| 摘要: |
| 针对含有信用风险的期权定价问题，提出了基于Klein模型的跳扩散过程下带有随机利率的脆弱期权定价模型;在一个连续时间金融市场中，根据风险中性假设得到股票价格和公司价值的跳扩散模型；在随机利率条件下，引入零息债券价格过程构造等价鞅测度，应用Itδ引理和鞅方法推导出了脆弱看涨期权定价公式；该模型考虑了跳风险且引入了随机利率，故更加切合实际情况，并且在一定的条件下可以退化为经典的Klein模型和B-S模型等。 |
| 关键词: 随机利率 期权定价 信用风险 跳扩散模型 |
| DOI： |
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| Pricing Vulnerable Options with Stochastic Interest Rates under Jump-diffusion Process |
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WANG Zhi-yuan，CHEN Ping
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| Abstract: |
| o solve the option pricing problem with credit risk, a vulnerable option pricing model with stochastic interest rate under jump-diffusion process based on Klein model is proposed. In a continuous-time financial market, the jump-diffusion model of stock price and company value is obtained under the assumption of risk neutrality. An equivalent martingale measure is constructed for the pricing process of interest-bearing bonds, and the pricing formula of vulnerable call option is derived by using the Itō lemma and martingale method. The model takes into account jump risk and introduces stochastic interest rate, so it is more practical and can be degenerated into classical Klein model and B-S model under certain conditions. |
| Key words: stochastic interest rate option pricing credit risk jump diffusion model |
