Q$2.(40$pt$)$ Write MATLAB codes to solve the following questions and discuss the answers on your answer

sheet in detail. All MATLAB source code files should be provided with your answer sheet. Use the

multiplicative binomial model with the CRR scheme.

$1$

$($a$)$ Plot the following option prices with n $=10$ : $1000,$ S$0=100,\backslash$sigma $=0\mathrm{.}4,$ r $=0\mathrm{.}05,$ K $=110,$

T $=0\mathrm{.}5,$ and report the prices when n $=1000.$

$$ Plain vanilla European call option

$$ Plain vanilla American put option

$$ Cash$-$or$-$nothing option with cash $=10$

$$ Asset$-$or$-$nothing option with f $=0\mathrm{.}1$