Write a pseudo$-$code for pricing the European call option at t $=0$ by the Monte

Carlo method. Implement the pseudo$-$code by Matlab with the following function interface.

function V $=$ Eur Call LVF MC$($S$0,$ K$,$ T$,$ r$,$ x$,$ M$,$ N$)$

$\%$

$\%$ Price the European call option of the LVF model by the Monte Carlo method

$\%$

$\%$ Input

$\%$ S$0$ initial stock price

$\%$ K $$ strike price

$\%$ T $$ maturity

$\%$ r $$ risk free interest rate

$\%$ x $$ vector parameters for the LVF $\backslash$sigma $,[$x$1,$ x$2,$ x$3]$

$\%$ M $$ number of simulated paths

$\%$ N $$ number of time steps, i$.$e$.,\backslash$delta t $=$ T $/$N$.$

$\%$

$\%$ Output

$\%$ V $$ European call option price at t $=0$ and S$0.$

$3.(20$ points$)$ Derive the computational scheme for the explicit method and write a pseudocode for the explicit method to solve $(1)$ with the initial and boundary conditions. Implement

the pseudo$-$code by Matlab with the following function interface.

function V$0=$ Eur Call LVF PDE$($S$0,$ K$,$ T$,$ r$,$ x$,$ Smax, M$,$ N$)$

$\%$

$\%$ Price the European call option of the LVF model by the explicit finite difference method.

$\%$

$\%$ Input

$\%$ S$0$ initial stock price

$\%$ K $$ strike price

$\%$ T $$ maturity

$\%$ r $$ risk free interest rate

$\%$ x $$ vector parameters for the LVF $\backslash$sigma $,[$x$1,$ x$2,$ x$3]$

$\%$ Smax $$ upper bound of the stock price

$\%$ M $$ number of stock price difference, i$.$e$.,\backslash$delta S $=$ Smax$/$M

$\%$ N $$ number of time steps, i$.$e$.,\backslash$delta t $=$ T $/$N$.$

$\%$

$\%$ Output

$\%$ V $0$ European call option price at t $=0$ and S$0.$

$4.(20$ points$)$ Compute the results from the Monte Carlo method with S$0=1,$ K $=1,$ T $=$

$0\mathrm{.}25,$ r $=0\mathrm{.}03,$ x $=[0\mathrm{.}2,0\mathrm{.}001,0\mathrm{.}003],$ M $=10,000$ and N $=100.$ Compare the results from

$2$

the explicit finite difference with S$0=1,$ K $=1,$ T $=0\mathrm{.}25,$ r $=0\mathrm{.}03,$ x $=[0\mathrm{.}2,0\mathrm{.}001,0\mathrm{.}003],$

Smax $=3,$ M $=30$ and N $=100.(20$ points$)$ Write a pseudo$-$code for pricing the European call option at $t=0$ by the Monte

Carlo method. Implement the pseudo$-$code by Matlab with the following function interface.

$(20$ points$)$ Derive the computational scheme for the explicit method and write a pseudo$-$

code for the explicit method to solve $(1)$ with the initial and boundary conditions. Implement

the pseudo$-$code by Matlab with the following function interface.

$(20$ points$)$ Compute the results from the Monte Carlo method with $S_0=1,K=1,T=$

$0\mathrm{.}25,r=0\mathrm{.}03,x=[0\mathrm{.}2,0\mathrm{.}001,0\mathrm{.}003],M=10,000$ and $N=100.$ Compare the results from

the explicit finite difference with $S_0=1,K=1,T=0\mathrm{.}25,r=0\mathrm{.}03,x=[0\mathrm{.}2,0\mathrm{.}001,0\mathrm{.}003],$

Smax$=3,M=30$ and $N=100.$

I WANT QUESTION $4$ ANSWERED BUT YOU WOULD NEED THE ABOVE PARTS AS WELL, CAN YOU PLEASE SHOW THE MATLAB PARTS AND THE INFORMATION FROM QUESTION $4$ BEING ENTERED INTO THE CODE THANK YOU!