Delta Hedging

Discussion in 'Options' started by trading1, Dec 12, 2012.

  1. Hi,

    If I hedge a call by being short the underlying (say SPY) and the price falls, I correct the delta by shorting more SPY, then if the price mean reverts surely I am going to lose on my Delta hedging? The new spy trade I got at rock bottom price, the price has gone up and I've lost - is that right?

    Is it correct to say that delta hedging carries with it a risk of the stock mean reverting, and conversely if the stock trends then I gain on the delta hedge. Is the right or have I missed something?

    Thank you for any help in understanding this process.
  2. sle


    If you are long an option and actively hedging delta, mean reversion is actually good for you. Lets imagine for a second that you bought an ATM call on SPY (about .5 delta) and sold delta in 50 SPY shares against it. Now, the market declines - the positive convexity of your call will decrease it's delta and you are still holding short 50 shares. So, at some point when the market declines sufficiently, you will find that you are actually very short the market. So you are going to buy some delta back at a lower price. If the market moves back up now, the shares you just purchased will make you money. Here is a sample progression of your trades if you are delta hedging a long gamma position:
    Day 1:
    SPY at 142
    -- buy 142 SPY call, delta=50
    -- sell 50 SPY @ 142
    * net delta = 0
    Day 2:
    SPY at 140
    -- long 142 SPY call, delta=40
    -- short 50 SPY
    * net delta = -10
    -- buy to cover 10 SPY for 140
    * now, net delta = 0
    Day 2:
    SPY at 142
    -- long 142 SPY call, delta=50
    -- short 40 SPY
    * net delta = 10
    -- sell short 10 SPY for 142
    * now, net delta = 0

    The sum result of your delta-hedging is buy 10 shares at 140 and sell 10 shares at 142.

    Now, if the market is trending down, you are buying delta back and the market keeps going lower. So, while you are not losing money (the gains on the short shares are covering your losses on the call), you are not necessarily making any either.

    Am I making sense?
  3. kapw7


  4. The math of hedging deltas is just arithmetic. But frequency is where I think some speculation comes in.. if your short premium your delta hedge costs money.. you bleed... so in a flat market means less hedging means more profit. When long premium more realized variance and a higher hedge frequency makes more money... realized variance means the amount of ground covered by the underlying... correct me if I'm wrong
  5. sle


    A number of questions come up once you are involved., Do you hedge (calculate deltas) at implied volatility or at some volatility that you have decided on? Do you assume that volatility stays constant at you strike (sticky strike), moves with the spot (sticky delta) or follows some other process? Do you over-hedge if you assume mean reversion and try to capture trends by under-hedging?

    Like many things in life (sex included) capturing volatility via delta hedging easy to do, but it's hard to do well.
  6. Yes, it all makes perfect sense [thank you]. I'll go back to the options pricing workbook.

    Thank you for pointing out the reverse situation when short premium.
  7. Yes! Finding crafty ways to extract gamma or keep your blood (short premium) is where I've been most curious... its more speculative then most and I first thought.... there is nothing neutral about neutral

    Parkinson number ratio..distribution of extremes..
    Or variance ratios... meaning relativity of variance to sampling frequence... the more variance the smaller the time frame the more reversion
  8. sle


    I had a bunch of cartoons drawn up about option greeks, delta hedging, various dynamics and trading strategies. Nothing complex, but in pictures instead of math formulas. My junior trader at [now a dead firm] called it "The Volatility Porn" - I will try to dig it up.
  9. Love to see that
  10. +1
    #10     Dec 13, 2012