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The State VariablesState variables Model and the Valuation Valuations Partial Differential EquationPartial differential equation (PDE)

In: Capital Market Finance

Author

Listed:
  • Patrice Poncet

    (ESSEC Business School)

  • Roland Portait

    (ESSEC Business School)

Abstract

In this chapter, asset prices are assumed to be governed by specialized Itô processes, namely diffusion processes that depend on state variables. These variables, intended to represent the state of the economy, also follow diffusion processes. These particular processes lead to very useful additional results. After introducing the framework and notation (Sect. 20.1), we provide two ways of defining the factors governing returns (Sect. 20.2), two versions of the Arbitrage Pricing Theory that can be applied in this context (Sect. 20.3), the partial differential equation governing asset prices (Sect. 20.4), some applications in modeling interest rates (Sect. 20.5), the pricing of assets in the risk-neutral universe (Sect. 20.6) and discounting under uncertainty using Feynman-Kac formula (Sect. 20.7).

Suggested Citation

  • Patrice Poncet & Roland Portait, 2022. "The State VariablesState variables Model and the Valuation Valuations Partial Differential EquationPartial differential equation (PDE)," Springer Texts in Business and Economics, in: Capital Market Finance, chapter 20, pages 847-869, Springer.
    • Handle: RePEc:spr:sptchp:978-3-030-84600-8_20
    DOI: 10.1007/978-3-030-84600-8_20
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