7 votes
Accepted

Proof of gamma profit formula

Assume you buy a plain vanilla call option at the price $V$ and the spot $S$. You immediately delta hedge buy selling $\partial V / \partial S$ units of the underlying asset. The underlying asset now ...
LocalVolatility's user avatar
6 votes

FX option trading questions

Yes, in the sense that it is assumed that the delta will be passed between participants at time of execution. Not necessarily. A non delta neutral trade may be used for speculation , or for hedging.
dm63's user avatar
  • 16.9k
5 votes

Why does volatility increase the expense of delta-hedging?

The key here is to observe that the volatility at the time the option is written is not exactly equal to the volatility that the markets actually experience during the option's lifetime. The seller ...
Brian B's user avatar
  • 14.7k
4 votes
Accepted

Is there any way to check my delta hedging is implemented correctly?

One way to check your hedging strategy would be to calculate its PNL distribution (histogram) of ( hedging strategy + option) . Mean PNL should be around 0, and shape should look like gaussian. ...
alexprice's user avatar
  • 861
4 votes

Swaptions Gamma Interview Questions

Using Taylor polynomials of 2nd order:$$V(r+h)\approx V(r) + \frac{\partial{V}}{\partial{r}}h +\frac{1}{2}\frac{\partial^2{V}}{\partial{r}^2}h^2$$ $$V(r-h)\approx V(r) - \frac{\partial{V}}{\partial{r}}...
MaPy's user avatar
  • 253
3 votes

What is the reason for adding 0.5 variance when calculating the ATM DNS of an option?

The delta neutral strike occurs when $N(d_1) = 0.5$, or when $d_1 = 0$. Now invert $$d_1 =\frac{\ln(S/K)+(r+\frac{1}{2}\sigma^2)T}{\sigma \sqrt{T}}$$ to solve for the strike $K$. You will have the ...
Newquant's user avatar
  • 769
2 votes
Accepted

Delta neutral strategy using a combination of put and call options

You could, for a particular vol, time to maturity, spot and strike have a delta neutral position by buying a certain amount of the put. But consider what would happen if the spot goes up: The delta ...
David Duarte's user avatar
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2 votes

Swaptions Gamma Interview Questions

Refreshing to see this type of question in this forum. Regarding the first part of the question (let's leave the detailed calculation aside for a moment), I think what the interview is trying to get ...
user35980's user avatar
  • 1,356
2 votes

How does a Delta Hedged portfolio yield the Risk-free?

I'll put here the answer provided in a comment by @dm63 (thanks by the way): The requirement that the portfolio earns the risk free rate is something we are imposing in order to calculate the ...
moumous87's user avatar
2 votes

Delta re-hedging with options

Delta hedging with other options would give you exposure to the implied vol dynamics of those options. Delta hedging with the underlying gives you exposure to the realized volatility of the underlying....
Arshdeep's user avatar
  • 1,905
2 votes

Delta-hedging frequency directly affects PnL, and not just PnL smoothness and variance?

If you look at just a single example, it may seem like the frequency of hedging directly effects the EV/Avg(Pnl), like in the situation you described where hedging every minute proved to be more ...
jrolo's user avatar
  • 41
1 vote

Delta-Gamma neutral vs Delta-Vega neutral

For a flat IV skew (not surface), the gamma neutral portfolio == the vega neutral portfolio. This is because Vega = s^2 * σ * T * gamma, so when the net gamma exposure is 0, the net vega exposure is 0,...
Newquant's user avatar
  • 769
1 vote

Delta-hedging frequency directly affects PnL, and not just PnL smoothness and variance?

Under the assumptions of GBM - namely that periodic returns are independent of one another - then hedging frequency will have 0 impact on the expected P/L over time. If there is autocorrelation in the ...
Newquant's user avatar
  • 769
1 vote

Confusion Regarding Dynamically Delta Hedging a Short Option

You never know for sure what will be the next market move. You assuming that underlying will continue to decline and in this case additional hedge will eat your collected premium. But what if ...
Yury Kochubeev's user avatar
1 vote
Accepted

Gamma-neutral delta-neutral call ratio spread

You are generally correct in thinking that this strategy should make money most of the time, however I would warn you to be very careful with strategies that earn a small amount of money most of the ...
klib's user avatar
  • 328
1 vote
Accepted

For what options does the "delta hedging rule" apply?

Chapter 5.5.2 (Hedging with One Stock) paragraph that includes (3) does not assume that the value of the payoff at any $t$ is Markovian, that is, it is a function of $S(t)$ only, so there is no "...
ir7's user avatar
  • 5,043
1 vote
Accepted

About the implied volatility as average volatility over the life of an option

Under your hypotheses, the implied volatility at which you close the trade out will be the forward volatility $\sigma_3$ where $\sigma_3<\sigma_2$, so you will make a loss on that. This loss will ...
dm63's user avatar
  • 16.9k
1 vote

Delta neutrality (derivation)

This discussion has also confused me slightly, so I will add something that is possibly clarifying, although most likely will not be. It is also a reminder that I need to stop programming and brush up ...
rubikscube09's user avatar
1 vote

How can Delta Neutrality profit you?

The EMH does not state that it is impossible to ever make money out of the market. We have good evidence to believe that markets are reasonably informationally efficient. However, that does not mean ...
Alex's user avatar
  • 688
1 vote
Accepted

Making portfolio Delta and Gamma neutral using 2 derivatives

The two formulations seem to be exactly the same. If I take the equations from the first method: $w_{D1}*\Delta_{D1} + w_{D2}*\Delta_{D2} = -2$ $w_{D1}*\Gamma_{D1} + w_{D2}*\Gamma_{D2} = -3$ And ...
Magic is in the chain's user avatar
1 vote

Delta neutral strategy using a combination of put and call options

Assuming that, after buying the options, you will no longer trade in the underlying or options, it only makes sense to buy a put, in addition to the call, if you want to bet that the price of the ...
Rodolfo Oviedo's user avatar
1 vote

Delta re-hedging with options

On top of my head, there are two reasons. One is that the underlying may not be accessible, while you can buy/sell options on exchange or OTC. The other (more important) reason is your position on ...
Will Gu's user avatar
  • 702
1 vote
Accepted

How frequently do traders rebalance their gamma hedges?

Commonly used procedures are to hedge; when a 1 SD move has happened, or when your delta position exceeds some risk limit, or once a day, or based on your desired delta position. All are used. I ...
dm63's user avatar
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