The Vega Matrix

Consider a collection of different options (various strikes and maturities) and a stock position. 

We calculate the Greek position of each individual option and weight those with volumes --> Greek position of book. 

- Book Delta --> weighted sums of individual deltas. 

- Book Gamma --> weighted sums of individual gammas. 

- Book Theta --> weighted sums of individuals thetas. 


However, the vega terms actually refers to different volatility parameters, one for each different strike and maturity. 

They are not completely correlated, as the market decided that options can live their own life. 

If we have a vol for each strike and maturity --> volatility view in book is represented by matrix of vega terms. 


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