Schweser Mock- Risk Neutral Probablilty for Decision Tree

[knight90]

Schweser Mock 2- Morning Session- Question # 37… Question- Value a two-period 40 call on the stock Given: Up move factor= 1.15 … rf= 4% … Delta of options over 1st period= .83… stock price= 45 Answer: Prob Up Move= (1.04-.87)/(1.15-.87) = .607 Value 2 up moves= (19.51)(.607^2) / (1.04^2) = 6.65 Value up-down move= (2)(.607)(.393)(5) / (1.04^2) = 2.21 total value= 8.86 I have 2 questions on this problem that I hope you guys can help me with… Isn’t the formula for the probability of an up move (1 + rf - Delta) / (Up Factor - Delta) ? So why .87 in the formula instead of .83 for the probablity of the up move? Also, why is the value of the up-down move multiplied by 2 instead of just [(prob up move)(prob down move)(5)]/[(1+rf)^2)]? Thanks

[tickersu]

@knight90

Schweser Mock 2- Morning Session- Question # 37… Question- Value a two-period 40 call on the stock Given: Up move factor= 1.15 … rf= 4% … Delta of options over 1st period= .83… stock price= 45 Answer: Prob Up Move= (1.04-.87)/(1.15-.87) = .607 Value 2 up moves= (19.51)(.607^2) / (1.04^2) = 6.65 Value up-down move= (2)(.607)(.393)(5) / (1.04^2) = 2.21 total value= 8.86 I have 2 questions on this problem that I hope you guys can help me with… Isn’t the formula for the probability of an up move (1 + rf - Delta) / (Up Factor - Delta) ? So why .87 in the formula instead of .83 for the probablity of the up move?The probability of an up move is [(1+Rf)-Down Factor]/(Up factor - Down Factor) Also, why is the value of the up-down move multiplied by 2 instead of just [(prob up move)(prob down move)(5)]/[(1+rf)^2)]? Up-down and down-up get you to the same place-- you can simplify by just calculating once and multiplying the result by 2. Draw the tree diagrams if it helps you see this.

Hope this helps!

[knight90]

got it… was substituting delta in for D in the formula instead of the down move factor… makes much more sense now lol. Thank you very much for the help