scholarly journals Valuing Multirisk Catastrophe Reinsurance Based on the Cox–Ingersoll–Ross (CIR) Model

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Wen Chao
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Threshold Model ◽  
Copula Function ◽  
Dartmouth College ◽  
Insurance Companies ◽  
Stochastic Interest Rates ◽  
Cir Model ◽  
Stochastic Interest ◽  
Catastrophe Reinsurance

Catastrophe risks lead to severe problems of insurance and reinsurance industry. In order to reduce the underwriting risk, the insurer would seek protection by transferring part of its risk exposure to the reinsurer. A framework for valuing multirisk catastrophe reinsurance under stochastic interest rates driven by the CIR model shall be discussed. To evaluate the distribution and the dependence of catastrophe variables, the Peaks over Threshold model and Copula function are used to measure them, respectively. Furthermore, the parameters of the valuing model are estimated and calibrated by using the Global Flood Date provided by Dartmouth College from 2000 to 2016. Finally, the value of catastrophe reinsurance is derived and a sensitivity analysis of how stochastic interest rates and catastrophe dependence affect the values is performed via Monte Carlo simulations. The results obtained show that the catastrophe reinsurance value is the inverse relation between initial value of interest rate and average interest rate in the long run. Additionally, a high level of dependence between catastrophe variables increases the catastrophe reinsurance value. The findings of this paper may be interesting to (re)insurance companies and other financial institutions that want to transfer catastrophic risks.

EFFICIENT DYNAMIC HEDGING FOR LARGE VARIABLE ANNUITY PORTFOLIOS WITH MULTIPLE UNDERLYING ASSETS

2020 ◽  
Vol 50 (3) ◽  
pp. 913-957
Author(s):  
X. Sheldon Lin ◽  
Shuai Yang
Keyword(s):  
Interest Rates ◽  
Computing Time ◽  
Insurance Companies ◽  
Insurance Company ◽  
Simulation Approach ◽  
Stochastic Interest Rates ◽  
Dynamic Hedging ◽  
Market Risks ◽  
Stochastic Interest ◽  
Hedging Portfolio

AbstractA variable annuity (VA) is an equity-linked annuity that provides investment guarantees to its policyholder and its contributions are normally invested in multiple underlying assets (e.g., mutual funds), which exposes VA liability to significant market risks. Hedging the market risks is therefore crucial in risk managing a VA portfolio as the VA guarantees are long-dated liabilities that may span decades. In order to hedge the VA liability, the issuing insurance company would need to construct a hedging portfolio consisting of the underlying assets whose positions are often determined by the liability Greeks such as partial dollar Deltas. Usually, these quantities are calculated via nested simulation approach. For insurance companies that manage large VA portfolios (e.g., 100k+ policies), calculating those quantities is extremely time-consuming or even prohibitive due to the complexity of the guarantee payoffs and the stochastic-on-stochastic nature of the nested simulation algorithm. In this paper, we extend the surrogate model-assisted nest simulation approach in Lin and Yang [(2020) Insurance: Mathematics and Economics, 91, 85–103] to efficiently calculate the total VA liability and the partial dollar Deltas for large VA portfolios with multiple underlying assets. In our proposed algorithm, the nested simulation is run using small sets of selected representative policies and representative outer loops. As a result, the computing time is substantially reduced. The computational advantage of the proposed algorithm and the importance of dynamic hedging are further illustrated through a profit and loss (P&L) analysis for a large synthetic VA portfolio. Moreover, the robustness of the performance of the proposed algorithm is tested with multiple simulation runs. Numerical results show that the proposed algorithm is able to accurately approximate different quantities of interest and the performance is robust with respect to different sets of parameter inputs. Finally, we show how our approach could be extended to potentially incorporate stochastic interest rates and estimate other Greeks such as Rho.

scholarly journals Two Approaches for a Dividend Maximization Problem under an Ornstein-Uhlenbeck Interest Rate

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2257
Author(s):  
Julia Eisenberg ◽  
Stefan Kremsner ◽  
Alexander Steinicke
Keyword(s):  
Optimal Control ◽  
Interest Rate ◽  
Interest Rates ◽  
Optimal Control Problems ◽  
Stopping Time ◽  
Maximization Problem ◽  
Control Problems ◽  
Stochastic Interest Rates ◽  
Stochastic Interest ◽  
And Behavior

We investigate a dividend maximization problem under stochastic interest rates with Ornstein-Uhlenbeck dynamics. This setup also takes negative rates into account. First a deterministic time is considered, where an explicit separating curve α(t) can be found to determine the optimal strategy at time t. In a second setting, we introduce a strategy-independent stopping time. The properties and behavior of these optimal control problems in both settings are analyzed in an analytical HJB-driven approach, and we also use backward stochastic differential equations.

