có nghĩa là, Y0 =, do đó giá trị đầu tiên của loạt bài là . Để chứng minh phương trình 4,18, nó đơn giản để làm việc với quá trình detrended , vì vậyAđăng nhập SnT là độc lập, giống nhau phân phối N (0, 1), cho kết quả trong phương trình 4,18, vì vậy nó có thể để tính toán xác suất phân tích các yếu tố tích lũy | The Unhedged Liability 145 to earn a risk-free rate of interest of r 12 per month. In the month t to t 1 the stock price changes from St to St 1. The option price at t is H t Yt VtSt Immediately before rebalancing at t the hedge portfolio from t - 1 has accumulated to H r Yf-1er 12 Ỷf-1Sf and the hedge required is H t . The difference H t - H t is the hedging error. If this difference is negative then the hedging error is a source of profit. This means that the replicating portfolio brought forward is worth more than we need to set up the rebalanced portfolio. As an example in Table we show the results from a single simulation of the hedging error for a two-year GMMB or European put option with monthly hedging. The strike price or guarantee at t 0 is K 100 which is equal to the fund at the start of the two-year projection. Management charges of 3 percent per year are deducted from the fund. The risk-free force of interest is assumed to be 6 percent the volatility for the hedge is 20 percent per year. The stock prices in the second column are calculated by simulating an accumulation factor each month from a regime-switching lognormal RSLN distribution. This is the real-world measure not the Q-measure because we are interested in the real-world outcome. The Q-measure is only used for pricing and constructing the hedge portfolio. In column 3 the stock part of the hedge is calculated this is - 0 97 2 - ln St 2 K r a2 2 2 - t 12 . r 72 - t 12 II a 72 - t 12 In column 4 the bond part of the hedge is given Ke-r 2-t 12 _ ln St 2 K r - a2J2 2 - t 12 72 - I 12 II Column 5 is the sum of columns 3 and 4 this is the Black-Scholes price at t months using the projected stock price at that time H t . This represents the cost of the hedge required to be carried forward to the next month. 146 DYNAMIC HEDGING FOR SEPARATE ACCOUNT GUARANTEES TABLE Single simulation of the hedging error for a two-year GMMB. Time Months t St Stock Part of Hedge Bond Part of Hedge BSP H
