The Partial Differential Equation Approach Under Geometric Brownian Motion

Carl Chiarella, Xuezhong (Tony) He () and Christina Sklibosios Nikitopoulos
Additional contact information
Christina Sklibosios Nikitopoulos: University of Technology Sydney

Chapter Chapter 9 in Derivative Security Pricing, 2015, pp 191-206 from Springer

Abstract: Abstract The Partial Differential Equation (PDE) Approach is one of the techniques in solving the pricing equations for financial instruments. The solution technique of the PDE approach is the Fourier transform, which reduces the problem of solving the PDE to one of solving an ordinary differential equation (ODE). The Fourier transform provides quite a general framework for solving the PDEs of financial instruments when the underlying asset follows a jump-diffusion process and also when we deal with American options. This chapter illustrates that in the case of geometric Brownian motion, the ODE determining the transform can be solved explicitly. It shows how the PDE approach is related to pricing derivatives in terms of integration and expectations under the risk-neutral measure.

Keywords: Payoff Function; Geometric Brownian Motion; Underlying Asset; Kolmogorov Equation; Exercise Price (search for similar items in EconPapers)
Date: 2015
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:dymchp:978-3-662-45906-5_9

Ordering information: This item can be ordered from
http://www.springer.com/9783662459065

DOI: 10.1007/978-3-662-45906-5_9

Access Statistics for this chapter

More chapters in Dynamic Modeling and Econometrics in Economics and Finance from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().