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  • The Risk of Tranches Created from Residential MortgagesThis paper examines the risk in the tranches of ABSs and ABS CDOs that were created from residential mortgages between 2000 and 2007. Using the criteria of the rating agencies, it tests how wide the AAA tranches can be under different assumptions about the correlation model and recovery rates. It concludes that the AAA ratings assigned to the senior tranches of ABSs were not unreasonable. However, the AAA ratings assigned to tranches of Mezz ABS CDOs cannot be justified. The risk of a Mezz ABS CDO tranche depends critically on the correlation between mortgage pools as well as on the correlation model and the thickness of the underlying BBB tranches. The BBB tranches of ABSs cannot be considered equivalent to BBB bonds for the purposes of subsequent securitizations. , J.Hull, A.White (2009) 
  • Bilateral counterparty risk valuation for interest-rate products: impact of volatilities and correlationsThe 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 framework for counterparty risk adjustments in presence of bilateral default risk, as developed more in detail in Brigo and Capponi (2008), including the default of the investor. We illustrate the symmetry in the valuation and show that the adjustment involves a long position in a put option plus a short position in a call option, both with zero strike and written on the residual net present value of the contract at the relevant default times. We allow for correlation between the default times of the investor and counterparty, and for correlation of each with the underlying risk factor, namely interest rates. We also analyze the often neglected impact of credit spread volatility. We include Netting in our examples, although other agreements such as Margining and Collateral are left for future work. , D.Brigo, A.Pallavicini, V.Papatheodorou (2009) 
  • Fitting the Smile, Smart Parameters for SABR and HestonIn this paper we revisit the problem of calibrating stochastic volatility models. By finding smart initial parameters, we improve robustness of Levenberg-Marquardt. Applying this technique to the SABR and Heston models reduces calibration time by more than 90% compared to global optimization techniques such as Simplex or Differential Evolution. , P.Gauthier, P.H.Y, Rivaille (2009) 
  • Analytical Formulas for Local Volatility Model with Stochastic Rates This paper presents new approximation formulae of European options in a local volatility model with stochastic interest rates. This is a companion paper to our work on perturbation methods for local volatility models http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1275872 for the case of stochastic interest rates. The originality of this approach is to model the local volatility of the discounted spot and to obtain accurate approximations with tight estimates of the error terms. This approach can also be used in the case of stochastic dividends or stochastic convenience yields. We finally provide numerical results to illustrate the accuracy with real market data. , E.Benhamou, E.Gobet, M.Miri (2009) 
  • Efficient Simulation of the Double Heston ModelStochastic volatility models have replaced Black-Scholes model since they are able to generate a volatility smile. However, standard models fail to capture the smile slope and level movements. The Double-Heston model provides a more flexible approach to model the stochastic variance. In this paper, we focus on numerical implementation of this model. First, following the works of Lord and Kahl, we correct the analytical call option price formula given by Christoffersen et al. Then, we compare numerically the discretization schemes of Andersen, Zhu and Alfonsi to the Euler scheme. , P. Gauthier, D. Possamai (2009) 
  • Prices Expansion in the Wishart ModelUsing probability change techniques introduced by Drimus for Heston model, we derive a n-th order expansion formula of Wishart option price in terms of Black-Scholes price and Black-Scholes Greeks. Numerical results are given for the second order case. Thanks to this new approximation, the smile implied by Wishart model can be better understood. The sensitivity of Delta and Vega to the volatility (respectively Vanna and Volga) indeed appear explicitly in this formula. En route to our formula, we present a number of new - to our knowledge - results on Laplace transforms and moments of the integrated Wishart processes. , P. Gauthier, D. Possamai (2009) 
  • Efficient Simulation of the Wishart ModelIn financial mathematics, Wishart processes have emerged as an efficient tool to model stochastic covariance structures. Their numerical simulation may be quite challenging since they involve matrix processes. In this article, we propose an extensive study of financial applications of Wishart processes. First, we derive closed-form formulas for option prices in the single-asset case. Then, we show the relationship between Wishart processes and Wishart law. Finally, we review existing discretization schemes (Euler and Ornstein-Uhlenbeck) and propose a new scheme, adapted from Heston's QEM discretization scheme. Extensive numerical results support our comparison of these three schemes. , P. Gauthier, D. Possamai (2009) 





















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