확장 선형 경로 공간 모형에 관한 3편의 에세이

Abstract

첫번째 에세이에서는 LPS 모형의 효율성과 정확성을 검증한다. LPS 모형의 정확성은 시간 축을 분할하는 term segments의 위치를 가격결정 오차가 작도록 식별함으로써 달성되며 LPS 모형의 효율성은 대표 표본경로를 그 경로에 도달할 확률과 상태가격을 곱한 확률가중 상태가격의 크기에 따라 나열함으로써 확립됨을 예제를 통해 알아본다. 두번째 에세이에서는 LPS 모형을 이용하여 개인의 사망위험과 시장의 이자율위험에 따라 가격이 결정되는 이색파생상품의 가격을 결정해보고 몬테카를로 시뮬레이션과 이변량 이항격자를 이용하여 구한 동일한 파생상품의 가격 및 오차를 비교해 봄으로서 LPS 모형의 타당성을 효율성과 정확성 측면에서 재차 검증한다. 세번째 에세이에서는 LPS 모형을 이용하여 변동연금 상품에 내재된 GMIB (Guaranteed Minimum Income Benefit)을 보험회사가 어떻게 평가하고 그에 수반되는 위험을 어떻게 관리하여야 하는가에 대하여 정적헷지와 동적헷지 측면에서 설명한다.; In the first essay, the performance and robustness of linear path space approximation method is tested. The performance of the model is sensitive to the term segments specification. The optimal position of the term segments guaranteeing the convergence of LPS model is specified considering the implied volatility surface of each factor. Given the asymptotic convergence over different strike levels, the efficiency of convergence is attained by ordering the importance of path based on the weighted pathwise value not by the path probability. In the second essay, price the mortality derivatives using linear path space method. As the first numerical example, we price the pure endowment contract. We assume that the hazard rate follows the mean reverting Brownian Gompertz process and the short rate follows the CIR process. The solution by linear path space method is compared with those obtained by Monte Carlo simulation and bivariate binomial approximation methods. Linear path space method performs well within a reasonable range of pricing error and with relatively small number of paths. As the second numerical example, we price the guaranteed minimum income benefits (GMIBs) within variable annuity contract under stochastic mortality environment. We find that the correlation to the steepening yield curve movement has a greater impact than that to the level movement of mortality curve movement within relatively short time horizons. In the third essay, we consider managing the risk of variable annuities. Variable annuities have grown tremendously in recent years, offering life insurers significant growth opportunities. These equity and interest rate structured products offer a broad range of guarantees to the policyholders, and insurers must manage their risks. The insurer?s risk management program must consider modeling and implementation challenges beyond that of the standard capital market approach. This paper proposes solutions to six significant issues: (1) computational efficiency, (2) impact of equity returns and interest rate correlations on the cost of guarantee, (3) uncertain surrendering of policies and withdrawal of account value, (4) internal transfer of funds, (5) suboptimal exercise of options, and (6) a cost/benefit analysis of a hedging program. These solutions are extended from the traditional capital market approach. Specifically, in this paper, we describe the fair valuation of the guarantees using a three factor model incorporating interest rate and equity risks. Then we use the Linear Path Space methodology to simulate and value the risks. Finally, we simulate the effectiveness of using a combined static-dynamic hedging program in dealing with the practical considerations mentioned above.