Risk analyses often require the revaluation of complex financial instruments over a large set
of risk factor scenarios. In many instances, especially in historical and Monte-Carlo simulation
approaches to Value-at-Risk, full revaluation is numerically-intensive and hence too costly.
Lattice models, for example, are flexible and convenient vehicles for pricing complex
derivatives, but repricing over many different factor scenarios is prohibitive. For that reason,
Taylor series approximations to the pricing function are employed based on partial derivatives
of the instrument with respect to the underlying value drivers. Hence, partial simulations of
non-linear derivatives are based on estimates of delta, gamma, vega and other relevant Greeks.
Likewise, partial revaluation of fixed income positions are based on duration and convexity
measures. Drawback is that the Taylor series approximations are only valid for relatively
small changes in the risk factors. This results in large approximation errors in the tails of the
value distribution—and especially tail information is relevant in risk analyses. Greeks are
not only relevant in shortcuts to revaluing derivatives, but also for describing their risk
profile. This allows the adequate hedging of derivative and fixed income positions. When the
underlying valuation model is complex, effective Greeks are approximated by numerical