A Numerical Approach to Pricing American Call Options under SVJD

Carl Chiarella, Boda Kang and Gunter H. Meyer

Chapter 7 in The Numerical Solution of the American Option Pricing Problem:Finite Difference and Transform Approaches, 2014, pp 169-198 from World Scientific Publishing Co. Pte. Ltd.

Abstract: In Chapter 3 we considered the simpler case of geometric Brownian motion plus jump-diffusion dynamics. In Chapter 4 we considered the case of stochastic volatility and jump-diffusion dynamics but in that case the volatility process was of the Heston type and the jumps were normally distributed. We showed, in particular how the transform method can be applied to this situation. In Chapter 5 we considered numerical approaches to the problem under Heston stochastic volatility dynamics. There we focused on the transform approach. In this chapter we consider the case, which combines stochastic volatility and jump-diffusion, as was postulated in Chapter 2 and more extensively in Chapter 4. This will allow a far more general structure to be investigated. In Sec. 7.1 we give some general considerations to the solution of the problem using various techniques and boundary solutions. In Sec. 7.2 we discuss the solution using the projected successive overrelaxation (PSOR) method to determine the “exact” solution. In Sec. 7.3 we discuss the componentwise splitting approach, which decomposes the discretised problem into three linear complementarity problems with tridiagonal matrices. These problems can be efficiently solved using the Brennan and Schwartz (1977, 1978) algorithm. The accuracy of the componentwise splitting (CS) method is increased by applying the Strang (1968) symmetrization. In Sec. 7.4, we give an outline of the method of lines solution to the problem. Finally, Sec. 7.5 discusses a numerical comparison between the different methods and shows that the method of lines (MOL) is indeed superior, probably because it calculates the price, the delta, the gamma and the free surface all at the same time.

Keywords: American Option; Early Exercise; Method of Lines; Finite Difference Approach; Integral Transform Approach; Numerical Methods (search for similar items in EconPapers)
Date: 2014
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.worldscientific.com/doi/pdf/10.1142/9789814452625_0007 (application/pdf)
https://www.worldscientific.com/doi/abs/10.1142/9789814452625_0007 (text/html)
Ebook Access is available upon purchase.

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:wsi:wschap:9789814452625_0007

Ordering information: This item can be ordered from

Access Statistics for this chapter

More chapters in World Scientific Book Chapters from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().