A Bayesian Pricing of Longevity Derivatives with Interest Rate Risks

2017 ◽  
Vol 0 (0) ◽  
Author(s):  
Atsuyuki Kogure ◽  
Takahiro Fushimi
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Mortality Risk ◽  
Interest Rate Risk ◽  
Stochastic Interest Rates ◽  
Rate Risk ◽  
Stochastic Interest ◽  
The Interest Rate ◽  
Longevity Bonds ◽  
Carter Model

AbstractMortality-linked securities such as longevity bonds or longevity swaps usually depend on not only mortality risk but also interest rate risk. However, in the existing pricing methodologies, it is often the case that only the mortality risk is modeled to change in a stochastic manner and the interest rate is kept fixed at a pre-specified level. In order to develop large and liquid longevity markets, it is essential to incorporate the interest rate risk into pricing mortality-linked securities. In this paper we tackle the issue by considering the pricing of longevity derivatives under stochastic interest rates following the CIR model. As for the mortality modeling, we use a two-factor extension of the Lee-Carter model by noting the recent studies which point out the inconsistencies of the original Lee-Carter model with observed mortality rates due to its single factor structure. To address the issue of parameter uncertainty, we propose using a Bayesian methodology both to estimate the models and to price longevity derivatives in line with (Kogure, A., and Y. Kurachi. 2010. “A Bayesian Approach to Pricing Longevity Risk Based on Risk Neutral Predictive Distributions.”

scholarly journals Valuing strategic investments under stochastic interest rates: A real option approach

2019 ◽  
Vol 16 (3) ◽  
pp. 89-97
Author(s):  
Luca Vincenzo Ballestra ◽  
Graziella Pacelli ◽  
Davide Radi
Keyword(s):  
Interest Rate ◽  
Option Pricing ◽  
Interest Rates ◽  
Real Option ◽  
Interest Rate Risk ◽  
Stochastic Interest Rates ◽  
Investment Projects ◽  
Rate Risk ◽  
Stochastic Interest ◽  
The Interest Rate

One of the most challenging issues in management is the valuation of strategic investments. In particular, when undertaking projects such as an expansion or the launch of a new brand, or an investment in R&D and intellectual capital, which are characterized by a long-term horizon, a firm has also to face the risk due to the interest rate. In this work, we propose to value investments subject to interest rate risk using a real options approach (Schulmerich, 2010). This task requires the typical technicalities of option pricing, which often rely on complex and time-consuming techniques to value investment projects. For instance, Schulmerich (2010) is, to the best of our knowledge, the first work where the interest rate risk is considered for real option analysis. Nevertheless, the valuation of investment projects is done by employing binomial trees, which are computationally very expensive. In the current paper, a different modeling framework (in continuous-time) for real option pricing is proposed which allows one to account for interest rate risk and, at the same time, to reduce computational complexity. In particular, the net present value of the cash inflows is specified by a geometric Brownian motion and the interest rate is modeled by using a process of Vasicek type, which is calibrated to real market data. Such an approach yields an explicit formula for valuing various kinds of investment strategies, such as the option to defer and the option to expand. Therefore, the one proposed is the first model in the field of real options that accounts for the interest rate risk and, at the same time, offers an easy to implement formula which makes the model itself very suitable for practitioners. An empirical analysis is presented which illustrates the proposed approach from the practical point-of-view and highlights the impact of stochastic interest rates in investment valuation.

Impacts of Jumps and Stochastic Interest Rates on the Fair Costs of Guaranteed Minimum Death Benefit Contracts

2008 ◽  
Author(s):  
Francois Quittard-Pinon ◽  
Rivo A Randrianarivony
Keyword(s):  
Interest Rates ◽  
Stochastic Interest Rates ◽  
Stochastic Interest

A Note on Exchange Options Under Stochastic Interest Rates

2010 ◽  
Author(s):  
Carole Bernard ◽  
Zhenyu Cui
Keyword(s):  
Interest Rates ◽  
Stochastic Interest Rates ◽  
Stochastic Interest ◽  
Exchange Options
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