Question: 2 . 6 Construction of implied volatility surface So far we have constructed an interpolation schemes in strike for each volatility tenor. We need a

2.6

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

1.6),

based on the following equation:

^{2} (T, K) T = {\begin{matrix} _{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{matrix}

where

T_{i}

and

T_{i + 1}

are the contiguous pair of tenors enclosing

T,

.

._{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 = f w d 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

t o K i n

moneyness

(s e e

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

a t (T_{1}, K_{1})

and the variance

a t

(T_{i + 1}, K_{i + 1}),

where

K_{i}

and

K_{i + 1}

are the moneyness equivalent strikes. The formula used

i n

0, T_{1}

would seem like

a s

a special case, however that

i s

conceptually identical

t o

the one used

i n T_{i}, T_{i + 1} i f w e

note that the variance

i n T = 0 i s

zero.

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

pre

-

computes all data necessary

t o

perform the interpolation

o f

the function

(T, K) a s e x -

plained above.

I t

should also perform

n o -

arbitrage checks described

i n

equation

(9),

but for

simplicity only for

K = f w d .

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!!!!!!!!

2.6 Construction of implied volatility surface So far we have constructed

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