N
nicolathompson
Member
Hi, I’ve been trying to sort out all the formulae / distributions in my head and have found the following 6 at various places in the notes. Am confused by the last two...
1. dSt = St(µdt + σdZt) under P (basic definition of Geometric Brownian motion)
2. dSt = St(rdt + σdZtildat) under Q (Chapter 15, p18)
3. St = Soexp[(µ-σ2/2)t + σZt] under P (basic definition of Geometric Brownian motion)
4. St = Soexp[(r-σ2/2)t + σZtildat] under Q (comes from using C-M-G theorem, chapter 14, p12)
Then why do these not match the same way (replace µ by r and Z by Ztilda)?
5. ln[(St+dt/St] has N(µdt, σ2dt) under P (Chapter 9)
6. ln[(St+dt/St] has N((r-σ2/2)dt, σ2dt) under Q (Calibrating binomial models, chapter 12)
1. dSt = St(µdt + σdZt) under P (basic definition of Geometric Brownian motion)
2. dSt = St(rdt + σdZtildat) under Q (Chapter 15, p18)
3. St = Soexp[(µ-σ2/2)t + σZt] under P (basic definition of Geometric Brownian motion)
4. St = Soexp[(r-σ2/2)t + σZtildat] under Q (comes from using C-M-G theorem, chapter 14, p12)
Then why do these not match the same way (replace µ by r and Z by Ztilda)?
5. ln[(St+dt/St] has N(µdt, σ2dt) under P (Chapter 9)
6. ln[(St+dt/St] has N((r-σ2/2)dt, σ2dt) under Q (Calibrating binomial models, chapter 12)