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| 摘要: |
| 本文研究了市场利率，基础资产价格及其波动率过程满足一类多元仿射跳扩散模型的远期生效期权定价问题，其中市场利率和波动率过程与基础资产相关且具有共同跳跃风险成分.利用Fourier反变换和远期测度技术，获得了欧式远期生效看涨期权价格的解析显示解.应用数值计算比较了利率，波动率过程对期权价格的不同表现，并分析了模型中主要参数对期权价格和对冲策略的影响.数值结果表明，利率和波动率因素，以及跳跃风险参数对期权价格有显著作用，这表明了多元仿射跳扩散模型具有较好拟合实际的能力. |
| 关键词: 多元仿射跳扩散模型 随机波动率 随机利率 远期生效期权 Fourier反变换 |
| DOI： |
| 分类号:O211.9 |
| 基金项目:国家自然科学基金资助（11461008）；广西财经学院青年教师科研发展基金（2018QNB07）. |
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| PRICING FORWARD-START OPTIONS IN A STOCHASTIC INTEREST RATE AND VOLATILITY MODEL WITH JUMP RISKS |
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XUE Guang-ming,DENG Guo-he
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| Abstract: |
| The pricing of the forward starting options is considered under an multi-factor affine jump diffusion model by introducing jump risks in stochastic interest rate, stochastic volatility and the underlying asset price process. The instantaneous volatility and the instantaneous interest rate are assumed to be correlated and have simultaneous correlated jumps with the underlying asset. Using the Fourier inverse transform method and the forward measure change technique, the closed explicit formulas for price of the European forward starting call options are obtained. Finally, some numerical examples are provided to examine performances of both the volatility and the interest rate on the option prices, and to analyze the impacts of the key parameters in this model on the option prices and the △ values, respectively. Numerical results show that the volatility, the interest rate, and the jump risks in this proposed model have more remarkable effects on the prices of option, which prove this model having good fits to reality. |
| Key words: multifactor affine jump diffusion model stochastic volatility stochastic interest rate forward starting options Fourier inverse transform |
