Albina Danilova - Research
Papers in Refereed Journals
Explicit construction of a dynamic Bessel bridge of dimension 3, with L. Campi and U. Çetin, Electronic Journal of Probability,18 (20). pp. 1-25, 2013.
Given a deterministically time-changed Brownian motion Z starting from 1, whose time-change V(t) satisfies V(t) > t for all t > 0, we perform an explicit construction of a process X which is Brownian motion in its own filtration and that hits zero for the first time at V(τ), where τ:= inf {t > 0: Zt = 0}. We also provide the semimartingale decomposition of X under the filtration jointly generated by X and Z. Our construction relies on a combination of enlargement of filtration and filtering techniques. The resulting process X may be viewed as the analogue of a 3-dimensional Bessel bridge starting from 1 at time 0 and ending at 0 at the random time V(τ). We call this a dynamic Bessel bridge since V(τ) is not known in advance. Our study is motivated by insider trading models with default risk, where the insider observes the firm's value continuously on time.
Equilibrium model with default and dynamic insider information, with L. Campi and U. Çetin, Finance and Stochastics, 17 (347), pp. 565-585, 2013.
We consider an equilibrium model à la Kyle–Back for a defaultable claim issued by a given firm. In such a market the insider observes continuously in time the value of the firm, which is unobservable by the market makers. Using the construction in Campi et al. (2011) of a dynamic three-dimensional Bessel bridge, we provide the equilibrium price and the insider’s optimal strategy. As in Campi and Çetin (2007), the information released by the insider while trading optimally makes the default time predictable in the market’s view at the equilibrium. We conclude the paper by comparing the insider’s expected profits in the static and dynamic private information case. We also compute explicitly the value of the insider’s information in the special cases of a defaultable stock and a bond.
Dynamic Markov bridges motivated by models of insider trading, with L. Campi and U. Çetin, Stochastic Processes and their Applications, 121 (3). pp. 534-567, 2011.
Given a Markovian Brownian martingale Z, we build a process X which is a martingale in its own filtration and satisfies X1=Z1. We call X a dynamic bridge, because its terminal value Z1 is not known in advance. We compute its semimartingale decomposition explicitly under both its own filtration View the MathML source and the filtration View the MathML source jointly generated by X and Z. Our construction is heavily based on parabolic partial differential equations and filtering techniques. As an application, we explicitly solve an equilibrium model with insider trading that can be viewed as a non-Gaussian generalization of the model of Back and Pedersen (1998) [3], where the insider’s additional information evolves over time.
Stock market insider trading in continuous time with imperfect dynamic information, Stochastics: an international journal of probability and stochastic processes, 82 (1). pp. 111-131, 2010.
In this paper, I study the equilibrium pricing of asset shares in the presence of dynamic private information. The market consists of a risk-neutral informed agent who observes the firm value, noise traders and competitive market makers who set share prices using the total order flow as a noisy signal of the insider's information. I provide a characterization of all optimal strategies and prove the existence of both Markovian and non-Markovian equilibria by deriving closed-form solutions for the optimal order process of the informed trader and the optimal pricing rule of the market maker. The consideration of non-Markovian equilibrium is relevant since the market maker might decide to re-weight past information after receiving a new signal. Also, I show that (1) there is a unique Markovian equilibrium price process that allows the insider to trade undetected and (2) the presence of an insider increases the market's informational efficiency, in particular, for times close to dividend payment.
Optimal investment with inside information and parameter uncertainty, with M. Monoyios and A. Ng, Mathematics and Financial Economics, 3 (1). pp. 13-38, 2010.
An optimal investment problem is solved for an insider who has access to noisy information related to a future stock price, but who does not know the stock price drift. The
drift is filtered from a combination of price observations and the privileged information, fusing a partial information scenario with enlargement of filtration techniques. We apply
a variant of the Kalman–Bucy filter to infer a signal, given a combination of an observation process and some additional information. This converts the combined partial and inside
information model to a full information model, and the associated investment problem for
HARA utility is explicitly solved via duality methods. We consider the cases in which the
agent has information on the terminal value of the Brownian motion driving the stock, and
on the terminal stock price itself. Comparisons are drawn with the classical partial information case without insider knowledge. The parameter uncertainty results in stock price inside
information being more valuable than Brownian information, and perfect knowledge of the
future stock price leads to infinite additional utility. This is in contrast to the conventional
case in which the stock drift is assumed known, in which perfect information of any kind
leads to unbounded additional utility, since stock price information is then indistinguishable
from Brownian information.
Book
Dynamic Markov Bridges: Theory and Applications in Financial Markets, with U. Çetin,
Working Papers
Risk aversion of market makers and asymmetric information , with U. Çetin.
We analyse the equilibrium impact of market makers' risk aversion on the equilibrium in a speculative market consisting of a risk neutral informed trader and noise traders. The unwillingness of market makers to bear risk causes the informed trader to absorb large shocks in their inventories. The informed trader's optimal strategy is to drive the market price to its fundamental value while disguising her trades as the ones of an uninformed strategic trader. This results in a mean reverting demand, price reversal, and systematic changes in the market depth. We also find that an increase in risk aversion leads to lower market depth, less efficient prices, stronger price reversal and slower convergence to fundamental value. The endogenous value of private information, however, is non-monotonic in risk aversion. Understanding Stochastic Volatility in Financial Markets , with C. Julliard.
We develop a tractable model in which trade is generated by asymmetry in agents’ information sets. We show that, even if news are not generated by a stochastic volatility process, in the presence of information treatment and/or order processing costs, the (unique) equilibrium price process is characterized by stochastic volatility. The intuition behind this result is simple. In the presence of trading costs, agents strategically chose their trading times. Since new information is released to the market only at trading times, the price process sampled at trading times is not characterized by stochastic volatility. But since trading and calendar times differ, the price process at calendar times is the time change of the price process at trading times – i.e. price movements on the calendar time scale are characterized by stochastic volatility. Our closed form solutions imply that i) stochastic volatility is a function of both number of and volume of trades, and that ii) the relative informativeness of numbers and volume of trades depends on the sampling frequency of the data. Testing empirically the above predictions, we find strong support for the model.