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550_445_2010 TA 03

# 550_445_2010 TA 03 - 550.445 Modeling and Analysis of...

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550.445 Modeling and Analysis of Securities and Financial Markets II, Spring 2010 TA Section 03 Peter C.L. Lin [email protected] 1 Homework Review 29.11 To calculate the convexity adjustment for the five-year rate define the price of a five year bond, as a function of its yield as G ( y ) = e - 5 y G prime ( y ) = - 5 e - 5 y G primeprime ( y ) = 25 e - 5 y . The convexity adjustment is 0 . 5 × 0 . 08 2 × 0 . 25 2 × 4 = 0 . 004 . Similarly for the two year rate the convexity adjustment is 0 . 5 × 0 . 08 2 × 0 . 25 2 × 4 × 2 = 0 . 0016 . We can therefore value the derivative by assuming that the five year rate is 8 . 4% and the two-year rate is 8 . 16%. The value of the derivative is 0 . 24 e - 0 . 08 × 4 = 0 . 174 . If the payo ff occurs in five years rather than four years it is necessary to make a timing adjustment. From equation (29.4) this involves multiplying the forward rate by exp parenleftBigg - 1 × 0 . 25 × 0 . 25 × 0 . 08 × 4 × 1 1 . 08 parenrightBigg = 0 . 98165 . The value of the derivative is 0 . 24 × 0 . 98165 e - 0 . 08 × 5 = 0 . 158 . 2 Siegel’s Exchange Rate Paradox (cont.) Last time, we showed that 1 Q has mean rate of change R f ( t ) - R ( t ) + σ 2 2

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550_445_2010 TA 03 - 550.445 Modeling and Analysis of...

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