Question $2$You have an asset currently worth $100$ with a volatility of $20\%$ p$.$a$.$ and using the binomial method you want to price an American put option that has a strike price of $97,$ and you can exercise the option earlier. The time to maturity of the option is $3$ months and you decide to choose $3$ time periods in your binomial lattice$\mathrm{.}1.$ What is the value of the above described option if the risk$-$free rate is $2\%$ p$.$a$.?[20$ marks$]2.$ Comment on the likely quality of your valuation. $[10$ marks$]1$