The tail risk management is of great significance in the investment process. As an extension of the asymmetric tail risk measure—Conditional Value at Risk (CVaR), higher moment coherent risk (HMCR) is compatible with the higher moment information (skewness and kurtosis) of probability distribution of the asset returns as well as capturing distributional asymmetry. In order to overcome the difficulties arising from the asymmetry and ambiguity of the underlying distribution, we propose the Wasserstein distributionally robust mean-HMCR portfolio optimization model based on the kernel smoothing method and optimal transport, where the ambiguity set is defined as a Wasserstein “ball” around the empirical distribution in the weighted kernel density estimation (KDE) distribution function family. Leveraging Fenchel’s duality theory, we obtain the computationally tractable DCP (difference-of-convex programming) reformulations and show that the ambiguity version preserves the asymmetry of the HMCR measure. Primary empirical test results for portfolio selection demonstrate the efficiency of the proposed model.
In the field of financial risk measurement, Asymmetric Laplace (AL) laws are used. The assumption of normalcy is used in traditional approaches for calculating financial risk. Asymmetric Laplace distribution, on the other hand, reveals the properties of empirical financial data sets much better than the normal model by leptokurtosis and skewness. According to recent financial data research, the regularity assumption is frequently broken. As a result, Asymmetric Laplace laws offer a simple, creative, and useful option to normal distributions when it comes to modeling financial data. We here engage AL distribution to explore specific formulas for the two commonly used risk measures, Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). The currency exchange rates data are used to and worked out to illustrate the proposed methodologies.
This paper proposes a new interest rate model by using uncertain mean-reverting differential equation. Based on the model, the pricing formulas of the zero-coupon bond, the interest rate ceiling and interest rate floor are derived respectively according to Yao-Chen formula. The symmetry appears in mathematical formulations of the interest rate ceiling and interest rate floor pricing formula. Furthermore, the model is applied to depict Hong Kong interbank offered rate (Hibor). Finally the parameter estimation by the method of moments and hypothesis test is completed.
Abstract. In the background where the domestic enterprises commonly have a weak protection consciousness against the exchange rate risk, this article makes a deep analysis based on the definition of exchange rate risk and its cause. By comparison of the traditional management method of exchange rate risk with another one based on financial engineering tools, it also deeply analyzes the method to use the financial engineering technology in the management of exchange rate risk, and concludes the primary purpose of exchange rate risk management is for hedging. This article proposes an optimal analysis method in two aspects, namely the minimum risk and maximum efficiency, for the forward-based optimal hedging, and proposes an optimal analysis method of dynamic hedging for the optimal hedging of option-based tools. Based on the description of the application of financial tools in foreign exchange futures, forward contract, currency exchange and foreign exchange option, it makes an empirical analysis on the management of foreign exchange risk by taking an assumed T company as the carrier and based on the trading tools of forward foreign exchange and currency option, which describes the operation procedure of financial tools in a more direct way and proves the efficiency of the optimal analysis method of this article.
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