Confused about value down in binomial distribution

CFA Level I
#1

Hi I am confused about the value down in binomial distribution defying my odds. An up move by 1 percent would make the value 1.01 times the current value. A down move of 1 percent according to me should make the value .99 times the current value but the book says (1/1.01) times the current value. Why would this be. Any thoughts Thanks

#2

I think by definition product of combinations +1%, -1% should be 1… so if up is +1.01 down is 1/1.01 to make 1.01 * 1/1.01 = 1

#3

Also, (1/1.01)=.990 so depending on the accuracy level you’re looking for they’re essentially the same, right? For the most accuracy CP’s explanation is best but generally it looks like they’re just using a different method.

#4

for 1 percent it makes valid assumption. but for higher values it has more decimals flowing in. for example 10% and so on for 10 percent down value = .9 but 1/1.1 = .909 almost equal to .91

#5

Good point. Never mind my shortcut/estimation then, do it the right way all the time.

#6

Ignore the book. For 1% Up move x* (1+0.01) = x * 1.01 Down move = x * (1-0.01) = x * 0.99