December 3rd, 2009, 10:23 am
On a related note, there is another issue which is terribly confusing. I want to calculate the value of project given by: . Here p is lognormally distributed. So I know that E[p]=exp[E[x]+0.5*Var[x]], where x=lnp and follows OU process. Expected value of x is given by: E[x]=x_0*exp[-k*t]+m*(1-exp[-k*t]). Using weekly data I estimate k=0.366, standard deviation of x=0.484, m=3.03, q=1, xo=ln(20) and r=0.1/52. To get the value of the project I substitute value of E[x] into E[p]. Because I want to value a project for a period of 30 years, and because I am using weekly values, T in the integral would equal=30*52=1560. So I integrate: . I get that the value of the project is 11 495. Now I want to use annual values, which in the end should give me very similar results. So to go from weekly to annual values I have: k=0.366*52=19.032, r=0.1, q=52, T=30, and sigma should be 0.484*sqrt(52)=3.49. Now the integral becomes: exp[-0.1t] This equals 4.51641*10^6, which is totally unreasonable. Can anyone spot a problem in my calculations?