Least Squares Monte Carlo: Application to Nested Simulation
Document ID: 2006-782 (previously 2006/003)
Published on: 30th June 2006
Author: Steven Morrison
The (real-world) projection of market-consistent liability values is a topical challenge for the global life industry. The projection of future market-consistent solvency levels and the projection of future levels of market-consistent embedded values both require an ability to estimate how current liability valuations will change across a range of future scenarios and timelines. The ‘brute force’ solution to this problem is nested simulation. That is, each time-point of a relevant real-world scenario has a nest of appropriately calibrated market-consistent scenarios that allow market-consistent liability valuation to be performed at that point. However, this is a seriously intensive approach from a computational perspective. For example, if market-consistent values were desired for every year of a 1000-scenario, 40-year projection, the nested simulation approach would require 40 million scenarios (assuming 1000 scenarios for each valuation). The attached note discusses an alternative approach to this problem that has been implemented in the banking sector for projecting the value of options for which closed-form valuations do not exist. The use of this technique reduces the required number of scenarios from 40 million to 40,000 (i.e. it has reduced the number of scenarios by a factor of 1000). Further, as it is statistical technique, it is potentially simpler to develop and calibrate than the approach of developing closed-form approximations for the market-consistent liability values.
