Portfolio Optimization under Partial Information with Expert Opinions: a Dynamic Programming Approach

This paper investigates optimal portfolio strategies in a market where the drift is driven by an unobserved Markov chain. Information on the state of this chain is obtained from stock prices and expert opinions in the form of signals at random discrete time points. As in Frey et al. (2012), Int. J. Theor. Appl. Finance, 15, No. 1, we use stochastic filtering to transform the original problem into an optimization problem under full information where the state variable is the filter for the Markov chain. The dynamic programming equation for this problem is studied with viscosity-solution techniques and with regularization arguments.Comment: 31 page

Diversification and Systemic Risk: A Financial Network Perspective

In this paper, we study the implications of diversification in the asset portfolios of banks for financial stability and systemic risk. Adding to the existing literature, we analyse this issue in a network model of the interbank market. We carry out a simulation study that determines the probability of a systemic crisis in the banking network as a function of both the level of diversification, and the connectivity and structure of the financial network. In contrast to earlier studies we find that diversification at the level of individual banks may be beneficial for financial stability even if it does lead to a higher asset return correlation across banks

Markov-modulated Affine Processes

We study Markov-modulated affine processes (abbreviated MMAPs), a class of Markov processes that are created from affine processes by allowing some of their coefficients to be a function of an exogenous Markov process. MMAPs allow for richer models in various applications. At the same time MMAPs largely preserve the tractability of standard affine processes, as their characteristic function has a computationally convenient functional form. Our setup is a substantial generalization of earlier work, since we consider the case where the generator of the exogenous process $X$ is an unbounded operator (as is the case for diffusions or jump processes with infinite activity). We prove existence of MMAPs via a martingale problem approach, we derive the formula for their characteristic function and we study various mathematical properties of MMAPs. The paper closes with a discussion of several applications of MMAPs in finance.Comment: 30 page

Market Volatility and Feedback Effects from Dynamic Hedging

In this paper we analyze in what way the demand generated by dynamic hedging strategies affects the equilibrium prices of the underlying asset. We derive an explicit expression for the transformation of market volatility under the impact of hedging. It turns out that market volatility increases and becomes price-dependent. The strength of the effects depend not only on the market share of portfolio insurance but also crucially on the heterogeneity of insured payoffs. We finally discuss in what sense hedging strategies calculated under the assumption of constant volatility are still appropriate, even if this assumption is obviously violated by their implementation.Black--Scholes Model, Dynamic Hedging, Volatility, Option Pricing, Feedback Effects

A Systematic Approach to Pricing and Hedging of International Derivatives with Interest-Rate Risk

We deal with the valuration and hedging of non path-dependent European options on one or several underlyings in a model of an international economy which allows for both interest rate and exchange rate risk. Using martingale theory we provide a unified and easily applicable approach to pricing and hedging Black-Scholes type options on stocks, bonds, forwards. futures and exchange rates. We also cover the pricing and hedging of options to exchange two Black-Scholes type options for one another. The contigent claims may pay off in arbitrary currencies.Arbitrage, interest rate risk, exchange rate risk, option pricing, hedging

Corporate Security Prices in Structural Credit Risk Models with Incomplete Information

The paper studies structural credit risk models with incomplete information of the asset value. It is shown that the pricing of typical corporate securities such as equity, corporate bonds or CDSs leads to a nonlinear filtering problem. This problem cannot be tackled with standard techniques as the default time does not have an intensity under full information. We therefore transform the problem to a standard filtering problem for a stopped diffusion process. This problem is analyzed via SPDE results from the filtering literature. In particular we are able to characterize the default intensity under incomplete information in terms of the conditional density of the asset value process. Moreover, we give an explicit description of the dynamics of corporate security prices. Finally, we explain how the model can be applied to the pricing of bond and equity options and we present results from a number of numerical experiments

Invisible Infections: A Partial Information Approach for Estimating the Transmission Dynamics of the Covid-19 Pandemic

In this paper, we develop a discrete time stochastic model under partial information to explain the evolution of Covid-19 pandemic. Our model is a modification of the well-known SIR model for epidemics, which accounts for some peculiar features of Covid-19. In particular, we work with a random transmission rate and we assume that the true number of infectious people at any observation time is random and not directly observable, to account for asymptomatic and non-tested people. We elaborate a nested particle filtering approach to estimate the reproduction rate and the model parameters. We apply our methodology to Austrian Covid-19 infection data in the period from May 2020 to June 2022. Finally, we discuss forecasts and model tests.Comment: 17 pages, 17 figure