Hi all,
I have just finished this question, and although the solutions make sense i am stumped as to why my approach isn't correct.
we are trying to find the value of an option v_0=exp(-0.02)*[50*P(S_1/S_0 <0.8) *P(R_1/R_0 <0.6))
we are given r=0.02 and sigma_s=0.32 and sigma_r=sqrt(0.15)
my approach would be to use that
S_1/S_0-lognormal(muT, \sigma^2T)
and since under black scholes mu is = r, we know mu=0.02
S_1/S_0-lognormal(0.02, 0.32^2)
R_1/R_0-lognormal(0.02, 0.15)
so P(S_1/S_0 <0.8)=P(Z<ln0.8-0.02/0.32)=0.22386
and P(R_1/R_0<0.6)=P(Z<ln0.6-0.02/sqrt(0.15))=0.08525
so v_0=exp(-0.02*)*[50*0.22386*0.08525)
=0.9346 which is not equal to the 1.61 which is the correct answer.
If anyone is able to let me know why we cant use this method that would be amazing please - is my assumption that under black scholes mu=r wrong?
Thank you
I have just finished this question, and although the solutions make sense i am stumped as to why my approach isn't correct.
we are trying to find the value of an option v_0=exp(-0.02)*[50*P(S_1/S_0 <0.8) *P(R_1/R_0 <0.6))
we are given r=0.02 and sigma_s=0.32 and sigma_r=sqrt(0.15)
my approach would be to use that
S_1/S_0-lognormal(muT, \sigma^2T)
and since under black scholes mu is = r, we know mu=0.02
S_1/S_0-lognormal(0.02, 0.32^2)
R_1/R_0-lognormal(0.02, 0.15)
so P(S_1/S_0 <0.8)=P(Z<ln0.8-0.02/0.32)=0.22386
and P(R_1/R_0<0.6)=P(Z<ln0.6-0.02/sqrt(0.15))=0.08525
so v_0=exp(-0.02*)*[50*0.22386*0.08525)
=0.9346 which is not equal to the 1.61 which is the correct answer.
If anyone is able to let me know why we cant use this method that would be amazing please - is my assumption that under black scholes mu=r wrong?
Thank you