22 votes
Accepted

Gamma Pnl vs Vega Pnl

For an option with price $C$, the P$\&$L, with respect to changes of the underlying asset price $S$ and volatility $\sigma$, is given by \begin{align*} P\&L = \delta \Delta S + \frac{1}{2}\...
Gordon's user avatar
  • 21.1k
15 votes

Stop-loss start-gain paradox: Why is it a 'paradox'?

I am one of the two authors of the paper. The continuity in time of the path of the underlying suggests that at every trading time, the strategy is self-financing. In fact, if the underlying random ...
peter carr's user avatar
12 votes
Accepted

What is gamma to do with realized volatility?

I like to think about this problem graphically. The pic below shows a call option value at some point before expiry as a function of the underlying. At the expense of stating an obvious fact, we note ...
Jan Stuller's user avatar
  • 6,098
11 votes
Accepted

Is short-gamma inherently a losing strategy?

You can't lose more than you invested by writing covered puts, because you keep enough cash to cover any potential losses from the puts. That's not to say that your losses can't be substantial, of ...
Chris Taylor's user avatar
  • 5,911
11 votes
Accepted

Would it be possible to combine long butterfly with long straddle, achieving profit no matter the outcome?

Your butterfly is short a straddle and long a strangle. If you add a long straddle with the same strike/notional you are now just long a strangle. The payoff for a strangle is zero if the terminal ...
Chris Taylor's user avatar
  • 5,911
9 votes
Accepted

What really is Gamma scalping?

Assuming all else remains equal (implied vol has not changed and very little time decay has occurred), Gamma scalping can best be explained by Gamma (or realized volatility) enhancing the value of a ...
AlRacoon's user avatar
  • 6,532
9 votes

What really is Gamma scalping?

Gamma scalping (being long gamma and re-hedging your delta) is inherently profitable because you make 0.5 x Gamma x Move^2 across the move from your option. (You get shorter delta on downmoves, so you ...
OGC's user avatar
  • 271
8 votes
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Replicate a Portfolio with Given Payoff

Consider the case where we are interested in decomposing a continuous and piece-wise linear European payoff function $V \left( S_T \right)$ over $n$ intervals with $n + 1$ node points $S_i$ for $i = 0,...
LocalVolatility's user avatar
7 votes

What really is Gamma scalping?

As long as you live in a world where implied and realized vol are the same, there is no net profit (or loss) from gamma scalping. However, if they are different, then you make a gain or loss which is ...
Bram's user avatar
  • 812
6 votes

Are there any good tools for back testing options strategies?

Providing my 2 cents here, listing 3 free methods below: CBOE's method: No code here, just a "white paper", thus you can code it with whatever language you desire. I kinda like this the ...
pangyuteng's user avatar
6 votes

Gamma Pnl vs Vega Pnl

Not sure this is a valid question! Gamma p/l is by definition the p/l due to realized volatility being different from implied. Vega p/l is by definition the p/l due to moves in implied volatility. ...
dm63's user avatar
  • 17.1k
6 votes
Accepted

Books on options trading with a practical bent?

In my opinion there is one modern author on the subject of practical options trading who stands head and shoulders above the rest, and that is Euan Sinclair. His most recent book is Volatility ...
Brian B's user avatar
  • 14.9k
5 votes
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How to understand the no call or put spread arbitrage condition

Let's focus on a European call option for the sake of the argument. Assume deterministic rates to keep notations uncluttered. Define $\Bbb{Q}$ as the probability measure associated to the money market ...
Quantuple's user avatar
  • 14.6k
5 votes

Why are there so many S&P 500 call options selling with strike @1000?

