ASM 17.12

[kyle.mcwhinnie]

Rendelman-Bartter has interest rates following Geometric Brownian motion. When I tried 17.12, I solved saying ln(R1/R0) = ln(0.09/0.08) follows normal distibution with mean =(a-0.5(σ^2))t = -0.005, and variation = (σ^2)t=0.01.

I then get Prob (R<0.09) = N[(ln(0.09/0.08) + 0.005) / 0.1] = N(1.22783).

The ASM manual has Prob (R1 < 0.09) = N(1.1778)

Does anyone know why my method is incorrect?

[mercer]

You're getting the mean wrong. The mean should be a*t=0 giving N[ln(.09/08)/.1] = N(1.1778)

[kyle.mcwhinnie]

Ok then here's my confusion. On ASM Pg. 227 Example 15B, see Errata. For the Normal process, the mean = (α -0.5 (σ^2))t. This is a geometric Brownian motion like question 17.12 we were discussing. Why is 0.5(σ^2)t subtracted from the mean for the logged process in Example 15B, but not 17.12?

[Abraham Weishaus]

I agree, 17.12 should be corrected.