Related papers: A Computational Approach to Hedging Credit Valuati…
We analyze the counterparty risk embedded in CDS contracts, in presence of a bilateral margin agreement. First, we investigate the pricing of collateralized counterparty risk and we derive the bilateral Credit Valuation Adjustment (CVA),…
In this work we present a general representation formula for the price of a vulnerable European option, and the related CVA in stochastic (either rough or not) volatility models for the underlying's price, when admitting correlation with…
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…
The X-valuation adjustment (XVA) problem, which is a recent topic in mathematical finance, is considered and analyzed. First, the basic properties of backward stochastic differential equations (BSDEs) with a random horizon in a…
A positive correlation between exposure and counterparty credit risk gives rise to the so-called Wrong-Way Risk (WWR). Even after a decade of the financial crisis, addressing WWR in both sound and tractable ways remains challenging.…
This article studies a portfolio optimization problem, where the market consisting of several stocks is modeled by a multi-dimensional jump-diffusion process with age-dependent semi-Markov modulated coefficients. We study risk sensitive…
This paper explores the application and significance of the second-order Esscher pricing model in option pricing and risk management. We split the study into two main parts. First, we focus on the constant jump diffusion (CJD) case,…
This article prices OTC derivatives with either an exogenously determined initial margin profile or endogenously approximated initial margin. In the former case, margin valuation adjustment (MVA) is defined as the liability-side discounted…
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…
Before the 2008 financial crisis, most research in financial mathematics focused on pricing options without considering the effects of counterparties' defaults, illiquidity problems, and the role of the sale and repurchase agreement (Repo)…
Jump stochastic volatility models are central to financial econometrics for volatility forecasting, portfolio risk management, and derivatives pricing. Markov Chain Monte Carlo (MCMC) algorithms are computationally unfeasible for the…
We study option pricing and hedging with uncertainty about a Black-Scholes reference model which is dynamically recalibrated to the market price of a liquidly traded vanilla option. For dynamic trading in the underlying asset and this…
We present a framework for hedging a portfolio of derivatives in the presence of market frictions such as transaction costs, market impact, liquidity constraints or risk limits using modern deep reinforcement machine learning methods. We…
We take the holistic approach of computing an OTC claim value that incorporates credit and funding liquidity risks and their interplays, instead of forcing individual price adjustments: CVA, DVA, FVA, KVA. The resulting nonlinear…
Multi-step stock price prediction over a long-term horizon is crucial for forecasting its volatility, allowing financial institutions to price and hedge derivatives, and banks to quantify the risk in their trading books. Additionally, most…
In this paper we study partial differential equations (PDEs) that can be used to model value adjustments. Different value adjustments denoted generally as xVA are nowadays added to the risk-free financial derivative values and the PDE…
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…
The question of pricing and hedging a given contingent claim has a unique solution in a complete market framework. When some incompleteness is introduced, the problem becomes however more difficult. Several approaches have been adopted in…
Research in quantitative finance has demonstrated that reinforcement learning (RL) methods have delivered promising outcomes in the context of hedging financial portfolios. For example, hedging a portfolio of European options using RL…
In financial mathematics, the calculation of the Greeks, especially the delta, is emphasized due to its role in risk management. In this article, we employ Malliavin calculus to determine the delta of European and Asian options, where the…