Stocks A and B are trading at $$100$ and $$105$ respectively. Stock A has a volatility of $0\mathrm{.}4$ and stock $B$ has a volatility of $0\mathrm{.}3.$

The risk$-$free rate is $4\%$ and there are no dividends.

The two stocks move independently of each other.

Price a derivative that pays Min$(A,B)$ the minimum of the two stocks in $1$ year. Create $1-$step trees for both stocks.

$$82\mathrm{.}71$

$$50\mathrm{.}21$

$$33\mathrm{.}45$

$$122\mathrm{.}29$