Kiểm tra căng thẳng cho không chắc chắn tham số Để sử dụng các kỹ thuật kiểm nghiệm căng thẳng không chắc chắn tham số, mô phỏng được lặp đi lặp lại bằng cách sử dụng tham số khác nhau thiết lập để xem hiệu quả của các giả định khác nhau về sản lượng | CompoundAnnual Ratchet Valuation 253 comfortably profitable at least before the life-of-contract guarantee cost is added whereas contracts C and D are not. Clearly contract D stands out here how can the insurer offer such generous terms One answer is in the use of simple rather than compound annual ratcheting. We saw earlier in this chapter that the simple annual ratchet is cheaper than the compound version. Also contract D uses averaging in determining the indexation. This means that the index value for determining the annual reset is averaged either on a monthly or a daily basis over the year prior to maturity. This decreases the volatility of returns greatly and makes the option cheaper although it does not necessarily reduce payouts to policyholders providing lower returns in rising markets and higher returns in falling markets. CAR with Life-of-Contract Guarantee The simple annual ratchet contract and the addition of a life-of-contract guarantee are not amenable to the analytic approach. A simple method of valuing the option in these cases is by stochastic simulation also called the Monte Carlo method. Recall that the Black-Scholes valuation of any derivative contract is the expected value of the discounted payoff under the risk-neutral distribution. In the standard Black-Scholes context that we are using in this chapter the risk-neutral distribution is lognormal with independent and identically distributed increments and with parameters for the annual log-return distribution of r d ơ112 and T2 where the d is the continuously compounded dividend yield rate. We will simulate the payoff under the option for say 100 000 projections of the stock price process and discount using the risk-free rate of interest. The mean value is the estimated Black-Scholes price of the option. We will use the Monte Carlo method in this section for the compound ratchet option with life-of-contract guarantee as well as in the next section for the simple annual ratchet with .
