Vega-weighted maturity

Money · April 28th, 2011, 6:02 am

Hi there,For structuered equity products with early termination possibility, I heard one way to compute the effective maturity is :-T_Maturity = Summation |Vega(i)| * Sqrt(T(i) --------------------------------------- Summation |Vega(i)| / Sqrt(T(i)Can somebody explain me the inituition of this formula ?thx,

cchoong · April 30th, 2011, 7:50 am

I assume the term SQRT(T(i)) is meant to be included in the Summation?

TinMan · April 30th, 2011, 10:54 am

The intuition is that it's a ridiculous idea, what if the volatility sensitivity changes sign?

Money · May 1st, 2011, 5:28 am

animeshsaxena · May 7th, 2011, 11:42 am

Let's just consider one option, say a european call. What is it's Vega S N'(d1) (sqrt(T-t))Put that in ur summation formula what do you get?Try adding more options....and see. For products with early termination this formula is not accurate.

Money · May 17th, 2011, 5:06 am

hi mate,sorry i don't understand , can you explain in detail ?thx

animeshsaxena · May 17th, 2011, 9:37 pm

Vega = S N'(d1) (sqrt(T-t))As per your formula T_Maturity = Summation |Vega(i)| * Sqrt(T(i)---------------------------------------Summation |Vega(i)| / Sqrt(T(i)so for only one option T_Maturity = S N'(d1) (sqrt(T-t)) * Sqrt(T-t)/(S N'(d1) (sqrt(T-t)) / Sqrt(T-t))which becomes T_Maturity = T-t for one option....similarly now add one more option..and see the pattern...For higher maturity option you have more vega...which is causing more weightage to the effective maturity. You can verify it by adding two european calls with different maturities.