带跳扩散过程的铁路货运期权定价模型

交通运输系统工程与信息 ›› 2015, Vol. 15 ›› Issue (2): 195-202.

带跳扩散过程的铁路货运期权定价模型

郭经纬，彭其渊^*

西南交通大学交通运输与物流学院，成都610031

收稿日期:2014-11-27 修回日期:2015-01-21 出版日期:2015-04-25 发布日期:2015-04-27
作者简介:郭经纬（1986-），男，河南洛阳人，博士生.
基金资助:
铁道部科技研究开发计划（2014X009）.

Railway Freight Option Pricing Model with Jump-diffusion Process

GUO Jing-wei，PENG Qi-yuan

School of Transportation and Logistics, Southwest Jiaotong Universiy, Chengdu 610031, China

Received:2014-11-27 Revised:2015-01-21 Online:2015-04-25 Published:2015-04-27

摘要/Abstract

摘要：

在铁路货运期权定价模型的基础上，构建带跳扩散过程的多期三叉树铁路货运期权定价模型，刻画在离散时间点，因随机到达的非市场性不确定性因素而造成的定价策略波动，并运用Girsanov 定理有效实行鞅测度变换，简化非线性跳变离散过程的求解，进而深入研究引入跳扩散过程的铁路货运期权定价问题.研究结果表明，跳跃次数与相关参数存在非线性关系，且相对于具有非单调性关系的期权执行价格及最优期权订购量，跳扩散过程对与其存在单调递增关系的期权价格具有更强的敏感性.同时，随着市场对跳跃信息消化能力及风险承担能力的增强，最优期权订购量逐步趋向稳定，不再随跳跃次数增加而产生较大变化.

关键词: 交通运输经济, 期权定价, 跳扩散过程, 鞅测度, 三叉树模型

Abstract:

In order to depict the fluctuations in railway freight option pricing strategy caused by the nonmarketing uncertainty which arrive at random discrete time points. A multi-phase trigeminal tree pricing model is established with jump diffusion process, then the transformation of martingale measure is carried out using Girasol theorem effectively which can simplify the solution of the nonlinear discrete jump process, and then the railway freight option pricing problem is researched with jump diffusion process. The case study illustrates that the jumping frequency has nonlinear relationship with the relevant parameters. And this paper presents that option price is more sensitive than the jumping frequency which has a monotonic relationship with it than exercise price and optimal ordering quantity of option, which has monotonously correlation with it. Meanwhile, with the marketing digestion ability to jump information and the risk bearing capacity enhance, the optimal ordering quantity of option gradually inclined to stable, no longer when it has great changes with the increasing of jumping frequency.

Key words: transportation economy, option pricing, jump-diffusion process, martingale measure, trigeminal tree model

中图分类号:

F532.5

郭经纬，彭其渊. 带跳扩散过程的铁路货运期权定价模型[J]. 交通运输系统工程与信息, 2015, 15(2): 195-202.

GUO Jing-wei，PENG Qi-yuan. Railway Freight Option Pricing Model with Jump-diffusion Process[J]. Journal of Transportation Systems Engineering and Information Technology, 2015, 15(2): 195-202.

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