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Within the context of risk integration, we introduce risk measurement stochastic holding period (SHP) models. This is done in order to obtain a ‘liquidity-adjusted risk measure’ characterized by the absence of a fixed time horizon. The underlying assumption is that—due to changes in market liquidity conditions—one operates along an ‘operational time’ to which the P&L process of liquidating a market portfolio is referred. This framework leads to a mixture of distributions for the portfolio returns, potentially allowing for skewness, heavy tails, and extreme scenarios. We analyze the impact of possible distributional choices for the SHP. In a multivariate setting, we hint at the possible introduction of dependent SHP processes, which potentially lead to nonlinear dependence among the P&L processes and therefore to tail dependence across assets in the portfolio, although this may require drastic choices on the SHP distributions. We also find that increasing dependence as measured by Kendall’s tau through common SHPs appears to be unfeasible. We finally discuss potential developments following future availability of market data. This chapter is a refined version of the original working paper by Brigo and Nordio (2010) [14].

The paper deals with the question of how to restore lost confidence in the results of internal models (especially market risk models). This is an important prerequisite for continuing to use these models as a basis for calculating risk-sensitive prudential capital requirements. The authors argue that restoring confidence is feasible. Contributions to this end will be made both by the reform of regulatory requirements under Basel 2.5 and the Trading Book Review and by refinements of these models by the banks themselves. By contrast, capital requirements calculated on the basis of a leverage ratio and prudential standardised approaches will not be sufficient, even from a regulatory perspective, owing to their substantial weaknesses. Specific proposals include standardising models with a view to reducing complexity and enhancing comparability, significantly improving model validation and increasing transparency as to how model results are determined, also over time. The article reflects the personal views of the authors.

We are concerned with determining the model risk of contingent claims when markets are incomplete. Contrary to existing measures of model risk, typically based on price discrepancies between models, we develop value-at-risk and expected shortfall measures based on realized P&L from model risk, resp. model risk and some residual market risk. This is motivated, e.g., by financial regulators’ plans to introduce extra capital charges for model risk. In an incomplete market setting, we also investigate the question of hedge quality when using hedging strategies from a (deliberately) misspecified model, for example, because the misspecified model is a simplified model where hedges are easily determined. An application to energy markets demonstrates the degree of model error.

This paper puts the concepts of model and calibration risks into the perspective of bid and ask pricing and marketed cash-flows which originate from the conic finance theory. Different asset pricing models calibrated to liquidly traded derivatives by making use of various plausible calibration methodologies lead to different risk-neutral measures which can be seen as the test measures used to assess the (un)acceptability of risks.

We consider the supOU stochastic volatility model which is able to exhibit long-range dependence. For this model, we give conditions for the discounted stock price to be a martingale, calculate the characteristic function, give a strip where it is analytic, and discuss the use of Fourier pricing techniques. Finally, we present a concrete specification with polynomially decaying autocorrelations and calibrate it to observed market prices of plain vanilla options.

We present a multivariate jump-diffusion model incorporating stochastic volatility and two-sided jumps for multicurrency FX markets, which is an extension of the univariate -OU-BNS model introduced by [2]. The model can be considered a multivariate variant of the two-sided -OU-BNS model (cf. [1]). We discuss FX option pricing and provide a calibration exercise, modeling two FX rates with a common currency by a bivariate model and calibrating the dependence parameters to the implied FX volatility surface.

The literature on stochastic models for the spot market of gas is dominated by purely stochastic approaches. In contrast to these models, Stoll and Wiebauer [14] propose a fundamental model with temperature as an exogenous factor. A model containing only deterministic, temperature-dependent and purely stochastic components, however, still seems not able to capture economic influences on the price. In order to improve the model of Stoll and Wiebauer [14], we include the oil price as another exogenous factor. There are at least two fundamental reasons why this should improve the model. First, the oil price can be considered as a proxy for the general state of the world economy. Furthermore, pricing formulas in oil price indexed gas import contracts in Central Europe are covered by the oil price component. It is shown that the new model can explain price movements of the last few years much better than previous models. The inclusion of oil price and temperature in the regression of a least squares Monte Carlo method leads to more realistic valuation results for gas storages and swing options.

Traditionally, banks estimate their economic capital which has to be reserved for unexpected credit losses with individual credit portfolio models. Many of those have its roots in the or in the framework, which were both launched in 1997. Motivated by the current regulatory requirements, banks are required to analyze how sensitive their models (and the resulting risk figures) are with respect to the underlying assumptions. Within this context, we concentrate on the dependence structure in terms of copulas in both frameworks. By replacing the underlying copula and using other popular competitors instead, we quantify the effect on the tail, in general, and on the risk figures in specific for a hypothetical loan portfolio.

Credit spreads provide information about implied default probabilities and recovery rates. Trying to extract both parameters simultaneously from market data is challenging due to identifiability issues. We review existing default models with stochastic recovery rates and try calibrating them to observed credit spreads. We discuss the mechanisms of credit auctions and compare implied recoveries with realized auction results in the example of Allied Irish Banks (AIB).

Currency carry trade is the investment strategy that involves selling low interest rate currencies in order to purchase higher interest rate currencies, thus profiting from the interest rate differentials. This is a well known financial puzzle to explain, since assuming foreign exchange risk is uninhibited and the markets have rational risk-neutral investors, then one would not expect profits from such strategies. That is, according to uncovered interest rate parity (UIP), changes in the related exchange rates should offset the potential to profit from such interest rate differentials. However, it has been shown empirically, that investors can earn profits on average by borrowing in a country with a lower interest rate, exchanging for foreign currency, and investing in a foreign country with a higher interest rate, whilst allowing for any losses from exchanging back to their domestic currency at maturity.

This paper explores the financial risk that trading strategies seeking to exploit a violation of the UIP condition are exposed to with respect to multivariate tail dependence present in both the funding and investment currency baskets. It will outline in what contexts these portfolio risk exposures will benefit accumulated portfolio returns and under what conditions such tail exposures will reduce portfolio returns.