Marco Francischello

Abstract: This paper studies the feedback between stock market fluctuations and wealth inequality dynamics. We do so by means of a dynamic consumption-based general equilibrium model with endogenous asset returns and a non-degenerate wealth distribution for a continuum of households. Households are heterogeneous in risk aversion and thus choose different expected portfolio returns and portfolio return volatilities, generating time-varying wealth inequality. We show how to solve the model analytically in terms of a cumulant generating function, which encodes information about all the moments of the distribution of risk aversion. With this result, we recover the unobservable distribution of risk aversion using time variation in the slope of the observable equity term structure. We also confront the model with US data on the wealth distribution to recover a second estimate of the distribution of risk aversion. By comparing the two estimates, we show quantitatively that there is significant feedback between stock price dynamics and wealth distribution dynamics.

Abstract: We develop an OLG model with heterogeneous agents and aggregate uncertainty to study optimal Ramsey taxation when the government can use a credible set of social security instruments. Social security mitigates the income effect in optimal labor tax smoothing and, together with heterogeneity, adds new redistributive motives to both labor and capital taxes while crowding out others. We calibrate the model on three different economies: the US, Netherlands, and Italy. We argue that the three countries would experience heterogeneous gains, in redistributive and efficiency terms, by moving from the status-quo allocations to those prescribed by a utilitarian Ramsey planner. Our simulations show that retirement benefits in the current economies are higher than their Ramsey-optimal level while we argue that the use of funded social security schemes, neglected in current actual policies, could be welfare improving.

Short Abstract: Structural estimation using the Simulated Method of Moments (SMM) aims to iteratively minimize the difference between moments from simulated and real-world data. We propose an approach to speed up this process by fitting a neural network that approximates the map between parameters and moments—an object that can be built by exploiting parallel computation.

Abstract: Since the 2008 global financial crisis, the banking industry has been using valuation adjustments to account for default risk and funding costs. These adjustments are computed separately and added together by practitioners as if the valuation equations were linear. This assumption is too strong and does not allow to model market features such as different borrowing and lending rates and replacement default closeout. Hence we argue that the full valuation equations are nonlinear, and this paper is devoted to studying the nonlinear valuation equations introduced in Pallavicini et al (2011).

We illustrate all the cash flows exchanged by the parties involved in a derivative contract, in presence of default risk, collateralisation with re-hypothecation and funding costs. Then we show how to obtain semi-linear PDEs or Forward Backward Stochastic Differential Equations (FBSDEs) from present-valuing said cash flows in an arbitrage-free setup, and we study the well-posedness of these PDEs and FBSDEs in a viscosity and classical sense.

Moreover, from a financial perspective, we discuss cases where classical valuation adjustments (XVA) can be disentangled. We show how funding costs are offset by treasury valuation adjustments when one takes a whole-bank perspective in the valuation, while the same costs are not offset by such adjustments when taking a shareholder perspective. We show that although we use a risk-neutral valuation framework based on a locally risk-free bank account, our final valuation equations do not depend on the risk-free rate. Finally, we show how to consistently derive a netting set valuation from a portfolio level one.

Abstract: We present a detailed analysis of interest rate derivatives valuation under credit risk and collateral modeling. We show how the credit and collateral extended valuation framework presented in Pallavicini et al. 2011, and the related collateralized valuation measure, can be helpful in defining the key market rates underlying the multiple interest rate curves that characterize current interest rate markets. A key point is that spot Libor rates are to be treated as market primitives rather than being defined by no-arbitrage relationships. We formulate a consistent realistic dynamics for the different rates emerging from our analysis and compare the resulting model performances to simpler models used in the industry. We include the often neglected margin period of risk, showing how this feature may increase the impact of different rates dynamics on valuation. We point out limitations of multiple curve models with deterministic basis considering valuation of particularly sensitive products such as basis swaps. We stress that a proper wrong way risk analysis for such products requires a model with a stochastic basis and we show numerical results confirming this fact.