ترکیب عادلانه قیمت گذاری و سرمایه مورد نیاز برای شرکت های بیمه غیر عمر
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|24243||2008||8 صفحه PDF||سفارش دهید||5975 کلمه|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Journal of Banking & Finance, Volume 32, Issue 12, December 2008, Pages 2589–2596
The aim of this article is to identify fair equity-premium combinations for non-life insurers that satisfy solvency capital requirements imposed by regulatory authorities. In particular, we compare target capital derived using the value at risk concept as planned for Solvency II in the European Union with the tail value at risk concept as required by the Swiss Solvency Test. The model framework uses Merton’s jump-diffusion process for the market value of liabilities and a geometric Brownian motion for the asset process; fair valuation is conducted using option pricing theory. We show that even if regulatory requirements are satisfied under different risk measures and parameterizations, the associated costs of insolvency – measured with the insurer’s default put option value – can differ substantially.
Recent developments in Europe include new solvency capital requirements that are based on the market value of assets and liabilities (Solvency II in the European Union; the Swiss Solvency Test). Insurance companies must ensure that their available economic capital suffices to cover the required solvency capital. In addition, competitive conditions in the insurance and capital markets should lead to equity-premium combinations that provide a net present value of zero for equityholders and policyholders. In this paper, we identify minimum safety levels using the default put option value for fair equity-premium combinations that simultaneously satisfy solvency capital requirements. In this setting, fair pricing is conducted using option pricing theory; solvency capital requirements are compared using the “value at risk” (Solvency II) and the “tail value at risk” (Swiss Solvency Test) approaches. In the literature on property-liability insurance, option pricing theory is employed for pricing insurance contracts and default risk in, e.g., Merton, 1977, Doherty and Garven, 1986, Cummins, 1988 and Cummins and Sommer, 1996, as well as D’Arcy and Dyer (1997). Recently, this approach has been used for capital allocation purposes, by, for example, Myers and Read, 2001, Sherris, 2006, Sherris and van der Hoek, 2006, Gründl and Schmeiser, 2007 and Yow and Sherris, 2007. Based on Fairley, 1979, Taylor, 1995 and Sherris, 2003 use an equilibrium framework in order to examine the interaction between capitalization of an insurer and rate making. General capital requirements under different model assumptions and safety levels are discussed in, e.g., Rytgaard and Savelli (2004); solvency capital calculations regarding the Swiss Solvency Test (SST) are presented in detail in Luder (2005). The literature generally focuses on fair pricing, capital structure, or solvency requirements. However, apart from rate making and capitalization (Taylor, 1995 and Sherris, 2003), these aspects are usually studied individually. In this paper, we add to the literature by combining fair pricing and solvency capital requirements to gain a better understanding of the effect of solvency regulation on the cost of insolvency (measured with the default put option value). The framework for the property-liability insurance company is based on Doherty and Garven (1986). The model incorporates corporate taxation and the risk of insolvency. In contrast to the setting in Doherty and Garven (1986), the model framework in this paper is extended by using Merton’s jump-diffusion process for the market value of liabilities and a geometric Brownian motion for the asset process. In numerical analyses, we first calculate fair equity-premium combinations for a given safety level (measured with the default put option value). Then, for the obtained capital structure, the target capital requirements according to Solvency II and SST are contrasted with the available economic capital. In addition, shortfall probabilities are also provided. The remainder of the paper is organized as follows. Section 2 describes the model framework of the property-liability insurer. Section 3 discusses concepts for solvency capital requirements under SST and Solvency II. Numerical results, including a sensitivity analysis, are contained in Section 4. Finally, Section 5 concludes.