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Binary funding impacts in derivative valuation
Mathematical Finance ( IF 1.6 ) Pub Date : 2020-09-14 , DOI: 10.1111/mafi.12287 Junbeom Lee 1 , Chao Zhou 2, 3, 4
Mathematical Finance ( IF 1.6 ) Pub Date : 2020-09-14 , DOI: 10.1111/mafi.12287 Junbeom Lee 1 , Chao Zhou 2, 3, 4
Affiliation
We discuss the binary nature of funding impact in derivative valuation. Under some conditions, funding is either a cost or a benefit, that is, one of the lending/borrowing rates does not play a role in pricing derivatives. When derivatives are priced, considering different lending/borrowing rates leads to semilinear backward stochastic differential equations (BSDEs) and partial differential equation (PDEs), and thus it is necessary to solve the equations numerically. However, once it can be guaranteed that only one of the rates affects pricing, linear equations can be recovered, and analytical formulae can be derived. Moreover, as a by‐product, our results explain how debt value adjustment (DVA) and funding benefits are dissimilar. It is often believed that considering both DVA and funding benefits results in a double‐counting issue but it will be shown that the two components are affected by different mathematical structures of derivative transactions. We find that funding benefit is related to the decreasing property of the payoff function, but this relationship decreases as the funding choices of underlying assets are transferred to repo markets.
中文翻译:
二进制资金对衍生品估值的影响
我们讨论了衍生工具估值中资金影响的二元性质。在某些情况下,融资要么是成本,要么是收益,也就是说,一种借贷利率在衍生产品定价中不起作用。当衍生产品定价时,考虑不同的借入/借入利率会导致半线性后向随机微分方程(BSDE)和偏微分方程(PDE),因此有必要对这些方程进行数值求解。但是,一旦可以保证只有一种汇率会影响定价,就可以恢复线性方程式,并可以得出分析公式。此外,作为副产品,我们的结果说明了债务价值调整的方式(DVA)与资金收益不同。人们通常认为,同时考虑DVA和资金收益会导致重复计算问题,但事实表明,这两个组成部分受衍生交易的不同数学结构影响。我们发现,资金收益与收益函数的递减属性有关,但是随着基础资产的资金选择转移到回购市场,这种关系减少。
更新日期:2020-09-14
中文翻译:
二进制资金对衍生品估值的影响
我们讨论了衍生工具估值中资金影响的二元性质。在某些情况下,融资要么是成本,要么是收益,也就是说,一种借贷利率在衍生产品定价中不起作用。当衍生产品定价时,考虑不同的借入/借入利率会导致半线性后向随机微分方程(BSDE)和偏微分方程(PDE),因此有必要对这些方程进行数值求解。但是,一旦可以保证只有一种汇率会影响定价,就可以恢复线性方程式,并可以得出分析公式。此外,作为副产品,我们的结果说明了债务价值调整的方式(DVA)与资金收益不同。人们通常认为,同时考虑DVA和资金收益会导致重复计算问题,但事实表明,这两个组成部分受衍生交易的不同数学结构影响。我们发现,资金收益与收益函数的递减属性有关,但是随着基础资产的资金选择转移到回购市场,这种关系减少。