premium adjusted delta – basic illustration

http://www.columbia.edu/~mh2078/FX_Quanto.pdf says “When computing your delta it is important to know what currency was used to pay the premium. Returning to the stock analogy, suppose you paid for an IBM call option in IBM stock that you borrowed in the stock-lending market. Then I would inherit a long delta position from the option and a short delta position position from the premium payment in stocks. My overall net delta position will still be long (why?), but less long than it would have been if I had paid for it in dollars.”

Suppose we bought an ATM call, so the option position itself gives us +50 delta and let us “control” 100 shares. Suppose premium costs 8 IBM shares (leverage of 12.5). Net delta would be 50-8=42. Our effective exposure is 42%

The long call gives us positive delta (or “positive exposure”) of 50 shares as underlier moves. However, the short stock position reduces that positive delta by 8 shares, so our portfolio is now slightly “less exposed” to IBM fluctuations.

2nd scenario. Say VOD ATM call costs 44 VOD shares. Net delta = 50 – 44 = 6. As underlier moves, we are pretty much insulated — only 6% exposure. Premium-adjusted delta is significantly reduced after the adjustment.

You may wonder why 2nd scenario’s ATM premium is so high. I guess
* either TTL(i.e. expiration) is too far,
* or implied vol is too high,
* or bid ask spread is too big, perhaps due to market domination/manipulation

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s