本文研究了带有 VaR (Value-at-Risk, 风险价值)约束的固定缴费(defined contribution, DC) 型养老金的最优投资问题。 基金管理者将基金账户财富投资于由无风险资产,指数债券以及股票 所组成的金融市场中, 其目标为使得终端财富在 VaR...本文研究了带有 VaR (Value-at-Risk, 风险价值)约束的固定缴费(defined contribution, DC) 型养老金的最优投资问题。 基金管理者将基金账户财富投资于由无风险资产,指数债券以及股票 所组成的金融市场中, 其目标为使得终端财富在 VaR 约束下的预期效用最大化。 本文模型考虑随 机的通货膨胀环境以及随机的薪资过程,风险资产的漂移项为随机变量,风险市场价格具有已知 的概率分布。 首先引入辅助过程, 将原问题转化为自融资问题。 然后应用 Lagrange 对偶理论和鞍 方法, 推导得到了 CRRA 效用下的最优投资策略。This paper investigates an optimal investment problem of defined contribution (DC) pension with VaR (Value-at-Risk) constraint. The fund managers invest his wealth in a financial market consisting of a risk-free asset, a stock and an index bond, with the objective of maximizing the expected utility of terminal wealth under VaR constraint. In this model, we take account into stochastic inflation and salary process. The drift terms of the risky assets are described by random variables, and the market price of risk has a known probability distribution. We first introduce an auxiliary process to transform the original problem into a self-financing optimization problem. Then using the Lagrange dual method and martingale method, we derive the optimal investment strategy under CRRA utility.展开更多
白糖期权因其独特的市场特征和定价难度,成为期权定价研究的重要对象。本文基于郑州商品交易所公布的2023年白糖期权数据,利用二叉树定价模型对白糖期权进行定价研究。同时,将基于二叉树模型所计算出的白糖期权理论价格与市场真实期权...白糖期权因其独特的市场特征和定价难度,成为期权定价研究的重要对象。本文基于郑州商品交易所公布的2023年白糖期权数据,利用二叉树定价模型对白糖期权进行定价研究。同时,将基于二叉树模型所计算出的白糖期权理论价格与市场真实期权价格进行对比分析。研究发现:一是二叉树模型能够较为精准地反映白糖期权的定价趋势,但通过该模型计算得到的理论价格与实际市场价格之间仍存在一定的差异;二是白糖看涨期权的MAPE和MAE较白糖看跌期权的MAPE和MAE低;三是以白糖看涨期权为例,随着行权价格的逐步提高,其MAE和MAPE的曲线偏离程度增加。通过本研究,期望能为白糖期权市场的定价提供理论支持,并为相关金融产品的创新和发展贡献力量。Due to its unique market characteristics and pricing difficulty, white sugar option has become its important object of option pricing research. Based on the data of sugar options in 2023 released by Zhengzhou Commodity Exchange, this paper studies the pricing of white sugar options by using the binary tree pricing model. Meanwhile, the theoretical price of sugar option based on the binary tree model and the real option price in the market are analyzed. The study shows that the binary tree model can accurately reflect the pricing trend of sugar option, but there is still some difference between the theoretical price calculated by the model and the actual market price;second, the MAPE and MAE of sugar call option are lower than the MAPE and MAE of sugar put option;and with sugar call option as an example, the curve deviation of MAE and MAPE increases with the gradual increase of the exercise price. Through this study, it is expected to provide theoretical support for the pricing of the white sugar options market, and to contribute to the innovation and development of related financial products.展开更多
文摘本文研究了带有 VaR (Value-at-Risk, 风险价值)约束的固定缴费(defined contribution, DC) 型养老金的最优投资问题。 基金管理者将基金账户财富投资于由无风险资产,指数债券以及股票 所组成的金融市场中, 其目标为使得终端财富在 VaR 约束下的预期效用最大化。 本文模型考虑随 机的通货膨胀环境以及随机的薪资过程,风险资产的漂移项为随机变量,风险市场价格具有已知 的概率分布。 首先引入辅助过程, 将原问题转化为自融资问题。 然后应用 Lagrange 对偶理论和鞍 方法, 推导得到了 CRRA 效用下的最优投资策略。This paper investigates an optimal investment problem of defined contribution (DC) pension with VaR (Value-at-Risk) constraint. The fund managers invest his wealth in a financial market consisting of a risk-free asset, a stock and an index bond, with the objective of maximizing the expected utility of terminal wealth under VaR constraint. In this model, we take account into stochastic inflation and salary process. The drift terms of the risky assets are described by random variables, and the market price of risk has a known probability distribution. We first introduce an auxiliary process to transform the original problem into a self-financing optimization problem. Then using the Lagrange dual method and martingale method, we derive the optimal investment strategy under CRRA utility.
文摘白糖期权因其独特的市场特征和定价难度,成为期权定价研究的重要对象。本文基于郑州商品交易所公布的2023年白糖期权数据,利用二叉树定价模型对白糖期权进行定价研究。同时,将基于二叉树模型所计算出的白糖期权理论价格与市场真实期权价格进行对比分析。研究发现:一是二叉树模型能够较为精准地反映白糖期权的定价趋势,但通过该模型计算得到的理论价格与实际市场价格之间仍存在一定的差异;二是白糖看涨期权的MAPE和MAE较白糖看跌期权的MAPE和MAE低;三是以白糖看涨期权为例,随着行权价格的逐步提高,其MAE和MAPE的曲线偏离程度增加。通过本研究,期望能为白糖期权市场的定价提供理论支持,并为相关金融产品的创新和发展贡献力量。Due to its unique market characteristics and pricing difficulty, white sugar option has become its important object of option pricing research. Based on the data of sugar options in 2023 released by Zhengzhou Commodity Exchange, this paper studies the pricing of white sugar options by using the binary tree pricing model. Meanwhile, the theoretical price of sugar option based on the binary tree model and the real option price in the market are analyzed. The study shows that the binary tree model can accurately reflect the pricing trend of sugar option, but there is still some difference between the theoretical price calculated by the model and the actual market price;second, the MAPE and MAE of sugar call option are lower than the MAPE and MAE of sugar put option;and with sugar call option as an example, the curve deviation of MAE and MAPE increases with the gradual increase of the exercise price. Through this study, it is expected to provide theoretical support for the pricing of the white sugar options market, and to contribute to the innovation and development of related financial products.
