All posts under category "Quantitative Finance / Q-Fin.RM"
The option is a financial derivative, which is regularly employed in reducing the risk of its underlying securities. However, investing in option is still risky. Such risk becomes much severer for speculators who utilize option as a means of leverage to increase their potential returns. In order to
(The third edition corrects minor typos and adds 3 chapters synthesized from published papers plus an appendix on maximum entropy distributions.) The monograph investigates the misapplication of conventional statistical techniques to fat tailed distributions and looks for remedies, when possible.
The model is aimed to discriminate the 'good' and the 'bad' companies in Russian corporate sector based on their financial statements data based on Russian Accounting Standards. The data sample consists of 126 Russian public companies- issuers of Ruble bonds which represent about 36% of total number
In this article we present a continuous time model for natural gas and crude oil future prices. Its main feature is the possibility to link both energies in the long term and in the short term. For each energy, the future returns are represented as the sum of volatility functions driven by motions.
We set up a structural model to study credit risk for a portfolio containing several or many credit contracts. The model is based on a jump--diffusion process for the risk factors, i.e. for the company assets. We also include correlations between the companies. We discuss that models of this type ha
In this paper, we model dependence between operational risks by allowing risk profiles to evolve stochastically in time and to be dependent. This allows for a flexible correlation structure where the dependence between frequencies of different risk categories and between severities of different risk
Inspired by the bankruptcy of Lehman Brothers and its consequences on the global financial system, we develop a simple model in which the Lehman default event is quantified as having an almost immediate effect in worsening the credit worthiness of all financial institutions in the economic network.
In this paper, we discuss the Cram'er-Lundberg model with investments, where the price of the invested risk asset follows a geometric Brownian motion with drift $a$ and volatility $sigma> 0.$ By assuming there is a cap on the claim sizes, we prove that the probability of ruin has at least an algebra
The present paper provides a multi-period contagion model in the credit risk field. Our model is an extension of Davis and Lo's infectious default model. We consider an economy of n firms which may default directly or may be infected by other defaulting firms (a domino effect being also possible). T
Many banks adopt the Loss Distribution Approach to quantify the operational risk capital charge under Basel II requirements. It is common practice to estimate the capital charge using the 0.999 quantile of the annual loss distribution, calculated using point estimators of the frequency and severity
We examine three methods of constructing correlated Student-$t$ random variables. Our motivation arises from simulations that utilise heavy-tailed distributions for the purposes of stress testing and economic capital calculations for financial institutions. We make several observations regarding the
We present a network-based framework for simulating systemic risk that considers shock propagation in banking systems. In particular, the framework allows the modeller to reflect a top-down framework where a shock to one bank in the system affects the solvency and liquidity position of other banks,
In this paper we develop a symbolic technique to obtain asymptotic expressions for ruin probabilities and discounted penalty functions in renewal insurance risk models when the premium income depends on the present surplus of the insurance portfolio. The analysis is based on boundary problems for li
The problem of stock hedging is reconsidered in this paper, where a put option is chosen from a set of available put options to hedge the market risk of a stock. A formula is proposed to determine the probability that the potential loss exceeds a predetermined level of Value-at-Risk, which is used t
This article presents a generic model for pricing financial derivatives subject to counterparty credit risk. Both unilateral and bilateral types of credit risks are considered. Our study shows that credit risk should be modeled as American style options in most cases, which require a backward induct
A simple example shows that losing all money is compatible with a very high Sharpe ratio (as computed after losing all money). However, the only way that the Sharpe ratio can be high while losing money is that there is a period in which all or almost all money is lost. This note explores the best ac
Starting from the requirement that risk measures of financial portfolios should be based on their losses, not their gains, we define the notion of loss-based risk measure and study the properties of this class of risk measures. We characterize loss-based risk measures by a representation theorem and
Regulation and risk management in banks depend on underlying risk measures. In general this is the only purpose that is seen for risk measures. In this paper we suggest that the reporting of risk measures can be used to determine the loss distribution function for a financial entity. We demonstrate
Intuitively, the default risk of a single borrower is higher when her or his assets and debt are denominated in different currencies. Additionally, the default dependence of borrowers with assets and debt in different currencies should be stronger than in the one-currency case. By combining well-kno
We consider the optimal trade execution strategies for a large portfolio of single stocks proposed by Almgren (2003). This framework accounts for a nonlinear impact of trades on average market prices. The results of Almgren (2003) are based on the assumption that no shares of assets per unit of time
The main purpose of this paper is to formalize the modelling process, analysis and mathematical definition of corruption when entering into a contract between principal agent and producers. The formulation of the problem and the definition of concepts for the general case are considered. For definit
The inverse first passage time problem asks whether, for a Brownian motion $B$ and a nonnegative random variable $zeta$, there exists a time-varying barrier $b$ such that $mathbb{P}{B_s>b(s),0leq sleq t}=mathbb{P}{zeta>t}$. We study a 'smoothed' version of this problem and ask whether there is a 'ba
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