2019/12/07 by Hyungbin Park, Park, Hyungbin
Economics, Econometrics and Finance · #FOS: Economics and business #Mathematical Finance (q-fin.MF) #q-fin.MF
paper · pdf · doi:10.48550/arxiv.1912.03404
arxiv created 2021/01/03 · arxiv updated 2021/01/05
This paper investigates the large-time asymptotic behavior of the sensitivities of cash flows. In quantitative finance, the price of a cash flow is expressed in terms of a pricing operator of a Markov diffusion process. We study the extent to which the pricing operator is affected by small changes of the underlying Markov diffusion. The main idea is a partial differential equation (PDE) representation of the pricing operator by incorporating the Hansen--Scheinkman decomposition method. The sensitivities of the cash flows and their large-time convergence rates can be represented via simple expressions in terms of eigenvalues and eigenfunctions of the pricing operator. Furthermore, compared to the work of Park (Finance Stoch. 4:773-825, 2018), more detailed convergence rates are provided. In addition, we discuss the application of our results to three practical problems: utility maximization, entropic risk measures, and bond prices. Finally, as examples, explicit results for several market models such as the Cox--Ingersoll--Ross (CIR) model, 3/2 model and constant elasticity of variance (CEV) model are presented.