283 research outputs found
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Modelling the fair value of annuities contracts: the impact of interest rate risk and mortality risk
The purpose of this paper is to analyze the problem of the fair valuation of annuities contracts. The market consistent valuation of these products requires a pricing framework which includes the two main sources of risk affecting the value of the annuity, i.e. interest rate risk and mortality risk. As the IASB has not set any specific guidelines as to which models are the most appropriate for these risks, in this note we consider a range of different models calibrated with historical data. We calculate the fair value of the annuity as a portfolio of zero coupon bonds, each with maturity set equal to the date of the annuity payments; the weights in the portfolio are given by the survival probabilities. Moreover, we focus on the additional information provided by stochastic simulations in order to define a suitable risk margin. The nature of the risk margin is one of the main key issues concerning the IASB and Solvency project
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Counterparty credit risk in a multivariate structural model with jumps
We present a multivariate version of a structural default model with jumps and use it in order to quantify the bilateral credit value adjustment and the bilateral debt value adjustment for equity contracts, such as forwards, in a Merton-type default setting. In particular, we explore the impact of changing correlation between names on these adjustments and study the effect of wrong-way and right-way risk
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A Gentle Introduction to Value at Risk
This paper is an introduction to the measurement of market risk in financial markets, with examples drawn mainly from commodity markets. In particular, we present the concept of VaR, its limits, the problems related to its estimation and backtesting. This is done at single asset and at portfolio level. Issues related to estimation error, measurement of portfolio risk contribution and how to cope with derivative positions are also considered. Other important issues like liquidity, operational and credit risk will not be dealt here. For a Gentle introduction to the measurement of counterparty credit risk see the companion paper by Ballotta, Fusai and Marena always available on the SSRN web site
Late Rejection of an Entire Polytetrafluoroethylene Carotid Patch with Complete Restitution of Vascular Continuity
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A Gentle Introduction to Default Risk and Counterparty Credit Modelling
In this paper we introduce the reader to the basic tools for the computation of Counterparty Credit Risk such as Credit Value Adjustment and Debt Value Adjustment. We also present the effect of mitigating clauses, like netting and collateral, in reducing the credit exposure. Detailed numerical examples are presented with reference to commodity derivatives
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Quanto Implied Correlation in a Multi-Lévy Framework
In this paper we apply the multivariate construction for Lévy processes introduced by Ballotta and Bonfiglioli (2014) to propose an integrated model for the joint dynamics of FX exchange rates and asset prices. We show that the proposed construction is consistent in terms of symmetries with respect to inversion and triangulation, and provides an insight into the quanto adjustment showing that this is affected by higher order cumulants of the pure jump part of the systematic risk factor. Using the Esscher transform, we relate Quanto options to vanilla call and put options, which allows for a fast calibration method to the vanilla and the Quanto market. As Quanto products offer significant exposure to the correlation between exchange rates and asset prices, they allow access to a market implied measure of this correlation. By means of a joint calibration exercise to the CME USD denominated Quanto futures on the Nikkei 225 index and both the Nikkei 225 and USDJPY market implied volatilities, we illustrate this approach for the case in which the driving process is assumed to be a Variance Gamma process
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The IASB Insurance Project for life insurance contracts: Impact on reserving methods and solvency requirements
In this communication, we review the fair value-based accounting framework promoted by the IASB Insurance Project for the case of a life insurance company. In particular, for the case of a simple participating contract with minimum guarantee, we show that the fair valuation process allows for the identification of a suitable safety loading to hedge against default risk; furthermore, we show that, when compared with the “traditional” accounting system based on the construction of mathematical reserves, the fair value approach offers a sounder reporting framework in terms of covering of the liability, implementation costs, volatility of assets and liabilities and solvency capital requirements
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Integrated Structural Approach to Credit Value Adjustment
This paper proposes an integrated pricing framework for Credit Value Adjustment of equity and commodity products. The given framework, in fact, generates dependence endogenously, allows for calibration and pricing to be based on the same numerical schemes (up to Monte Carlo simulation), and also allows the inclusion of risk mitigation clauses such as netting, collateral and initial margin provisions. The model is based on a structural approach which uses correlated Levy processes with idiosyncratic and systematic components; the pricing numerical scheme, instead, efficiently combines Monte Carlo simulation and Fourier transform based methods. We illustrate the tractability of the proposed framework and the performance of the proposed numerical scheme by means of a case study on a portfolio of commodity swaps using real market data
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Multivariate Lévy Models by Linear Combination: Estimation
In this paper we propose a simple and effective two-step procedure to estimate the multivariate Lévy model introduced by Ballotta and Bonfiglioli (2012). We assess our estimation approach via simulations, comparing the results with those obtained through a standard but more computationally intensive one-step maximum likelihood estimation. The proposed method is then applied to the computation of the intra-horizon Value at Risk for a portfolio of assets following the model under consideration
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Hedging of Asian options under exponential Lévy models: computation and performance
In this paper we consider the problem of hedging an arithmetic Asian option with discrete monitoring in an exponential Lévy model by deriving backward recursive integrals for the price sensitivities of the option. The procedure is applied to the analysis of the performance of the delta and delta-gamma hedges in an incomplete market; particular attention is paid to the hedging error and the impact of model error on the quality of the chosen hedging strategy. The numerical analysis shows the impact of jump risk on the hedging error of the option position, and the importance of including traded options in the hedging portfolio for the reduction of this risk
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