Modeling the Risk in Mortality Projections

Zhu, Nan; Bauer, Daniel J.

doi:10.1287/opre.2021.2255

Cited by 5 publications

(4 citation statements)

References 48 publications

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“…We assume that θ(t) and α(t) are {Ft}−measurable Let , then by logarithmic differentiation, we have Applying laws of logarithms and simplifying fraction, we get (21) The second operator in the FPE can be expressed as follows…”

Section: Proofmentioning

confidence: 99%

“…Another early model is the seasonal autoregressive integrated moving average (SARIMA) introduced by Liu et al (2020), effective for pricing simple temperature derivatives like heating degree day (HDD) and cooling degree day (CDD) swaps, capturing seasonality and long-term trends. Another approach is using the Ornstein-Uhlenbeck (OU) process, introduced by Zhu and Bauer (2022), which is a mean-reverting process suitable for pricing complex temperature derivatives, including HDD and CDD swap options. Additionally, other proposed models for temperature derivatives pricing include the regime-switching model (RS), allowing changes in statistical properties over time, the jump-diffusion model (JD) capturing sudden jumps in temperature data, and the stochastic volatility model (SV) handling temperature data volatility.…”

Section: Introductionmentioning

confidence: 99%

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Pricing Gamma Based Temperature Derivatives

Vwalika,

Dzupire

2024

Preprint

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Farmers are impacted by temperature as high temperatures during the rainy season can lead to a substantial decrease in crop production. To safeguard farmers from this risk, temperature derivatives can be used, but they are frequently mispriced. This study aims to address this issue by developing a Stochastic Differential Equation (SDE) for temperature, with the assumption that it conforms to a gamma distribution. A synthesis technique that effectively manages the auto correlation within the data is employed to deduce the SDE. The resulting pricing formula is based on the anticipated value derived from the SDE. Notably, the formulated equation’s outcome is not linked to the expected temperature itself, but rather hinges on the gamma distribution parameters and the trigger temperature. This approach yields accurate forecasts for both price predictions and temperature projections. The model is found to predict temperature with R2 = 91%, MSE = 0.14, and MAPE = 1.3%. When used to price call option, the prices decrease with increase in trigger value, which is more realistic. Thus, the model is more flexible.

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Section: Proofmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Pricing Gamma Based Temperature Derivatives

Vwalika,

Dzupire

2024

Preprint

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“…Li and Liu [14] specifcally gave solution for the optimal dynamic trading strategy between a riskless asset and a risky asset with momentum. Te dynamics models refect the long-term projections variability and are wellsuited for fnancial applications where long-term demographic uncertainty is relevant [15].…”

Section: Option Hedgingmentioning

confidence: 99%

Hybrid Power Generation Supply Chain Financing and Purchasing Strategies with Option Hedging against Disruption

Dong

Xia

et al. 2023

Discrete Dynamics in Nature and Society

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Environmental pollution has stimulated cleaner and sustainable energy (CSE) resource consumption which fuels low-carbon electric-power growth. This consumption is particularly affected by two factors. One of them is the power grid’s capital size in the electricity supply chain (ESC) and the other is the carbon emission reduction level elasticity of electricity consumption. Further, the financial strategy directly exerts quantifiable influence on one of the factors of capital size, while the procurement strategy plays a role in another factor. However, the impact of strategic behavior on all participants in the ESC remains unexplored. Thus, we construct a game model for the ESC consisting of two heterogeneous power plants and a strategic power grid with financial constraints, in order to analyze the purchasing and financing strategies for low-carbon electric-power consumption and examine the profit scenario from the credit and option hedging. We find that for the power grid, high self-owned funds level or affluent credit line encourages procurement. And when considering the power grid funds are uniformly distributed on or are constant, this funds property variation surely imposes influence on the wind electricity purchases. We find price elasticity of demand shows monotonic on the purchase when the power grid funds are constant but not necessarily when funds are uniformly distributed. The two power plants pursue the most favorable scenario for profit-maximizing by means of credit interest rate. Whether the power plants increase the financial credit interest is contingent upon option portfolios, the grid’s fund property, and wind yield conditions. We also find whether the relations between the two power plants are competitive or complementary depending on the wind yield rate. Numerical study shows that when the power grid funds are uniformly distributed, executing the double option seems to be the most profitable choice for the power grid and the traditional energy power plant, whereas with the uniform distribution of the grid’s funds, executing the call option but abandoning put is the most profitable to the traditional energy power plant. Moreover, under the grid’s fund of uniform distribution, it can both motivate power user consumption for clean energy generation and expand the power grid’s capital size.

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“…Xu et al (2020) develop a multi-cohort mortality model for age-cohort mortality rates with common factors across cohorts as well as cohort-specific factors. Zhu and Bauer (2022) propose a Gaussian framework for describing the stochastic evolution of mortality projections rather than realized mortality rates.…”

Section: Introductionmentioning

confidence: 99%

A calendar year mortality model in continuous time

Hainaut¹

2023

ASTIN Bull.

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This article proposes a continuous time mortality model based on calendar years. Mortality rates belong to a mean-reverting random field indexed by time and age. In order to explain the improvement of life expectancies, the reversion level of mortality rates is the product of a deterministic function of age and of a decreasing jump-diffusion process driving the evolution of longevity. We provide a general closed-form expression for survival probabilities and develop it when the mean reversion level of mortality rates is proportional to a Gompertz–Makeham law. We develop an econometric estimation method and validate the model on the Belgian population.

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Modeling the Risk in Mortality Projections

Cited by 5 publications

References 48 publications

Pricing Gamma Based Temperature Derivatives

Pricing Gamma Based Temperature Derivatives

Hybrid Power Generation Supply Chain Financing and Purchasing Strategies with Option Hedging against Disruption

A calendar year mortality model in continuous time

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