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  • 1
    Publication Date: 2020-07-01
    Description: This paper studies the effect of variance swap in hedging volatility risk under the mean-variance criterion. We consider two mean-variance portfolio selection problems under Heston’s stochastic volatility model. In the first problem, the financial market is complete and contains three primitive assets: a bank account, a stock and a variance swap, where the variance swap can be used to hedge against the volatility risk. In the second problem, only the bank account and the stock can be traded in the market, which is incomplete since the idiosyncratic volatility risk is unhedgeable. Under an exponential integrability assumption, we use a linear-quadratic control approach in conjunction with backward stochastic differential equations to solve the two problems. Efficient portfolio strategies and efficient frontiers are derived in closed-form and represented in terms of the unique solutions to backward stochastic differential equations. Numerical examples are provided to compare the solutions to the two problems. It is found that adding the variance swap in the portfolio can remarkably reduce the portfolio risk.
    Electronic ISSN: 2227-9091
    Topics: Economics
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  • 2
    Publication Date: 2020-07-01
    Description: We study numerical algorithms for reflected anticipated backward stochastic differential equations (RABSDEs) driven by a Brownian motion and a mutually independent martingale in a defaultable setting. The generator of a RABSDE includes the present and future values of the solution. We introduce two main algorithms, a discrete penalization scheme and a discrete reflected scheme basing on a random walk approximation of the Brownian motion as well as a discrete approximation of the default martingale, and we study these two methods in both the implicit and explicit versions respectively. We give the convergence results of the algorithms, provide a numerical example and an application in American game options in order to illustrate the performance of the algorithms.
    Electronic ISSN: 2227-9091
    Topics: Economics
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  • 3
    Publication Date: 2020-07-16
    Description: We present a statistical model which can be employed to understand the contagion dynamics of the COVID-19, which can heavily impact health, economics and finance. The model is a Poisson autoregression of the daily new observed cases, and can reveal whether contagion has a trend, and where is each country on that trend. Model results are exemplified from some observed series.
    Electronic ISSN: 2227-9091
    Topics: Economics
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  • 4
    Publication Date: 2020-07-01
    Description: An essential input of annuity pricing is the future retiree mortality. From observed age-specific mortality data, modeling and forecasting can take place in two routes. On the one hand, we can first truncate the available data to retiree ages and then produce mortality forecasts based on a partial age-range model. On the other hand, with all available data, we can first apply a full age-range model to produce forecasts and then truncate the mortality forecasts to retiree ages. We investigate the difference in modeling the logarithmic transformation of the central mortality rates between a partial age-range and a full age-range model, using data from mainly developed countries in the Human Mortality Database (2020). By evaluating and comparing the short-term point and interval forecast accuracies, we recommend the first strategy by truncating all available data to retiree ages and then produce mortality forecasts. However, when considering the long-term forecasts, it is unclear which strategy is better since it is more difficult to find a model and parameters that are optimal. This is a disadvantage of using methods based on time-series extrapolation for long-term forecasting. Instead, an expectation approach, in which experts set a future target, could be considered, noting that this method has also had limited success in the past.
    Electronic ISSN: 2227-9091
    Topics: Economics
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  • 5
    Publication Date: 2020-07-01
    Description: This paper provides an econometric analysis aiming at evidencing the dynamics showed by the S&P 500 market index during the period of 4 January 2001–28 April 2020, in which the subprime crisis has taken place and the COVID-19 crisis has begun. In particular, we fit a three-regime switching model that allows market parameters to behave differently during economic downturns, with the regimes representative of the tranquil, volatile, and turbulent states. We document that the tranquil regime is the most frequent for the whole period, while the dominant regime is the volatile one for the crisis of 2008 and the turbulent one for the first four months of 2020. We fit the same model to the returns of the Dow Jones Industrial Average index and find that during the same period of investigation, the most frequent regime has been the tranquil one, while the volatile and turbulent regimes share the same frequencies. Additionally, we use a multinomial logit model to describe the probabilities of volatile or turbulent regimes. We show that, in the case of the S&P 500 index, the returns from the Volatility Index (VIX) index are significant for both the volatile and the turbulent regimes, while the gold, WTI oil, and the dollar indices have some explanatory power only for the turbulent regime.
