Friday, November 9, 2012

why market makers delta hedge -- my take again

A1: earn bid/ask spread
A2: Well the same kind of problem as the unhedged long call -- insufficient insulation.

Q: why do vol market makers take the trouble to maintain a dynamic hedge?

Say I am long call (IBM for eg). Tiny rises are welcome, but tiny drops hurt pnl. As a MM (i.e. market maker), i need to minimize any negative impact to my pnl, which threatens to destabilize me, and the SS (i.e. sell side) infrastructure.

Therefore on the SS we must immediately delta-hedge our long call, usually by short stock. Net delta = 0. This insulates us from both positive and negative impacts. (But then what's our profit model? [Q1])

Most of the time during a single day IBM would move relatively slowly and by relatively small magnitude, so our initial delta hedge should suffice, but next day we should probably re-hedge or "dynamic hedging". Key question -- What if we don't?

Say our initial call delta is +44, so initial hedge short 44 shares and achieve 0 delta. Next day our call delta becomes +55 [1], net delta is +11. (What's the problem? [Q2]), so we short more stocks.

The nice thing (due to long gamma) is, we Sell IBM when it rises, and Buy when it drops. However, Bid/ask spread [2] and commission hurts the profit. Nevertheless, this is a standard SS strategy -- long gamma and delta hedge dynamically.

Doesn't work if we are short gamma.

[1] Over a longer period such as a day, underlier move is often too big for our delta hedge. (Big foot for small shoe).

[2] Note we PAY the bid/ask spread as market taker. Alternatively, it would be perfect if we hedge-sell/hedge-buy the stock using limit orders, thereby earning the bid/ask spread.

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