Why do we use differing risk-neutral probabilities of up move and down move in options valuation using binomial tree while in bonds we assume that up move and down move both have the same probability 50/50.
I can take it as given, no problem, but was curious.
Personally, I hate the fact that they refer to them as probabilities. They’re weights; nothing more, nothing less.
Binomial trees are designed to prevent arbitrage opportunities.
In a binomial tree used for option pricing, the arbitrage transactions to avoid are cash-and carry and reverse cash-and-carry: the way to prevent that is for the expected value of the stock to increase at the risk-free rate. The weighted average of the up and down prices must therefore be the previous stock price increased at the risk-free rate; the up and down weights (risk-neutral probabilities) are calculated to ensure that weighted average.
In a binomial interest rate tree, the arbitrage transactions to avoid are the purchase and sale of Treasury securities for different prices. To avoid that, the tree is calibrated at each time period to price Treasuries the same as the prices from the underlying spot curve. To calibrate the tree, the relationship between rates at a given time is determined by the volatility (each rate is the lower rate times e^(2_σt_)) and the lowest rate is adjusted until the Treasury is priced correctly; the weights on the up and down interest rate movements are both 0.5.
There’s nothing special about using weights of 0.5 and 0.5; we could just as easily use 0.4 and 0.6 if we wanted to, calibrate the tree with those weights, and then use those weights when we use the tree. It’s easier to remember 0.5 and 0.5, so we use those.
Dear S2000magician,
it’s better late than never. Thank you for explanation!! I’m sure a lot of folks would find this helpful. Curriculum certainly does not cover this properly.
Apologies for late reply. First week of June was hell of a time, and afterwards anything related to CFA was hibernated from my head for a while for the sake of sanity 
Believe me, I understand.
I’m glad that the explanation helped.