This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: MAFS 5030 Quantitative Modeling of Derivatives Securities Solution to Homework One Course Instructor: Prof. Y.K. Kwok 1. There will be two coupons before delivery: one in 6 months and one just prior to delivery. Using the present value formula: $94 . 6 = F + $4 e . 1 + $4 e . 05 , where F is the forward price, $4 is the coupon amount and interest is compounded continuously at the rate of 10%. We obtain F = $94 . 6 e . 1 $4 e . 05 $4 = $96 . 34 . Alternatively, we can interpret coupons as negative cost of carry and apply the formula: F = S D B ( τ ) , where D is the sum of present value of the coupons. We then have F = $94 . 6 $4 e . 05 $4 e . 1 e . 1 = $96 . 34 . 2. Consider the fixedleg and floatingleg of a swap of unit notional. Suppose the current time is indexed by 0 (i.e. t = 0), and t = 1 means one year away from now. Fixedleg At t = 1 4 , receives 10% 2 = 0 . 05 of interest. At t = 3 4 , receives 10% 2 = 0 . 05 of interest. Floatingleg At t = 1 4 , receives L 1 2 parenleftbigg 1 4 parenrightbiggparenleftbigg 3 4 1 4 parenrightbigg = 1 2 L 1 2 parenleftbigg 1 4 parenrightbigg . Here, L 1 2 parenleftbigg 1 4 parenrightbigg denotes halfyear LIBOR reset at an earlier time t = 1 4 . At t = 3 4 , receives L 1 2 parenleftbigg 1 4 parenrightbiggparenleftbigg 3 4 1 4 parenrightbigg = 1 2 L 1 2 parenleftbigg 1 4 parenrightbigg . 1 Discount bond prices observed at t = 0: B parenleftbigg , 1 4 parenrightbigg = 0 . 972 , B parenleftbigg , 3 4 parenrightbigg = 0 . 918. The floating rate bond that receives 1 + 1 2 L 1 2 parenleftbigg 1 4 parenrightbigg at time 1 4 is now priced at 0 . 992. This gives the present value of 1 2 L 1 2 parenleftbigg 1 4 parenrightbigg = 0 . 992 B parenleftbigg , 1 4 parenrightbigg = 0 . 992 . 972 = 0 . 02 . Also, the implied present value of 1 2 L 1 2 parenleftbigg 1 4 parenrightbigg = B parenleftbigg , 1 4 parenrightbigg B parenleftbigg , 3 4 parenrightbigg = 0 . 972 . 918 = 0 . 054 . Therefore, the present value of the floatingleg payments is $0 . 02 + $0 . 054 = $0 . 074 per unit notional. The present value of the fixedleg payments is . 05 bracketleftbigg B parenleftbigg , 1 4 parenrightbigg + B parenleftbigg , 3 4 parenrightbiggbracketrightbigg = ($0 . 05)(0 . 972 + 0 . 918) = $0 . 0945 per unit notional....
View
Full
Document
This note was uploaded on 02/01/2012 for the course MATH A taught by Professor A during the Spring '11 term at HKU.
 Spring '11
 A
 Derivative

Click to edit the document details