Eco 400
State elements of a monopsony
(6 points) As a pricing actuary of an insurer, you are asked to provide comments on the new variable annuity (VA) business with GMAB, GMMB, GMIB, and GMWB riders. The following features are offered in the products: No floor value in the first 5 policy years . After the 5" policy year, an annual ratchet feature if no withdrawals were made (I point) Explain how these features impact the value of the embedded options in the riders. When pricing the products, your mortality assumption is based on the industry average. (b) (1 point) (i) Explain how this assumption could be adjusted in order to make the products more competitive. (ii) Suggest one way to manage the longevity risk after making this change. The Chief Risk Officer of the company is mostly concerned about the risks inherent in GMWBs. (c) (1 point) (i) Identify the financial instruments that can be used to hedge against the following financial risks inherent in the GMWB: stock market volatility increase in stock market volatility. (ii) State two reasons why the risks in the GMWB cannot be perfectly hedged. Suppose that the VA benefits are tied to a reference portfolio, whose value follows either a geometric Brownian motion (Black-Scholes) or a Regime-Switching-GARCH model (RS-GARCH). The actuarial risk management team utilizes four assumption sets to analyze the effectiveness of hedging GMMBs, assuming delta-hedging is used. The hedging is performed based on the hedging assumptions below, while the test assumptions are used to simulate outcomes for the analysis of hedge effectiveness. Assumption Set Hedging Assumption Test Assumption I Assume that the policyholder The policyholder conforms to the will not surrender his contract hedging assumption Assume that the policyholder II will lapse his contract if the The policyholder conforms to the moneyness ratio hits 150% hedging assumption Assume that the policyholder The policyholder does not conform to III will not surrender his contract the hedging assumption and lapses when the moneyness ratio hits 150% Assume that the policyholder The policyholder actually lapses his IV will lapse his contract if the contract once the moneyness ratio moneyness ratio hits 175% hits 150% Your assistant provides the table below showing key statistics for the net hedging error for each combination of assumption set and model: Mean StDev 95% CTE 99% VaR Assumption Black- RS Black- RS- Black- RS- Black- RS- Set Scholes GARCH Scholes GARCH Scholes GARCH Scholes | GARCH 0.0 -0. 0.7 1.8 1.6 3.6 1.9 4.4 II -0.1 -1.1 0.8 2.0 1.9 3.6 2.2 4.4 III 0.5 -0.6 1.7 2.4 2.7 3.7 2.9 4.3 IV 1.2 0.0 3.8 4.0 8.2 7.7 8.6 8.3 You have reviewed the results and tell your assistant that the results for Assumption Set III and IV may have been switched. (d) (3 points) (i) Justify your assertion. (ii) Identify and explain the conclusions that can be drawn from comparing the above results after switching the results for Assumption Set III and IV. (iii) Compare the above results with respect to the following aspects between the Black-Scholes and RS-GARCH models (assuming that insurer uses delta-hedging under the Black-Scholes model to manage the risk of the GMMBs): Risk measures (including standard deviation) . Model risk Hedging error (iv) Explain whether dynamic lapsation should be hedged, based on the comparison in part (iii)
