“Smart” Nested Simulation: Learning from Option Traders
Document ID: 2007-214 (previously Issue 3)
Published on: 31st July 2007
Author: Steven Morrison
Having developed models for market-consistent valuation of their balance sheets, actuaries are now looking to take these models a stage further, asking the question: how will my balance sheet change as I project forward during the course of a best-estimate stochastic projection? This naturally leads to the concept of ‘nested’ or ‘stochastic-on-stochastic’ simulation, with best-estimate ‘outer’ scenarios branching into market-consistent ‘inner’ scenarios at various points in time. This is a new and challenging problem for actuaries. However, it is a problem that option traders and financial engineers have faced for some time, in the context of valuation of American options. Motivated by this problem, academics have developed some smart methods as alternatives to ‘full’ nested simulation, potentially requiring far fewer scenarios. Such methods have been implemented by investment banks to price and hedge the American options that they trade. In this note, we briefly describe one of the more popular methods that has emerged –“Least Squares Monte Carlo” –which we believe may provide a promising practical technique to actuaries interested in projection of market-consistent balance
