$2\mathrm{.}6$ Construction of implied volatility surface

So far we have constructed an interpolation schemes in strike for each volatility tenor. We need

a second interpolation scheme to obtain the volatility at maturities $T$ which are not exactly the

volatility tenors. To compute $(T,K)$ we use a linear in variance interpolation scheme along

moneyness lines $($see section $1\mathrm{.}6),$ based on the following equation:

${}^2(T,K)T=\{\begin{array}{cc}{}_1^2(K_1)T,& T{T}_1\\ \frac{T_{i+1}-T}{T_{i+1}-T_i}{}_i^2(K_i)T_i+\frac{T-T_i}{T_{i+1}-T_i}{}_{i+1}^2(K_{i+1})T_{i+1},& T_i{T}_N\end{array}$

where $T_i$ and $T_{i+1}$ are the contiguous pair of tenors enclosing $T,$ i$.$e$.{}_{i+1}(K)K_i{K}_{i+1}{T}_i{T}_{i+1}K\frac{K}{G_0(T)}=\frac{K_i}{G_0(T_i)}=\frac{K_{i+1}}{G_0(T_{i+1})}(T_1,K_1)(T_{i+1},K_{i+1})K_i{K}_{i+1}0,T_1{T}_i,T_{i+1}T=0(T,K)K=fwd{T}_i$ and

${}_{i+1}(K)$ are the associated smile functions, $K_i$ and $K_{i+1}$ are respectively the strikes for tenor

$T_i$ and $T_{i+1}$ equivalent $toKin$ moneyness $(see$ equation $(7))$

$\frac{K}{G_0(T)}=\frac{K_i}{G_0(T_i)}=\frac{K_{i+1}}{G_0(T_{i+1})}$

Effectively equation $(12)$ interpolates linearly the variance $at(T_1,K_1)$ and the variance $at$

$(T_{i+1},K_{i+1}),$ where $K_i$ and $K_{i+1}$ are the moneyness equivalent strikes. The formula used $in$

$0,T_1$ would seem like $as$ a special case, however that $is$ conceptually identical $to$ the one used

$in{T}_i,T_{i+1}ifwe$ note that the variance $inT=0is$ zero.

Implement the two functions below. The first function construct smiles for all tenors and

pre$-$computes all data necessary $to$ perform the interpolation $of$ the function $(T,K)asex-$

plained above. $It$ should also perform $no-$arbitrage checks described $in$ equation $(9),$ but for

simplicity only for $K=fwd.$ The second function performs the actual interpolation. Note that

the second function should support vectorial calls.

Please someone help me with the matlab code about the

function volSurf!! HELP! I need code!!Please test it also!PLS$!!$

HELP!!!!HELP!!!!!!!!