Tut2S2 - 60f8 3. [3 points] Assume a one—period model...

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Unformatted text preview: 60f8 3. [3 points] Assume a one—period model securities market model with two assets SI and .32. The prices at time 0 and at time 1 are respectively given by: 1.1 1.1 1.1 1.1 §(0) : [1 , 2.5], 50,9) = WOOCDOO Is the market arbitrage—free? Explain your answer. NC lac (cw/9e 91? “we €173) 5‘ “ (“Lin 3 fl], ‘: .—— twain/neg ., :3) \’ [Uh [anhk (\(’(‘:¢Vnk (a,ch \xfl \Itc -; \ 5)}? Hefe <2 x R .313 n 0 walk heulvofl px obaip: L33: QUUPL)©5‘,¢L( ,.| - y 3 . . . 7, Q A, QI/ ~1- g—QL‘ (Ll ‘ 4‘on3 no ‘yelohom G" l l . . , 7 %/ “ L} 5%de Vi 0<Q\<\ 3.5:8/..\Q|*é/l<<i* le9+ HQL((1) 4. [15 points] ‘H‘ére are the assumptions on the market useful to answer (a),(b),(c),(d),(e) Ed exg,‘ and (f) on this page and on the following page. 1‘? Assume a one—period model securities market model with two assets 81 and 52. The prices at (LL), L.) time 0 and at time 1 are respectively given by: a 1.1 P 8 V62" ~ 1.1 6 gk ' __ *\ S(0)=[1, 4], S(1,Q): ( Q63 ,elfifiQ) LY}, 91% 7 . ’l "‘ ._ (a What is the risk—free rate in the market? Justify your answer. C LBS I w ) ~l~l :(.l~1f)l 31: (00/0 £031 432 walla (Jive/o ; w V K r (b) Is the market arbitrage—free? Explain your answer. i i l: G)\+QZ“‘C\QZJ¥(QH .‘ 6 t; r“ r I l l~| 4243 Sow stoma , A 1% €chva (P?) ‘34) Q“ 370 Ofleqmfih. ‘ EDIE“? “9L . v A ’3 ‘ lq Lt :. 369” 66a; 4- Ucb ifirmyw‘h ‘1, 31. “(L 223/ ’— n q ‘ y lo ‘0 «(y (3 a +05?“ - Q QM Sir) (kl (L0? 046 (L ' VA k it is colloiltcxg v§me r jH/lc Cf hem;me Egfld‘imo ( (On (10%“ EX “A mm: ; M a“ \ \th q»; I; 03% 1-93 wgem W o<¢u <l 3 O<¢Y3 <‘ 7of8 Ci! 0.: C" U! (c) Give the. possible price(s) for a security that has a payoff: §3(1,SZ) : [ Is the price unique? Justify your answer. Hint: Try to replicate S3 in this market. Cl 2 . g} f p A ‘ ’3 ’5 1') I SSVU-Q xv! 6‘ g. + 82,332, : 8?) he“ C58 ex; ex $4” (can 2‘ (LWL (9. x\.\ +eLK2§ -: So 8‘ x H .+Q.L'>(6 :: 52, --l©r2X 3 ’1 5 \CchK q @i X H 491% )9 5 f / I” ‘/ , 2% 8‘ 2: 8L:b :\ CULQ:GIX\+%Z><\1 / ((1) Let (a, b) be the range of possible values for the third Arrow—Debreu security, (73 that preserve 8 R YA \Q A the no—arbitrage property of the market. Give the possible price(s) of a security 34(1, 82) 2 [ 3 1 m9 '0 ' 3 as a function of a and b. 1 RS t_,3 of.) _ M.) ‘9 SL1 : (33 ‘l" g 3 63> +82. '3 \ ‘2 «5 [’« I A r L + PLKKC 0k S)“ : t, e: + frqu 6;? C2 Q (i i A / l (0) Is the market complete? Justify. \ 2 NO ‘~ v g V: A I cl '3 \ g \t \ 5 Re“ mmgfi» (3 “A (“TEE \ '\ 1") ~ «l, .i' c“ r °-l m. a» e Ex 9‘ re‘ <— «C :3 » + ' «Q Do Sikh's“ “L (9a )9?) o \SRCLLK, 50‘“? V??? (ML ...
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This note was uploaded on 01/16/2011 for the course ACTSC actsc 446 taught by Professor Idk.. during the Spring '09 term at Waterloo.

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Tut2S2 - 60f8 3. [3 points] Assume a one—period model...

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