arXiv subjects

Damir Filipović

Publications and source records attributed to Damir Filipović.

23 records · Page 2Linked to original sources

arXiv2011

Conditional Density Models for Asset Pricing

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.

q-fin.PR↗

arXiv2011

Density Approximations for Multivariate Affine Jump-Diffusion Processes

We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess all polynomial moments. We establish parametric conditions which guarantee existence and differentiability of transition densities of affine models and show how they naturally fit into the approximation framework. Empirical applications in credit risk, likelihood inference, and option pricing highlight the usefulness of our expansions. The approximations are extremely fast to evaluate, and they perform very accurately and numerically stable.

math.ST↗

arXiv2011

Affine processes on positive semidefinite matrices

This article provides the mathematical foundation for stochastically continuous affine processes on the cone of positive semidefinite symmetric matrices. This analysis has been motivated by a large and growing use of matrix-valued affine processes in finance, including multi-asset option pricing with stochastic volatility and correlation structures, and fixed-income models with stochastically correlated risk factors and default intensities.

math.PR↗

arXiv2011

Concave Distortion Semigroups

The problem behind this paper is the proper measurement of the degree of quality/acceptability/distance to arbitrage of trades. We are narrowing the class of coherent acceptability indices introduced by Cherny and Madan (2007) by imposing an additional mathematical property. For this, we introduce the notion of a concave distortion semigroup as a family $(Ψ_t)_{t\ge0}$ of concave increasing functions $[0,1]\to[0,1]$ satisfying the semigroup property $$ Ψ_s\circΨ_t=Ψ_{s+t},\quad s,t\ge0. $$ The goal of the paper is the investigation of these semigroups with regard to the following aspects: representation of distortion semigroups; properties of distortion semigroups desirable from the economical or mathematical perspective; determining which concave distortions belong to some distortion semigroup.

q-fin.RM↗

arXiv2011

Optimal Investment and Premium Policies under Risk Shifting and Solvency Regulation

Limited liability creates a conflict of interests between policyholders and shareholders of insurance companies. It provides shareholders with incentives to increase the risk of the insurer's assets and liabilities which, in turn, might reduce the value policyholders attach to and premiums they are willing to pay for insurance coverage. We characterize Pareto optimal investment and premium policies in this context and provide necessary and sufficient conditions for their existence and uniqueness. We then identify investment and premium policies under the risk shifting problem if shareholders cannot credibly commit to an investment strategy before policies are sold and premiums are paid. Last, we analyze the effect of solvency regulation, such as Solvency II or the Swiss Solvency Test, on the agency cost of the risk shifting problem and calibrate our model to a non-life insurer average portfolio.

q-fin.PM↗