The Difference between LSMC and Replicating Portfolio in Insurance Liability Modeling

Abstract

Solvency II requires insurers to calculate the 1-year value at risk of their balance sheet. This involves the valuation of the balance sheet in 1 year's time. As for insurance liabilities, closed-form solutions to their value are generally not available, insurers turn to estimation procedures. While pure Monte Carlo simulation set-ups are theoretically sound, they are often infeasible in practice. Therefore, approximation methods are exploited. Among these, least squares Monte Carlo (LSMC) and portfolio replication are prominent and widely applied in practice. In this paper, we show that, while both are variants of regression-based Monte Carlo methods, they differ in one significant aspect. While the replicating portfolio approach only contains an approximation error, which converges to zero in the limit, in LSMC a projection error is additionally present, which cannot be eliminated. It is revealed that the replicating portfolio technique enjoys numerous advantages and is therefore an attractive model choice.

Neural Network for Pricing and Universal Static Hedging of Contingent Claims

“…Glasserman and Yu [2004] show that for a single-period problem, the regress later algorithm gives a higher coefficient of determination and a lower covariance matrix for the estimated coefficients. Pelsser and Schweizer [2016] show that as the approximation error from the regression in the regress later approach vanishes, the coefficients obtained are perfect regardless of the measure used for calibration. This property can be leveraged for problems where one has to work with mixed probability measures, examples of which include computing potential future exposures of Bermundan Swaptions in Feng et al [2016], and computing the capital valuation adjustment in Jain et al [2019a], where one has to work simultaneously with both the risk-neutral and the real-world measures.…”

Rolling Adjoints: Fast Greeks along Monte Carlo scenarios for early-exercise options

“…Impact of inexact discretization scheme. We briefly study through numerical experiments the convergence of the method when an Euler discretization scheme is used for the simulation of the scenarios instead of an exact scheme as given in Equation (25). An Euler discretization of the SDE given by Equation 24is…”

“…For all the experiments here we simulate 90,000 scenarios, using an exact discretization scheme as given by Equation (25). We use a recursive bifurcation scheme for bundling with 2 3 bundles at each time step.…”

“…The major challenge for regress-later or portfolio replication schemes arises for derivatives that exhibit strong path dependency, which, as Pelsser and Schweizer (2016) (25) demonstrate, often implies a higher problem dimensionality. Finding a suitable regression basis for pricing such derivatives, especially one for which the conditional expectations are readily available is therefore challenging.…”

“…This approach has commonly been referred to as regression later (or, regress-later), or also, as in Beutner et al (2015)(3), as replicating portfolio. An extensive comparative analysis of the regress-now (the usual LSMC) versus portfolio replication scheme can be found in Beutner et al (2013)(4) and (25).…”