I'm also currently working on analyzing option-implied RNDs. I'm no expert but a couple of comments: In addition to volume, you want to look at the open interest of the different strikes to conclude ...
Quantoisseur's user avatar
5 votes

Optimal delta-hedging frequency when gamma scalping

The model I quite like as a base-case/rule of thumb is the Hoggard, Whalley, and Wilmott (1994) model. Assuming GBM - the number of shares, $N$, per interval is: $$N = Δ(S+dS,t+dt)- Δ(S,t)≈ Γ*dS$$ ...
Newquant's user avatar
  • 769
4 votes
Accepted

Shorting an option every day vs shorting only at maturity

Draw a picture. For each scenario, there are obvious circumstances that the payoff for each would be better. For the N day option, the payoff would be better if there was a slow gradual decline in ...
RandyF's user avatar
  • 719
4 votes
Accepted

What instruments help me receive a premium?

no, generally speaking only options has time premium. I strongly advise you to avoid mixing 2 positions (short 1 option, long another one) in your mind just because they are independent, so just ...
optionstrade.info's user avatar
4 votes

Replicate a Portfolio with Given Payoff

I provide a general algorithm and an implementation in R to solve those kinds of problems in general: Financial Engineering: Static Replication of any Payoff Function. For your example: ...
vonjd's user avatar
  • 27.4k
4 votes

Stop-loss start-gain paradox: Why is it a 'paradox'?

The strategy seems to be self financing because the investor's only actions are to buy stock in the market when the stock price increases to the exercise price K, simultaneously borrowing K dollars, ...
dm63's user avatar
  • 17.1k
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
  • 263
4 votes

Is there an advantage trading options based on deep in the money Open Interest Volume ratio

I don't mean to suggest such a large topic, but it would certainly be worth reading about delta-hedging with regards to your question. Since such a large percentage of options are delta-hedged, the ...
MonteCarloSims's user avatar
4 votes

Delta Hedging/ Exchange for Currency Options

I am assuming you are short EUR and long USD based on your description of your hedges. I am also assuming the size of your hedges and your fx position are the same. In the first example of a hedge ...
AlRacoon's user avatar
  • 6,532
4 votes

Are there any books/articles on how to use options to be long volatility (implied or realized)?

What not to do What you are asking us, without knowing, is related to how to price a variance swap. Well, under a general diffusion process, variance swaps can be priced by forming a suitably ...
Stéphane's user avatar
  • 2,476
4 votes
Accepted

Calculate borrow/loan or repo rate

I believe, they are testing two things here: That you know the Put-Call Parity (with dividends) That you can successfully rearrange an equation The Put-Call Parity with continuously compounded ...
jmh's user avatar
  • 138
4 votes

Why are these deep in-the-money FLEX options seemingly bought at a discount?

SPY pays dividends ~1.8%, and the expiry is ~3y (as of date was 2018, 2021 expiry), so the it looks like there is a discount Assuming $0 time value $$OptionValue=Intrinsic Value+Time Value $$ $$...
ryc's user avatar
  • 401
3 votes
Accepted

How to approximate the Carr-Madan decomposition formula?

Carr-Madan formula tells you that the European-style payoff $f(F_T)$ can be decomposed as: $$f(F_T)=f(\kappa) + f'(\kappa) [(F_T - \kappa)^+ - (\kappa - F_T)^+] + \int_0^{\kappa} f''(K) (K-F_T)^+ \ d ...
Quantuple's user avatar
  • 14.6k
3 votes

How to apply Kelly criterion to a portfolio made by a stock plus a option?

Kelly is mostly based upon assets with zero correlation made independent of each other. The way I approximate Kelly for multiple bets with correlation is: Assume after your first bet the capital is ...
Mike's user avatar
  • 31
3 votes

What does it mean for an option strategy to be leveraged

There is a little known Greek called "lambda" or leverage which equals Delta times Stock price divided by option price $\lambda=\frac{\Delta . S}{c}$. So if $\lambda>1$ the option could be said to ...
nbbo2's user avatar
  • 11.3k
3 votes

Implied volatility of a complex options position

Yes, and in fact this is a quoting convention in FX derivatives; for flys straddles and reversals. It is applied to Legs by often by symmetric delta, and strike-by-delta formulas is used to convert ...
JBerstein's user avatar
  • 101

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