Consider a $6-$month $($two$-$period$)$ European put with the strike price K$=21.$ The risk$-$free interest rate $R$ for continuous compounding is equal to $12\%.$

If the price of the option underlying stock obeys the binomial dynamics as follows, please find the put option values $p_{},p_{ud},p_{ud},p_u,p_d$ and $p_0$ at nodes D$,$ E$,$ F$,$ B$,$ C$,$ and A by using no$-$arbitrage argument.

Besides, find the corresponding delta ${}_u^p,{}_d^p,$ and ${}_0^p$ at nodes B$,$ C$,$ A$.$

Ans.