{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chapter4

# Chapter4 - Investment Science Chapter 4 Solutions to...

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

Investment Science Chapter 4 Solutions to Suggested Problems Dr. James A. Tzitzouris 4.1 (One forward rate) f 1 , 2 = (1 + s 2 ) 2 (1 + s 1 ) - 1 = 1 . 069 2 1 . 063 - 1 = 7 . 5% 4.2 (Spot Update) Use f 1 ,k = ± (1 + s k ) k 1 + s 1 ² 1 / ( k - 1) - 1 . Hence, for example, f 1 ,k = ± (1 . 061) 6 1 . 05 ² 1 / 5 - 1 = 6 . 32% . All values are f 1 , 2 f 1 , 3 f 1 , 4 f 1 , 5 f 1 , 6 5 . 60 5 . 90 6 . 07 6 . 25 6 . 32 1

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

View Full Document
(Construction of a zero) Use a combination of the two bonds: let x be the number of 9% bonds, and y teh number of 7% bonds. Select x and y to satisfy 9 x + 7 y = 0 , x + y = 1 . The ﬁrst equation makes the net coupon zero. The second makes the face value equal to 100. These equations give x = - 3 . 5, and y = 4 . 5, respectively. The price is P = - 3 . 5 × 101 . 00 + 4 . 5 × 93 . 20 = 65 . 90. 4.5 (Instantaneous rates) (a) e s ( t 2 ) t 2 = e s ( t 1 ) t 1 e f t 1 ,t 2 ( t 2 - t 1 ) = f t 1 ,t 2 = s ( t 2 ) t 2 - s ( t 1 ) t 1 t 2 - t 1 (b) r ( t ) = lim t t 1 s ( t ) t - s ( t 1 ) t 1 t - t 1 = d [ s ( t ) t ] dt = s ( t ) + s 0 ( t ) (c) We have d (ln x ( t )) = r ( t ) dt, = s ( t ) dt + s 0 ( t ) dt, = d [ s ( t ) t ] . Hence, ln x ( t ) = ln x (0) + s ( t ) t, and ﬁnally that x ( t ) = x (0) e s ( t ) t . This is in agreement with the invariance property of expectation dynamics. Investing continuously give the same result as investing in a bond that matures at time t . 4.6
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 8

Chapter4 - Investment Science Chapter 4 Solutions to...

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

View Full Document
Ask a homework question - tutors are online