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Financial Engineering PrinciplesA Unified Theory for Financial Product Analysis and Valuation phần 3

Trong những nghiên cứu này, mỗi lần một người vào bệnh viện, họ được tính là một trường hợp mới. Vì vậy, nếu một người đã phải nhập viện ba lần, cùng một người được tính là ba trường hợp. Bây giờ chúng ta biết rằng tỷ lệ | 38 PRODUCTS CASH FLOWS AND CREDIT TABLE 2.1 Comparisons of Yield-to-Maturity and Current Yield for a Semiannual 6 Coupon 2-Year Bond Price Yield-to-Maturity Current Yield 102 4.94 5.88 100 6.00 6.00 98 7.08 6.12 and current yield are identical. Further current yield does not have nearly the price sensitivity as yield to maturity. Again this is explained by current yield s focus on just the coupon return component of a bond. Since current yield does not require any assumptions pertaining to the ultimate maturity of the security in question it is readily applied to a variety of nonfixed income securities. Let us pause here to consider the simple case of a six-month forward on a five-year par bond. Assume that the forward begins one day after a coupon has been paid and ends the day a coupon is to be paid. Figure 2.13 illustrates the different roles of a risk-free rate R and current yield Yc . As shown one trajectory is generated with R and another with Yc. Clearly the purchaser of the forward ought not to be required to pay the seller s opportunity cost calculated with R on top of the full price clean price plus accrued interest of the underlying spot security. Accordingly Yc is subtracted from R and the resulting price formula becomes F S11 T R - Yc for a forward clean price calculation. For a forward dirty price calculation we have Fd Sd 1 T R - Yc Af where Fd the full or dirty price of the forward clean price plus accrued interest Sd the full or dirty price of the underlying spot clean price plus accrued interest Af the accrued interest on the forward at expiration of the forward The equation bears a very close resemblance to the forward formula presented earlier as F S 1 RT . Indeed with the simplifying assumption that T 0 Fd reduces to Sd Af. In other words if settlement is immediate rather TLFeBOOK Cash Flows 39 Of course these particular prices may or may not actually prevail in expiration date FIGURE 2.13 Relationship between Yc and R over time. than sometime