Worst of Autocallable II

2.Theta Analysis
The Autocall Theta Analysis provides some very interesting results.
The analysis was done today morning when the Spot was somewhere close to 4% above strike.
Spot has moved by -1.2% today. And the Gamma plus Postfix Values from this analysis on SAN.MC are almost very close to the actual Delta change on the option.

The methodology adopted:

• A given set of spots was considered for SAN and for TEF. For these spots, the option price was calced for each of the dates from now to the 21st

The Spot sets were taken as

• a) The present Spot on SAN and TEF b) One Percent Bump on SAN c) One Percent Bump on TEF
• a) -2% Bump on SAN and TEF and from there b) One Percent Bump on SAN c) One Percent Bump on TEF
• a) -4% Bump on SAN and TEF and from there b) One Percent Bump on SAN c) One Percent Bump on TEF
• a) -6% Bump on SAN and TEF and from there b) One Percent Bump on SAN c) One Percent Bump on TEF

Point to note is -4% of Spot on TEF behaves most strangely as it is close to strike. The Data might include some noise as at -4% there is no convergence. Unit Deltas were calced but the Dollar delta can easily be calced from fx and notional from Data.

To Confirm, at present spot and at -2% spot, the levels are above autocall strike. At -4% it is just below strike and at -6% it goes below level

Price Change with SAN on Diff Dates with different spot sets:

Price Change with TEF on Diff Dates with different spot sets:

A little less importantly: I studied the theta on TEF as well. The delta on TEF behaves very strangely, I'm not sure it is not purely noise as SAN gives the majority of delta and on margin Delta on TEF behaving wierdly

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.