Dear Tutors, If one needs to Vega-hedge a portfolio with some options, shares and inevitably some risk-free asset, the main question is to calculate Vega for the share price. Let us assume the BS model. What is the Vega for the stock price? My naive answer is 0. Any help would be greatly appreciate. Many thanks, Actuarial student
You're quite right. It might seems odd as you could reason that if the market changes its estimate of volatility, then the market's view of the worth of the share would change too, but that's not what vega is about. Vega for the share is the senstivity of the share price to changes in volatility, keeping all other parameters fixed. "All other parameters" includes the share price and so vega for the share is indeed zero. The same logic applies for rho, theta amd lambda for the share.
