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## Monday, December 26, 2011

### computing delta value from BS formula - unrealistic

Delta is the option-valuation change due to a small change in underlier. We are asking "using the BS formula as a prediction of real market, if there's a \$.01 change in underlier, what's the change in bid/ask of this listed option?"

Assumption -- all the bid/ask quoters in the option market use roughly the same BS formula. Obviously unrealistic. I don't feel this assumption would help make delta a random variable.

Assumption -- large number of bid/ask quoters responding to the underlier change. Realistic? I doubt it. Many quotes may ignore the spot change. I guess a small number of dealers/funds might _concentrate_ on a sector and are responsible for a disproportional part of the order book on that option. If they ignore the spot change, then bid/ask will stay constant and delta is 0!

Assumption -- no change in i-vol when underlier changes. I feel real players in the market are emotional and may respond emotionally to whatever event causing the \$.01 change. These emotional reactions can /effect/ a change in i-vol. I think some trend recognition machines may recognize this small change as part of a trend. I don't feel such a market response is random.

What if the change is not \$.01 but a 2% change?

Assumption -- underlier price change is fairly slow and small. Obviously unrealistic. Therefore the change in option bid/ask in response to underlier change doesn't always follow math model.

More important factor -- An option is often held along with an underlier position as part of a strategy. When underlier moves, the holder may want to adjust her option position. One choice is adjusting her option quotes (limit orders). If she is a powerful market maker, then her new quote can move the best bid/ask. Therefore option valuation as measured by mid price may not move according to any math model.