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The purpose of this paper is introducing rigorous methods and formulas for bilateral counterparty risk credit valuation adjustments (CVA's) on interest-rate portfolios. In doing so, we summarize the general arbitrage-free valuation…
Credit Value Adjustment (CVA) is the difference between the value of the default-free and credit-risky derivative portfolio, which can be regarded as the cost of the credit hedge. Default probabilities are therefore needed, as input…
The popularity of Conditional Value-at-Risk (CVaR), a risk functional from finance, has been growing in the control systems community due to its intuitive interpretation and axiomatic foundation. We consider a nonstandard optimal control…
According to the IEC 61508 functional safety standard, it is required to estimate the achieved safety integrity of the system due to random hardware failures. For a safety function operating in a low demand mode, this measure is the average…
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…
Credit risk assessment is a crucial aspect of financial decision-making, enabling institutions to predict the likelihood of default and make informed lending decisions. Two prominent methodologies in credit risk modeling are logistic…
The pressure-correction method is a well established approach for simulating unsteady, incompressible fluids. It is well-known that implicit discretization of the time derivative in the momentum equation e.g. using a backward…
This work studies the dynamic risk management of the risk-neutral value of the potential credit losses on a portfolio of derivatives. Sensitivities-based hedging of such liability is sub-optimal because of bid-ask costs, pricing models…
In this short paper, we study the simulation of a large system of stochastic processes subject to a common driving noise and fast mean-reverting stochastic volatilities. This model may be used to describe the firm values of a large pool of…
Analytical, free of time consuming Monte Carlo simulations, framework for credit portfolio systematic risk metrics calculations is presented. Techniques are described that allow calculation of portfolio-level systematic risk measures…
We study dynamic hedging of counterparty risk for a portfolio of credit derivatives. Our empirically driven credit model consists of interacting default intensities which ramp up and then decay after the occurrence of credit events. Using…
Valuation of Credit Valuation Adjustment (CVA) has become an important field as its calculation is required in Basel III, issued in 2010, in the wake of the credit crisis. Exposure, which is defined as the potential future loss of a default…
We introduce a new method to calculate the credit exposure of European and path-dependent options. The proposed method is able to calculate accurate expected exposure and potential future exposure profiles under the risk-neutral and the…
We introduce an innovative theoretical framework to model derivative transactions between defaultable entities based on the principle of arbitrage freedom. Our framework extends the traditional formulations based on Credit and Debit…
We present a new, tractable method for solving and analyzing risk-aware control problems over finite and infinite, discounted time-horizons where the dynamics of the controlled process are described as a martingale problem. Supposing…
We consider a liquidation problem in which a risk-averse trader tries to liquidate a fixed quantity of an asset in the presence of market impact and random price fluctuations. The trader encounters a trade-off between the transaction costs…
Markov switching models are often used to analyze financial returns because of their ability to capture frequently observed stylized facts. In this paper we consider a multivariate Student-t version of the model as a viable alternative to…
We propose a multivariate framework for modeling dependent default times that extends the classical Cox process by incorporating both common and idiosyncratic shocks. Our construction uses c\`adl\`ag, increasing processes to model…
Stress testing, and in particular, reverse stress testing, is a prominent exercise in risk management practice. Reverse stress testing, in contrast to (forward) stress testing, aims to find an alternative but plausible model such that under…
This thesis develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time finance, does not rely on stochastic integrals or other probabilistic…