Fixed-income performance contributions of complex bonds

Abstract We consider the problem of finding the single-period fixed-income performance contributions of a generic security with a complex cash-flow structure. We extend the traditional fixed-income contribution model, based on the duration and the convexity, to include securities with generic floating-rate coupons and possibly with embedded call, put, or convertibility options. Using this method we […]

A risk decomposition framework consistent with performance measurements

Abstract We define a framework to compute the risk contributions of a portfolio consistently with a given performance-measurement schema. The framework has a wide array of applications, such as risk attribution, and matches the standard risk decomposition when the portfolio has a linear dependence on the factor exposures. We go beyond the traditional risk-decomposition approach, […]

Projection performance contributions of non-linear portfolios

Abstract We define a theoretical framework to exactly measure the additive risk-driver contributions to the performance of an investment portfolio. The approach is based on first principles, is non local and is especially suitable for non-linear portfolios. We consider a single-period return and assume that the generated cash flows are reinvested in the portfolio itself. […]

Non perturbative key-rate contributions to bond returns

Abstract We show a non-perturbative method to split the bond return into components coming from the different key-rates, the credit spread, the carry term, and another couple of minor components. We explicitly show the results for the case of a fixed-rate coupon bond with a price computed using cash-flow discounting with a yearly-compounded yield curve. […]

Seasonality of dividend point indexes

Abstract We analyse a variety of dividend-point indexes, typically used to determine the payoff of dividend derivatives. We show strong evidence of seasonality patterns for all indexes examined. Since dividend-point reset with irregular time intervals, we find the need to use a different seasonality function for the current or any future period. We determine the […]

Risk measure, XVA Analysis, Cost of Capital and Central Counterparties Workshop

In this workshop a number of topics were discussed. In primis several valuation adjustments (denoted by the generic name XVA) such as CVA, FVA, and KVA. The level of all the seminars was very high and you needed some previous knowledge of the subject in order to fully appreciate them. I want to highlight three […]

Finite difference methods for sensitivity computations

Abstract We describe some basic finite-difference methods to estimate the derivatives of a generic smooth function. For a function of one variable we provide the derivation of the standard forward difference, backward difference, and central difference approximation of the first and second derivatives. We also derive the expression for the second-order cross partial derivative for […]