A Stochastically Correlated Bivariate Square-Root Model

IF 2.1 Q2 BUSINESS, FINANCE International Journal of Financial Studies Pub Date : 2024-03-25 DOI:10.3390/ijfs12020031
Allan Jonathan da Silva, Jack Baczynski, José Valentim Machado Vicente
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Abstract

We introduce a novel stochastically correlated two-factor (i.e., bivariate) diffusion process under the square-root format, for which we analytically obtain the corresponding solutions for the conditional moment-generating functions and conditional characteristic functions. Such solutions recover verbatim those of the uncorrelated case which encompasses a range of processes similar to those produced by a bivariate square-root process in which entries are correlated in the standard way, that is, via a constant correlation coefficient. Note that closed-form solutions for the conditional characteristic and moment-generating functions are not available for the latter. We focus on the financial scenario of obtaining closed-form expressions for the exact price of a zero-coupon bond and Asian option prices using a Fourier cosine series method.
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随机相关的双变量方根模型
我们在平方根格式下引入了一种新的随机相关双因子(即双变量)扩散过程,并通过分析得到了条件矩生成函数和条件特征函数的相应解。这些解与无相关情况下的解完全相同,无相关情况下的过程与二元平方根过程产生的过程相似,二元平方根过程中的条目以标准方式(即通过恒定相关系数)相关。需要注意的是,后者的条件特征函数和时刻生成函数没有闭式解。我们将重点放在利用傅立叶余弦级数法获得零息债券和亚洲期权价格精确价格的闭式表达式这一金融场景上。
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来源期刊
CiteScore
3.70
自引率
8.70%
发文量
100
审稿时长
11 weeks
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