tailieunhanh - Additional Praise for Fixed Income Securities Tools for Today’s Markets, 2nd Edition phần 9

Được thành lập vào năm 1807, John Wiley & Sons là công ty xuất bản lâu đời nhất độc lập tại Hoa Kỳ. Với các văn phòng tại Bắc Mỹ, Châu Âu, Úc và châu Á, Wiley là trên toàn cầu cam kết phát triển và tiếp thị in ấn và | Pricing American and Bermudan Bond Options in a Term Structure Model 401 .1976 earlier dates. This section therefore focuses on the pricing of American and Bermudan options. The following example prices an option to call 100 face of a coupon bond at par on any coupon date. Assume that the riskneutral interest rate process over six-month periods is as in the example of Chapter 9 .6489 .3511 . .6489 .3511 With this tree and the techniques of Part Three the price tree for a coupon bond maturing in years may be computed to be 100 .6489 100 .8024 .3511 .1976 .6489 100 .3511 100 Note that all the prices in the tree are ex-coupon prices. So for example on date 2 state 2 the bond is worth after the coupon payment of has been made. The value of the option to call this bond at par is worthless on the maturity date of the bond since the bond is always worth par at maturity. On any date before maturity the option has two sources of value. First it can be exercised immediately. If the price of the bond is P and the strike price is K then the value of immediate exercise denoted VE is 402 FIXED INCOME OPTIONS VE max p - K 0 Second the option can be held to the next date. The value of the option in this case is like the value of any security held over a date namely the expected discounted value in the risk-neutral tree. Denote this value by VH. The option owner maximizes the value of the option by choosing on each possible exercise date whether to exercise or to hold the option. If the value of exercising is greater the best choice is to exercise while if the value of holding is greater the best choice is to hold. Mathematically the value of the option V is given by V max VE VH For more intuition about the early exercise decision consider the following two strategies. Strategy 1 is to exercise the option and hold the bond over the next period. Strategy 2 is .