Please refer to the attachments.
14. (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 (a) (/ 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) (1) 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 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% Val Assumption Black- RS- Black- RS- Black- RS Black- RS- Set Scholes GARCH Scholes GARCH Scholes GARCH Scholes GARCH I 0.0 -0.7 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) (1) 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).15. (7 points) You work in the hedging department of LMN, a company selling variable annuities with a GMWB rider. Your manager is interested in understanding more about volatility management strategies and asks you to prepare a memo. (a) (1.5 points) Describe principal objectives of volatility management strategies of equity-based guarantee products from the perspectives of manufacturer and client respectively. LMN currently uses a capped volatility strategy to manage volatility risks. LMN targets a 60% allocation to the S&P500 index. The trigger level for the company is 30%. The sum of squared daily returns of the portfolio from the last 21 business days is now 0.0081 (i.e., )" ri = 0.0081, where r, = daily return of the portfolio from / business days ago). Assume that there are 252 business days in a year and 100% is the maximum equity allocation. (b) (1.5 points) Determine the equity allocation of the portfolio after any changes driven by the capped volatility strategy. (c) (0.5 points) Describe actions, if any, to take to achieve the changes in equity allocation in part (b). Your co-worker mentions that he had just read about VIX-indexed volatility management strategies. He stated that the VIX-indexed fee rider enables the company to charge clients for all of the hedging costs of the company as they occur and that this in turn makes it a good strategy for dealing with spikes in volatility. (d) (I point) Critique your coworker's thoughts on VIX-indexed volatility management strategies.LMN is considering adopting a different volatility management strategy that balances both LMN's and the clients' perspectives. The company has been provided the following information on various volatility management strategies. VIX- Joint VIX Capped Target Capital Volatility Volatility Preservation indexed fee & cap fees volatility Reduction in 15% 61% 94% 26% 40% volatility cost Vega 0.40% 0.12% 0.03% 0.36% 0.24% Cumulative fees 100 100 100 101 101 Returns 2000-09 -0.25% -0.55% -0.06% -0.73% -0.61% Returns 2010-17 6.05% 5.40% 2.82% 6.20% 6.06% Volatility 2000-09 11.05% 8.19% 5.26% 12.92% 11.05% Volatility 2010-17 8.52% 7.60% 4.55% 8.65% 8.51% A consulting firm recommended a joint VIX-indexed and capped volatility strategy as the volatility management strategy. (e) (2.5 points) Evaluate the recommended strategy
