{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Solution to Homework One

# Solution to Homework One - MAFS 5030 Quantitative Modeling...

This preview shows pages 1–3. Sign up to view the full content.

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 0 . 1 + \$4 e 0 . 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 0 . 1 - \$4 e 0 . 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 - 0 . 05 - \$4 e - 0 . 1 e - 0 . 1 = \$96 . 34 . 2. Consider the fixed-leg and floating-leg 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. Fixed-leg At t = 1 4 , receives 10% 2 = 0 . 05 of interest. At t = 3 4 , receives 10% 2 = 0 . 05 of interest. Floating-leg 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 half-year 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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Discount bond prices observed at t = 0: B parenleftbigg 0 , 1 4 parenrightbigg = 0 . 972 , B parenleftbigg 0 , 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 0 , 1 4 parenrightbigg = 0 . 992 - 0 . 972 = 0 . 02 . Also, the implied present value of 1 2 L 1 2 parenleftbigg 1 4 parenrightbigg = B parenleftbigg 0 , 1 4 parenrightbigg - B parenleftbigg 0 , 3 4 parenrightbigg = 0 . 972 - 0 . 918 = 0 . 054 . Therefore, the present value of the floating-leg payments is \$0 . 02 + \$0 . 054 = \$0 . 074 per unit notional. The present value of the fixed-leg payments is 0 . 05 bracketleftbigg B parenleftbigg 0 , 1 4 parenrightbigg + B parenleftbigg 0 , 3 4 parenrightbiggbracketrightbigg = (\$0 . 05)(0 . 972 + 0 . 918) = \$0 . 0945 per unit notional. The value of the swap to the fixed-rate payer with notional one million = \$1 , 000 , 000 × (0 . 074 - 0 . 0945) = - \$20 , 500 .
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 6

Solution to Homework One - MAFS 5030 Quantitative Modeling...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online