A stock currently trades at $\backslash (\backslash$$ $100\backslash ),$ with a volatility of $\backslash (25\backslash \%\backslash )$ per year and a continuous dividend yield of $\backslash (2\backslash \%\backslash ).$ The risk$-$free rate is $\backslash (5\backslash \%\backslash )$ per year, continuously compounded. Consider a European call option with a strike price of $\backslash (\backslash$$ $100\backslash )$ and $6$ months to expiration $(\backslash ($ T$=0\mathrm{.}5\backslash )$ years$).$ a$)(10$ points$)$ Using a one$-$stage binomial tree, calculate the price of the European call option. b$)(10$ points$)$ Extend to a two$-$stage binomial tree. Calculate the option price. c$)(10$ points$)$ Now use a three$-$stage binomial tree. Calculate the option price. d$)(5$ points$)$ Using the Black$-$Scholes$-$Merton model, compute the price of the same European call option. Compare the results from the one$-$stage, two$-$stage, three$-$stage binomial trees, and BSM$.$ Briefly explain why the prices converge as the number of stages increases.