Description: This paper shows how the results of copula based capital aggregation models can always be locally approximated by relatively simple formulas. The paper defines the concepts of diversification factor and tail correlation matrix and describes methods for estimating these quantities from simulated data. We show how these ideas can be put into practice as both computational shortcuts and presentation tools.

Description: This paper develops an option pricing model that takes cost of capital concepts as its foundation rather than dynamic replication. The resulting model, called the 'C' measure in this paper, is related to the family of Affine Jump Diffusion models that are well known in the finance literature, so it is fairly easy to understand and implement. We argue that this is a reasonable model to use for estimating equity implied volatilities that are beyond the five- to 10-year horizon that can typically be observed in today‘s capital markets. The paper concludes with a short discussion of how to grade from observable market data to the 'C' measure.

Description: Regularization, by means of trading restrictions, is an effective way to obtain sparse replicating portfolios. By including only the most relevant replicating instruments, the resulting portfolio is more efficient computationally, easier to interpret, and better able to approximate the liability on an out-of-sample basis. The instruments selected depend largely on their respective trading costs. This paper evaluates a number of alternative methods for specifying trading costs. We find that trading costs based on simple statistics of the instrument and liability cash flows are an effective choice in practice. Presented at 2010 Enterprise Risk Management Symposium, Society of Actuaries, April 12-15, 2010.

Description: Panelists discuss economic capital, capital modeling, and hedge modeling, especially for guaranteed living benefits [GLBs] on variable annuities. Session 34PD of the 2005 Valuation Actuary Symposium.

Description: Economic capital is an embedded part of the banking risk management and regulatory framework. The insurance industry has relied on rating agency and regulatory formulas that have been criticized as overcapitalizing and not appropriately differentiating risk drivers in the capital formulation. The emergence of C-3 Phase I and C-3 Phase II have introduced an economic approach to capital in the insurance industry. This half-day seminar takes a detailed look at the subject of economic capital. From the Record of the Society of Actuaries 2005, Volume 31, No. 1: 2005 New Orleans Life Spring Meeting, May 22-24, 2005, Session 9 Seminar.