CALCULATING VARIABLE ANNUITY LIABILITY "GREEKS" USING MONTE CARLO SIMULATION. Issue 2 (5th January 2015)

• Record Type: Journal Article
• Authors: Cathcart, Mark J.; Lok, Hsiao Yen; McNeil, Alexander J.; Morrison, Steven
• Is Part Of: ASTIN bulletin. Volume 45:Issue 2(2015)
• Page Start: 239
• Page End: 266
• Publication Date: 2015-01-05
• Subjects: Stochastic simulation, -- Monte Carlo estimation, -- variable annuity, -- Greeks, -- sensitivities, -- Heston stochastic volatility model, -- pathwise method, -- likelihood-ratio method, -- stochastic interest rates; Insurance -- Mathematics -- Periodicals; Risk (Insurance) -- Mathematics -- Periodicals; 368.01
• DOI: 10.1017/asb.2014.31
• Languages: English
• ISSNs: 0515-0361

Abstract

Abstract: The implementation of hedging strategies for variable annuity products requires the calculation of market risk sensitivities (or "Greeks"). The complex, path-dependent nature of these products means that these sensitivities are typically estimated by Monte Carlo methods. Standard market practice is to use a "bump and revalue" method in which sensitivities are approximated by finite differences. As well as requiring multiple valuations of the product, this approach is often unreliable for higher-order Greeks, such as gamma, and alternative pathwise (PW) and likelihood-ratio estimators should be preferred. This paper considers a stylized guaranteed minimum withdrawal benefit product in which the reference equity index follows a Heston stochastic volatility model in a stochastic interest rate environment. The complete set of first-order sensitivities with respect to index value, volatility and interest rate and the most important second-order sensitivities are calculated using PW, likelihood-ratio and mixed methods. It is observed that the PW method delivers the best estimates of first-order sensitivities while mixed estimation methods deliver considerably more accurate estimates of second-order sensitivities; moreover there are significant computational gains involved in using PW and mixed estimators rather than simple BnR estimators when many Greeks have to be calculated.