This section describes how to generate a time series such as AR(1) with non-linear structure of dependence, defined by using a two-dimensional copula C(u, v). The series is stationary, but the procedure can be easily generalized to non-stationary series. Thus, let u = F(xt), v = F(xt -1). According to (5) the joint distribution of the time series is as follows:
F (xi, X2… Xt) = C(X1,X2)1C(X2,X3)1 . ..C(xr-2 ,XT-l):C (XT-1,xr) (14)
Let known realization xt. Joint distribution xt and xt+1 are settings per copula C(F(xt +1), F(xt)) = C(u, v) where the denoted u = F(xt +1), v = F(xt). Then conditional distribution xt + 1 is set as
It is worth noting we can take advantage of copulas’ remarkable property that allows us to model the joint distribution of C(u1, … uk) separately fr... Read More
Kirill Boldyrev, Dmitry Andrianov, and Sergey Ivliev
Abstract Nowadays stress-testing is a popular framework for the analysis of the financial stability of different markets’ institutes and objects. This work proposes a new approach to trading book stress-testing by building price paths based on generalized autoregressive conditional the heteroskedasticity (GARCH) model with Pareto distribution for the random fluctuation of prices and t-copula for describing the dependency structure between factors.
Keywords Copula theory • Extreme value theory • GARCH • Pareto distribution • Stress-testing • Stylized facts
JEL Classification C49, G17
Stress-testing is a set of various techniques which allows the gauging of an institute’s vulnerability to “severe, but plausible” ... Read More
Our GM model extension is divided into two stages. During the first stage, the market-maker loses its knowledge about possible real asset value, while conditions for informed and uninformed traders remain the same. During the second stage, in addition to uncertainty for the market-maker about possible real asset value, we introduce errors of informed participants.
The disruption of the modification sequence is motivated by conservation of research chronology, when in the beginning our task was to search for a market- maker’s strategy, since it was the hardest stage of GM model modification.
The first stage of modification is a relaxation of the assumption about the market- maker’s knowledge of possible real asset value (V and V). This is the same as in the work of Das (2005)... Read More
Visualization is a crucial component to Adaptive Stress Testing. Visualization draws attention on emerging risks, and can help build intuition on how different risks are interconnected.
We can use heatmaps to prioritize attention to escalating high probability scenarios (red) and then escalating lower probability scenarios (Fig. 19).
Risk managers will focus first on the imminent threats, or escalating high PStress scenarios. Escalating low PStress scenarios are emerging scenarios, and still offer the potential for exerting control through proactive risk management. Black Swans could be lurking underneath stable low PStress scenarios, which calls for harnessing social intelligence to probe deeper into hidden fault lines.
We can also use network graphs to visualize emerging risk themes... Read More
Risk interactions play the most important role, because of the existence of close economic, organizational and technological ties between risk owners. The occurrence of some risks (operational, credit, market ones) for some parties implies the emergence of risks for their counterparties. The subsequent chain reaction of credit and market risks propagate through exchange within the economy. In recent decades, these relations have been developing more intensively than ever before, because of market globalization and technological progress.
This causal relationship can be illustrated by a typical example of the domino effect in business environment: discontent of the local population (i. e... Read More
In this section we present briefly the statistical models recently introduced by Curato and Lillo (2013) describing the high frequency dynamics of price changes for a large tick size asset in trade time. We want to show that these models are able to reproduce the phenomenon of clustering for log-returns and the scaling of hypercumulants Aq (n) in trade time.
The building blocks of these models are simple: the distribution of price changes caused by 1 transaction, i. e. Ap(i, и = 1), and the statistical properties of the dynamics of the bid-ask spread s (i). In our model we impose a coupling between the process of the price changes and of the spread in order to reproduce the price – change clustering.
We consider first a benchmark model, hereafter called i. i.d... Read More