surfaces that are stable over time is important since otherwise risk measurement of derivatives portfolios, pricing of exotic options and calculation of hedge parameters will be prone to include significant errors. The first method that we develop leads to an optimization problem which is formulated as a convex quadratic program with linear constraints which can be solved very efficiently. The second estimation method that we develop in the dissertation makes it possible to produce local volatility surfaces of high quality, which are consistent with market prices and stable over time. The high quality of the surfaces estimated with the second method is the crucial input to the research which has resulted in the last three papers of the dissertation. The stability of the estimated local volatility surfaces makes it possible to build a realistic dynamic model for the equity index derivatives market. This model forms the basis for the stochastic programming (SP) model for option hedging that we develop in the dissertation. We show that the SP model, which uses generated scenarios for the squared local volatility surface as input,  outperforms the traditional hedging methods that are described in the literature. Apart from having an accurate view of the variance of relevant risk factors, it is when building a dynamic model also important to have a good estimate of the expected values, and thereby risk premia, of those factors. We use a result from recently published research which lets us recover the real-world density from only a cross-section of observed option prices via a local volatility model. The recovered real-world densities are then used in order to identify and estimate liquidity premia that are embedded in option prices. We also use the recovered real-world densities in order to test how well the option market predicts the realized statistical characteristics of the underlying index. We compare the results with the performance of commonly used models for the underlying index. The results show that option prices contain a premium in the tails of the distribution. By removing the estimated premia from the tails, the resulting density predicts future realizations of the underlying index very well.

Competition over access for mates has led to the evolution of many striking examples of morphological traits and behaviour in animals. The rapid development of the sexual selection field in recent decades have dramatically advanced our understanding of what traits make individuals more successful in attracting mates and how preferences for mates evolve over time. However, till now, research in this field has put less emphasis on the mechanisms that underlie variation in mate choice and sexual behaviour. Cognitive processes could potentially be key drivers of individual variation in mating preferences and sexual behaviours and therefore deserve further investigation. In this thesis, I used guppies artificially selected for relative brain size as the model system to study the association between brain size, cognitive ability and various aspects of mate choice. Previous studies in this model system showed that large-brained individuals of both sexes outperformed small-brained individuals in cognitive tests. Here I quantified their sexual behaviours and mating preferences to provide novel empirical data concerning the association between brain size, cognitive ability and sexual selection. In dichotomous choice preference tests based on visual cues, comparisons between large-brained and small-brained guppies showed important differences in their assessment of mate quality. These results are not driven by pre-existing visual biases caused by the artificial selection since further investigation of the visual capacity of these fish detected no differences between large-brained and small-brained individuals in their sensitivity to colour or in their capacity to resolve spatial detail. I also quantified sexual behaviour in male guppies artificially selected for relative brain size and found no difference in the behaviours of large-brained and small-brained males in a single male-single female non-competitive scenario. On the contrary, in a more complex social setting I found a reduction in large-brained males in the rate of courtship towards females and dominance displays towards other males when exposed to different degrees of predation threat and different numbers of male competitors. However, this reduction in behavioural intensity did not result in a lower access to copulation with females for large-brained males. I likewise evaluated female sexual behaviour and found that large-brained females had higher behavioural flexibility such that they decreased their receptiveness towards males more strongly under higher levels of predation threat. Together, these results provide novel empirical evidence that brain size and cognitive ability are tightly linked to mating preferences and sexual behaviours. These findings suggest that brain size and cognitive ability might be important mechanisms behind variation in mating preferences and in sexually selected traits across and within species. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 2: Manuscript. Paper 3: Manuscript. Paper 5: Manuscript.</p>