Worst of Autocallables I

1. Delta Analysis
The methodology adapted was as follows:

• Take an Autocall with common underlyings ( NESN and NOVN) and expiry in 2011, with a coupon payment and early redemption on worst off performer
• So as to remove extreneous factors, including cross gamma, one of the underlyings was kept constant and the analysis was run on NOVN. Also the Normal structure of autocall product with put was assumed to be without put. This assumption would not make a difference to deltas
• With an intent to simulating the spots going to some percentage of strike and finding price of option, the spots were kept constant and the strikes were adjusted accordingly ( so that the vol params are not affected)
• Two cases are required:

Case 1) The autocalling date has just passed, and the next autocall date is in a year.

Case 2) The autocalling date is in two days

• From the price of the option, we can calculate the deltas and find out how option behaves. The results are as follows:

Price Curve wrt spot

Delta Curve wrt Spot

On delta, the second derivative, there is a slight amount of noise, due to which the curve is not perfectly smooth
Conclusion:

• Delta Values after about 85% of spot start showing a change and increase in case of Autocall with short time to maturity.
• The influence on Postfix deltas to do ( assuming products do not autocall ) is that
  A) In case of one underlying below 80%, There should be negl delta to do postfix, assuming it does not autocall.
  B) In case of one of the underlyings being between 85-100% there could be between a reasonable and significant amount of delta to unwind.
  C) Assuming we are short the autocall, and that the product does not early redeem. We always have to sell stocks, and not sometimes buy as the Euclid Model was showing sometime back.
• Cross Gamma effects, in case both Stocks are below the 100% limit, would not be significant (except that the net delta would be distributed accordingly between the two stocks). The Graphs on the worst off stock would look similar to above curves in this case also, though it might change between the two stocks at some time.