    Electronic ISSN: 2227-9091
    Topics: Economics
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  • 6
    Publication Date: 2020-07-06
    Description: We studied the volatility assumption of non-life premium risk under the Solvency II Standard Formula and developed an empirical model on real data, the Danish fire insurance data. Our empirical model accomplishes two things. Primarily, compared to the present literature, this paper innovates the fitting of Danish fire insurance data using a composite model with a random threshold. Secondly we prove, by fitting the Danish fire insurance data, that for large insurance companies the volatility of the standard formula is higher than the volatility estimated with internal models such as composite models, also taking into account the dependence between attritional and large claims.
    Electronic ISSN: 2227-9091
    Topics: Economics
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  • 7
    Publication Date: 2020-07-02
    Description: In this study, we use Neural Networks (NNs) to price American put options. We propose two NN models—a simple one and a more complex one—and we discuss the performance of two NN models with the Least-Squares Monte Carlo (LSM) method. This study relies on American put option market prices, for four large U.S. companies—Procter and Gamble Company (PG), Coca-Cola Company (KO), General Motors (GM), and Bank of America Corp (BAC). Our dataset is composed of all options traded within the period December 2018 until March 2019. Although on average, both NN models perform better than LSM, the simpler model (NN Model 1) performs quite close to LSM. Moreover, the second NN model substantially outperforms the other models, having an RMSE ca. 40% lower than the presented by LSM. The lower RMSE is consistent across all companies, strike levels, and maturities. In summary, all methods present a good accuracy; however, after calibration, NNs produce better results in terms of both execution time and Root Mean Squared Error (RMSE).
    Electronic ISSN: 2227-9091
    Topics: Economics
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  • 8
    Publication Date: 2015-06-04
    Description: New risk-based solvency requirements for insurance companies across European markets have been introduced by Solvency II and will come in force from 1 January 2016. These requirements, derived by a Standard Formula or an Internal Model, will be by far more risk-sensitive than the required solvency margin provided by the current legislation. In this regard, a Partial Internal Model for Premium Risk is developed here for a multi-line Non-Life insurer. We follow a classical approach based on a Collective Risk Model properly extended in order to consider not only the volatility of aggregate claim amounts but also expense volatility. To measure the effect of risk mitigation, suitable reinsurance strategies are pursued. We analyze how naïve coverage as conventional Quota Share and Excess of Loss reinsurance may modify the exact moments of the distribution of technical results. Furthermore, we investigate how alternative choices of commission rates in proportional treaties may affect the variability of distribution. Numerical results are also figured out in the last part of the paper with evidence of different effects for small and large companies. The main reasons for these differences are pointed out.
    Electronic ISSN: 2227-9091
    Topics: Economics
    Published by MDPI
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  • 9
    Publication Date: 2015-09-11
    Description: In this paper, we study the valuation of stochastic cash flows that exhibit dependence on interest rates. We focus on insurance liability cash flows linked to an index, such as a consumer price index or wage index, where changes in the index value can be partially understood in terms of changes in the term structure of interest rates. Insurance liability cash flows that are not explicitly linked to an index may still be valued in our framework by interpreting index returns as so-called claims inflation, i.e., an increase in claims cost per sold insurance contract. We focus primarily on the case when a deep and liquid market for index-linked contracts is absent or when the market price data are unreliable. Firstly, we present an approach for assigning a monetary value to a stochastic cash flow that does not require full knowledge of the joint dynamics of the cash flow and the term structure of interest rates. Secondly, we investigate in detail model selection, estimation and validation in a Heath–Jarrow–Morton framework. Finally, we analyze the effects of model uncertainty on the valuation of the cash flows and how forecasts of cash flows and interest rates translate into model parameters and affect the valuation.
    Electronic ISSN: 2227-9091
    Topics: Economics
    Published by MDPI
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  • 10
    Publication Date: 2015-09-15
    Description: This paper develops an extended financial stress measure that considers the supervisory objective of identifying risks to the stability of the financial system. The measure provides a continuous and bounded signal of financial stress using daily public market data. Broad coverage of material financial system markets over time is achieved by leveraging dynamic credit weights. We consider how this measure can be used to monitor, analyze, and alert financial system stress.
    Electronic ISSN: 2227-9091
    Topics: Economics
    Published by MDPI
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