CONDITIONAL DENSITY MODELS FOR ASSET PRICING

Damir Filipović, Lane P. Hughston and Andrea Macrina
Additional contact information
Damir Filipović: Swiss Finance Institute and École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
Lane P. Hughston: Department of Mathematics, University College London, London WC1E 6BT, United Kingdom and Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
Andrea Macrina: Department of Mathematics, King's College London, London WC2R 2LS, United Kingdom and Institute of Economic Research, Kyoto University, Kyoto 606-8501, Japan

Chapter 9 in Finance at Fields, 2012, pp 225-248 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractWe model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the price process is driven by Brownian motion, an associated "master equation" for the dynamics of the conditional probability density is derived and expressed in integral form. By a "model" for the conditional density process we mean a solution to the master equation along with the specification of (a) the initial density, and (b) the volatility structure of the density. The volatility structure is assumed at any time and for each value of the argument of the density to be a functional of the history of the density up to that time. In practice one specifies the functional modulo sufficient parametric freedom to allow for the input of additional option data apart from that implicit in the initial density. The scheme is sufficiently flexible to allow for the input of various types of data depending on the nature of the options market and the class of valuation problem being undertaken. Various examples are studied in detail, with exact solutions provided in some cases.

Keywords: Mathematical Finance; Financial Mathematics; Risk Management; Asset Pricing; Computational Finance; Derivatives; Option Pricing; Portfolio Optimization (search for similar items in EconPapers)
Date: 2012
References: Add references at CitEc
Citations: View citations in EconPapers (10)

Downloads: (external link)
https://www.worldscientific.com/doi/pdf/10.1142/9789814407892_0009 (application/pdf)
https://www.worldscientific.com/doi/abs/10.1142/9789814407892_0009 (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:9789814407892_0009

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 ().