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tutorial5sol - TUTORIAL 5 WEEK 6 ECON3107/ECON5106...

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Unformatted text preview: TUTORIAL 5 WEEK 6 ECON3107/ECON5106 Economics of Finance ANSWERS 1. The Q matrix derived from the elemental payment combinations B0, S0, Bg, Sg, Bb, Sb, Bgg, Sgg, Bgb, Sgb, Bbg, Sbg, Bbb, Sbb is as follows: B S Bg Sg Bb Sb Bgg Sgg Bgb Sgb Bbg Sbg Bbb Sbb Q = 1 . 10 1 . 5- 1- 1 1 . 10 0 . 8- 1- 1 1 . 10 1 . 5- 1- 1 1 . 10 0 . 8- 1- 1 1 . 10 1 . 5- 1- 1 1 . 10 0 . 8- 1- 1 1 . 10 1 . 5 1 . 10 0 . 8 1 . 10 1 . 5 1 . 10 0 . 8 1 . 10 1 . 5 1 . 10 0 . 8 1 . 10 1 . 5 1 . 10 0 . 8 g b gg gb bg bb ggg ggb gbg gbb bgg bgb bbg bbb p S = ( 1 1 0 0 0 0 0 0 0 0 0 0 0 0 ) The atomic security price vector can be derived from the Q matrix and its corresponding p S vector: p atom = p S Q- 1 The result is summarized in the table below: Period 1: p g = 0 . 3896 p b = 0 . 5195 Period 2: p gg = 0 . 1518 p gb = p bg = 0 . 2024 p bb = 0 . 2699 Period 3: p ggg = 0 . 0591 p ggb = p gbg = p bgg = 0 . 0789 p gbb = p bgb = p bbg = 0 . 1051 p bbb = 0 . 1402 i) In period 3, this European Call option should be left to expire worthless in all but states ggg,ggb,bgb, .and bgg . In states ggb,bgb, and bgg the option will be worth $3 . 00 since it can be used to buy a stock worth $18 . 00 for only $15 . 00. In state ggg the option will be worth $18 . 75 since it can be used to buy a stock worth $33 . 75 for only $15 . 00. Hence, the (14 1) state-contingent vector of cash flows c CALL associated with this option is given by c CALL = ( 0 0 0 0 0 0 18 . 75 3 3 0 3 0 0 0 ) . Therefore, the price of the Call option is p CALL = p atom c CALL = 1 . 8186 . 1 ii) If this Put option is held until time period 3, it should be exercises in states gbb, bgb, bbg and bbb. For instance, the option will be worth $5.40 in states gbb, bgb or bbg since it can be used to sell a stock worth only $9.60 for $15.00. Figure below shows the situation diagrammatically. The values in thestock worth only $9....
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tutorial5sol - TUTORIAL 5 WEEK 6 ECON3107/ECON5106...

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