# V. Technical Methods and Interpolations

It is essential to understand the risk of simultaneous default by several entities, particularly when it comes to credit derivatives such as basket credit default swaps. The joint probability of default and its correlation are key to understanding this risk. The correlation between two random variables X and Y is given by the formula : correlation(X, Y) = covariance(X, Y) / (σ_X * σ_Y) Where: - covariance(X, Y) is the covariance between X and Y. - sigma_X and sigma_Y are the standard...
L'ajustement de la valeur de financement (FVA) reflète le coût de financement des dérivés non collatéralisés au-dessus du taux de rendement sans risque, qui est typiquement l’€STR ou OIS* en Europe. Pour illustrer le FVA, considérons un swap non collatéralisé entre une banque et un client. Dans cet accord de swap, la banque et le client échangent des flux de trésorerie basés sur différents taux d'intérêt. Il est important de noter qu'aucun des deux partis ne poste de...
The LASSO (Least Absolute Shrinkage and Selection Operator) method, developed by Robert Tibshirani in 1996, efficiently predicts outcomes while maintaining an accurate and minimalist model. In LASSO regression, the objective function minimizes the residual sum of squares (RSS) plus a penalty term involving a regularization parameter (λ) and coefficients (β_j) for predictors. The penalty term encourages coefficient shrinkage towards zero, balancing data fit and model simplicity.
Understanding Fractional Differentiation: Think of it as measuring temperature now vs. its trend over time. In finance: 1. Asset Price Models: Traditional views vs. Fractional differentiation's long-term memory, e.g., Fractional Brownian Motion. 2. Risk Management: Models like VaR become more accurate. 3. Options Pricing: Enhanced with past price trends. 4. Interest Rates: Captures past rate shifts, refining models. It bridges current data with past patterns, vital in quantitative finance.
Cubic spline interpolation helps investors estimate bond yields at any maturity with smooth, precise curves. It's superior for capturing market dynamics, reducing risk, and aiding confident decision-making compared to linear methods. #Finance #Investment #DataAnalysis

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