PLEASE SOLVE STEP BY STEP AND PLEASE PROVIDE MATLAB CODE WITH OUTPUT SCREENSHOTS:

Consider a stochastic volatility model for stock price $[$here the volatility is denoted by $]$:

$d{S}_t=r{S}_{t}dt+{}_t{S}_{t}d{W}_t$

$d{}_t=a(-{}_t)dt+d{B}_t$

Here $r,a,,$ are all positive constants, and $($W$,$ B$)$ is a two$-$dimensional Brownian motion with covariance matrix

$\left[\begin{array}{cc}1& \\ & 1\end{array}\right]$

In this model the volatility $$ is itself a $($mean$-$reverting$)$ stochastic process. We are interested in estimating the price of a vertical spread with maturity $T.$ That is$,$

$[$:$(S_T-K_2{)}^{+}=(exp(Y_T)-K{)}^{+}\}{Y}_t{Y}^{-}{Y}_{t_{i+1}}^{-}=Y_{t_i}^{-}+(r-\frac{1}{2}{}^2)(t_{i+1}-t_i)+\sqrt[\phantom{2}]{t_{i+1}-t_i}{Z}_{i+1}$ and $Y_{t_0}^{-}=Y_0\{Zi\}{Y}^{-}r{e}^{-rT}(exp(Y_T)-K{)}^{+}{S}_0,r,K,T0,Tm{t}_i=\frac{i}{m}T,i=0,1,2,3,$dotsdotsdots.$mr,a,,,S_0,{}_0,K1,K2,T,m,nr=0\mathrm{.}1,a=3,=0\mathrm{.}2,=0\mathrm{.}1,S_0=20,{}_0=0\mathrm{.}25,T=1,K1=20,K2=22,=0\mathrm{.}5,m=50,n=10000Y^{-}$