Convergence rates of large-time sensitivities with the Hansen-Scheinkman decomposition. (English) Zbl 1484.91487
Summary: 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 our work
[Finance Stoch. 22, No. 4, 773–825 (2018; Zbl 1416.91382)],
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.
MSC:
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 60J70 | Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) |
| 35Q91 | PDEs in connection with game theory, economics, social and behavioral sciences |
Keywords:
large-time analysis; Markov process; sensitivity; PDE representation; Hansen-Scheinkman decompositionCitations:
Zbl 1416.91382References:
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