x******a
发帖数: 6336 | 1 sell a call option with T=1 year. Then delta-hedge this option each day.
what is the P/L? I was told it is Gamma. But I think it is 2Gamma. | l*******1
发帖数: 113 | 2 1/2*gamma*(realized vol-implied vol)*S^2 | r**a
发帖数: 536 | 3 How/Where did you get this formula? I do not think it is correct. In my
opinion, the simple answer of the question is that the numerical factor
should be 1/2.The complicated answer is the following
$$
P&L_t=1/2*gamma*(realized local variance-expected local variance)*S^2,
$$
where $P&L_t$ is the instantaneous P&L and expected local variance is also called "BS forward implied variance. The derivation should be the same to
the eq.3.4 in Gatheral's book "the volatility surface".
【在 l*******1 的大作中提到】
: 1/2*gamma*(realized vol-implied vol)*S^2
| L**********u
发帖数: 194 | | r**a
发帖数: 536 | 5 profit and loss distruibtion (or function), which is nothing but the
difference between tomorrow's price and today's price. For details, u can
check "Market Risk Analysis" by Alexander, which is one of my favoriates.
【在 L**********u 的大作中提到】
: what does P/L mean?
| L**********u
发帖数: 194 | 6 Thanks a lot
【在 r**a 的大作中提到】
: profit and loss distruibtion (or function), which is nothing but the
: difference between tomorrow's price and today's price. For details, u can
: check "Market Risk Analysis" by Alexander, which is one of my favoriates.
| L**********u
发帖数: 194 | 7 Thanks a lot
【在 r**a 的大作中提到】
: profit and loss distruibtion (or function), which is nothing but the
: difference between tomorrow's price and today's price. For details, u can
: check "Market Risk Analysis" by Alexander, which is one of my favoriates.
| z****g
发帖数: 1978 | 8 o, where is the time decay? | r**a
发帖数: 536 | 9 Precisely, I take the BS equation to replace theta by something else just as the author did in the book "the volatility surface" when he derived Eq.3.4. The time decay in this derivation is hidden in the implied variance term. In fact, if u believe the BS equation and Dupire's model, then the result is rigorous, i.e. the instantaneous P&L function I mentioned is the rigorous one instead of an approximation.
Actually, the simplest way to estimate of P&L is nothing but the multi-variable Taylor expansion under variables of P&L. For example, u can also consider the delta–gamma–vega–theta–rho approximation, etc. In those kinds of approx, the time decay is more explicit. Since I am not a practitioner, I do not know which kind of approximation is more important.
【在 z****g 的大作中提到】
: o, where is the time decay?
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