Comments on the Pricing Equations in Finance

Gunter H. Meyer

Chapter 1 in The Time-Discrete Method of Lines for Options and Bonds:A PDE Approach, 2015, pp 1-56 from World Scientific Publishing Co. Pte. Ltd.

Abstract: The two dominant pricing equations of these notes are the Black Scholes equation for the price V (S, t) of an option ${L_{BS}}V \equiv {1 \over 2}{\sigma ^2}{S^2}{V_{SS}} + (r - q)SV - rV - {V_t} = 0{\mkern 1mu} {\mkern 1mu} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1.1)$ for 0 < S < ∞ and t ∈ (0, T ], and the bond equation for the price B(r, t) of a discount bond $L_B B \equiv {1 \over 2}w^2 B_{rr} + (u - \lambda w)B_r + rB + B_t + 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1.2)$ for, usually, 0 < r < ∞ and t ∈ (0, T ], where t = T - τ for calendar time τ denotes the time to expiry. Both equations are augmented by the values V (S, 0) and B(r, 0) at expiration t = 0 and by boundary conditions on V and B which are determined by the specific application. The aim is to find “a solution” of the pricing equation which also satisfies the given side conditions…

Keywords: Options; Bonds; PDE Formulation; Numerical Solution; Method of Lines; Stochastic Volatility; Jump Diffusion; Uncertain Parameters (search for similar items in EconPapers)
Date: 2015
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.worldscientific.com/doi/pdf/10.1142/9789814619684_0001 (application/pdf)
https://www.worldscientific.com/doi/abs/10.1142/9789814619684_0001 (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:9789814619684_0001

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 ().