index volatility reconstruction using underlying stocks

l1c3jchongzi · January 4th, 2013, 10:40 am

Hi All, I implement Avellaneda's paper "Reconstructing volatility" for reconstructing the index implied vol skew using underlying stocks' implied vol skew. But for DJX index the results are not satisfactory.The skew of reconstructing vol skew is much smaller than the market value, I mean much lower for small strike and larger for high strike. Actually, I found the slopes of underlying stocks implied vol skew are close to the reconstructing vol skew, and much smaller than the market index implied vol skew. Can anybody explain the problem?

gpop · January 23rd, 2013, 3:13 pm

There is an options market for each underlying stock and for the index itself. Unless the arbitrageurs are stongly active in those markets, the underlyers' skew and the index skew are not supposed to be linked by a deterministic function - except in theory as shown by Avellaneda's paper http://www.math.nyu.edu/faculty/avellane/Avellaneda.pdf - as they function as separated option markets and the skew is an indication of demand/offer accross the different strikes.Hoping it is clearer for you