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This paper investigates the calibration of co-movement indices such as the implied correlation index (ICX) and the herd behavior index (HIX) to different kind of stochastic processes. Both of them give an accurate description of the future level of market fear. The implied correlation index emerges when we match the observed index option price with the corresponding model price. The underlying model assumes that the individual stocks are characterized by a log-normal distribution whereas the dependence structure is described by a Gaussian copula. The herd behavior index is obtained by comparing the observed market situation with the extreme theoretical situation where all the market is driven by one single factor. This alternative measure is model-free. As an illustration, we will use the Dow Jones Industrial Average spanning from January $2000$ until October $2009$ to construct both time series. The numerical study undertakes the hard task to find a suitable model for them. These models are built by combining a stochastic differential equation with a monotonic mapping function which maps the definition domain to the unit interval. The such obtained diffusion process preserve, to some extent, the fundamental properties of the so-called herd behavior indices.

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This book covers recent developments in the interdisciplinary fields of actuarial science, quantitative finance, risk- and asset management. The authors are leading experts from academia and practice who participated in Innovations in Insurance, Risk- and Asset Management, an international conference held at the Technical University of Munich in 2017. The topics covered include the mathematics of extreme risks, systemic risk, model uncertainty, interest rate and hybrid models, alternative investments, dynamic investment strategies, quantitative risk management, asset liability management, liability driven investments, and behavioral finance. This timely selection of topics is highly relevant for the financial industry and addresses current issues both from an academic as well as from a practitioner's point of view.

Dynamic Hedging --- Uncertainty Quantification --- Actuarial Science --- Copula --- Exchange-Traded Funds --- Autoregressive Hidden Markov Models --- Fixed Income --- Reinsurance --- Stochastic Processes for Finance --- Risk Measure --- Bayesian Finance --- Insurance --- Replicating Portfolio --- Risk Classification --- Stochastic Dominance

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This thesis provides an algorithm for calculating the Herd Behaviour Index (HIX), which is a model-free measure introduced by Dhaene et al. (2012), aiming at quantifying the degree of co-movement implied in the stock market. The algorithm is demonstrated through calculating the HIX for the Dow Jones Industrial Average (DJIA), namely the DJ-HIX, in January 2008. Different from the practice of Dhaene et al. (2012), it uses the minimal necessary information about the options of the DJIA and its constituents. The results show that, while the DJ-HIX computed by the algorithm are on average 10% higher than the results given by Dhaene et al. (2012), they follow almost the same trend. It is revealed that, by using different methodologies for determining the K-support, the results may deviate significantly. It is recommended to take further research on the issue to find an ideal criterion for the K-support determination.

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The business of life insurers is highly influenced by the interest rate curve, as their future benefits are discounted by it. However, there is no straightforward assumption to determine the correct discount curve. In this thesis we will investigate the Heath, Jarrow and Morton method to model a proper discount curve. Using forward rate data provided by the Bank of England, we apply this stochastic model to determine the future dynamics of the discount curve. Afterwards, we apply this framework to price two classical life insurance products and examine the impact of future unpredictable changes in the discount curve on the future policy values of these products. This risk is called systematic interest rate risk.

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Every company takes risks in one way or another. If a risk pays off, the company can than use this gain, material or immaterial, to its benefit, but if the risk goes wrong, this can lead to huge losses and even bankruptcy. Therefore, most companies hold some capital resources in reserve in order to compensate possible losses. Those reserves are often referred to as economic capital. As companies face different risks, they can assign separate amounts of economic capital to offset the exposure to these risks and remain economically solvent. However, companies often look at risks simultaneously because the gains from one risk may compensate the loss of another. Instead of assigning economic capital separately for every risk, a company tries to find an aggregated amount of capital to cover all the risks at once. This concept is known as `capital aggregation'. By aggregating capital, less economic capital is usually needed to remain economically solvent and more capital is available for investments. However, it is a priori difficult to find a clear cut method in order to correctly connect risks and determine the total amount of aggregated capital. This thesis discusses four different methods to obtain the economic capital of linearly aggregated risks.