Consider using a binomial model to price a non$-$dividend paying security $($e$.$g$.$ a stock$)$ where the true probability of an up$-$move is p$=0\mathrm{.}5$p$=0\mathrm{.}5.$ The initial value of the stock is S$0=100$S$0=100.$ Let P$0$P$0$ denote the time t$=0$t$=0$ price of a European put option on the stock with strike KK that expires after some fixed periods.$$

Now suppose that some favorable news about the stock come about. This will cause an immediate change in the price's up$-$move probability $($say to p$=0\mathrm{.}7$p$=0\mathrm{.}7).$ What do you think should happen to P$0$P$0$ according to risk$-$neutral pricing?