10% increase and 10% decrease in the price equals oringinal price possible, increase, decrease, example

sharksfan

hi
in the probability distribuitions they are saying that a 10% increase and a 10% decrease would bring the price to the initial level. how is that possible. for example

initial price = 50$
10% increase = (100+10)*50/100 = 55
now the new price = 55
at this point a 10% decrease is 10% of 55 = 5.5 and so the new price = 49.5

similarly if we do the 10% decrease first and then do a 10% increase on the new price then we get the same 49.5 again.

but the book says 1.1*50/1.1 = 50

why would a 10 percent decrease use division when in fact it should be

1.1 * 50 - 1.1*50*10/100 = 1.1 * 50 [100 - 10]/100 = 1.1 * 50 * 90 / 100

there is no way i can see how 90/100 would equal 1/1.1 (which ignores a good rounding error) and then bring the final value to 50 instead of 49.5

this is really killing me. i would sincerely appreciate a quick and compelling response.

thanks
kiran

homie

ravali your calcs assume that the option holder has committed to the position. But these are all valuations where you are assessing the probability of a price rise vs price drop.

For ex if price of gas shot up 5% on a $2 today and would drop the next day by 5%, my today's and next day's prices would be $2.10 and $1.99 resp.

OTH, if I think the prob of the %5 rise in gas price today is 60% and the 5% drop is 40%, the expected price of gas for tomorrow would be .6*2*1.05[1.26]+.4*2/1.05[.76]=2.02.

hth