Economy – Quantitative Finance – Pricing of Securities
Scientific paper
2010-10-21
Economy
Quantitative Finance
Pricing of Securities
To appear in International Journal of Theoretical and Applied Finance, Volume 15, Number 1 (2012), Special Issue on Financial
Scientific paper
We 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.
Filipovic Damir
Hughston Lane. P.
Macrina Andrea
No associations
LandOfFree
Conditional Density Models for Asset Pricing does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Conditional Density Models for Asset Pricing, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Conditional Density Models for Asset Pricing will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-423007