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FIN 4750 - Question 12.26 So=$30 K=$29(a d1=lnSoK Rf...

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Question 12.26 S o =$30 Rf=5% T= 13 K=$29 δ=25% (a) d1= + + lnSoK Rf δ22Tδ * T = +. +. . ln3029 05 252213 25 * 13 = 0.42252 N(d1)= 66.367% d2=d1- δ* T =0.42252-.25* 13 =0.2782 N(d2)= 60.956% C=So*N(d1)-K - e rT *N(d2)=30*.66367-29* -. * / e 05 1 3 *.60956=$2.52 The price of a European call is $2.52. (b) Since it’s not optimal to exercise a non-paying dividend American option before the expiration date, the value of the American call and the European call are equal. www.de Therefore, C=So*N(d1)-K - e rT *N(d2)=30*.66367-29* -. * / e 05 1 3 *.60956=$2.52 The price of an American call is $2.52. (c) N(-d1)=N(-.42252)= 0.33632 N(-d2)=N(-.2782)= 0.39043 P= K - e rT *N(-d2)- So*N(-d1) = 29* -. * / e 05 1 3 *.39043- 30*.33632=$1.05 The price of a European put is $1.05. (d) C-P=So-K - e rT 2.52-1.05=30-29 -. * / e 05 1 3 1.47=1.47 Since both sides are equal, put-call parity holds. Question 13.20 So=$0.85 for 1 Canadian dollar. K=$0.85 for 1 Canadian dollar. δ =4% r= 5%
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rf=4% T=3/4 Value of a European call option to buy one Canadian dollar for US $0.85: d1= + - lnSoK r + rf δ22Tδ * T = . . +. -. + . / . ln0 850 85 05 04 0 04223 4 04 * / 3 4 = 0.2338 3 d2= d1- δ* T =.23383-.04* / 3 4 = 0.1992 N(d1)= 0.5924 N(d2)= 0.5789 C=So* - * e rf T *N(d1)-K - e rT *N(d2) =0.85* - . * . e 0 04 0 75 *0.5924-0.85 - . * . e 0 05 0 75 *0.5789= $0.0147 Use put-call parity to calculate a European put option to sell one Canadian dollar for US $0.85:
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