23
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}\...
- 21.2k
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 ...
- 251
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 ...
- 6,308
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 ...
- 5,931
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 ...
- 5,931
10
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 ...
- 281
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 ...
- 6,652
8
votes
Accepted
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,...
- 6,084
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 ...
- 812
7
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 ...
- 14.9k
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 ...
- 299
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.
...
- 17.5k
5
votes
Accepted
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 ...
- 14.7k
5
votes
Swaptions Gamma Interview Questions
Using Taylor polynomials of 2nd order:$$V(r+h)\approx V(r) + \frac{\partial{V}}{\partial{r}}h +\frac{1}{2}\frac{\partial^2{V}}{\partial{r}^2}h^2$$
$$V(r-h)\approx V(r) - \frac{\partial{V}}{\partial{r}}...
- 283
5
votes
Why are there so many S&P 500 call options selling with strike @1000?
I'm also currently working on analyzing option-implied RNDs. I'm no expert but a couple of comments:
In addition to volume, you want to look at the open interest of the different strikes to conclude ...
- 760
5
votes
Optimal delta-hedging frequency when gamma scalping
The model I quite like as a base-case/rule of thumb is the Hoggard, Whalley, and Wilmott (1994) model.
Assuming GBM - the number of shares, $N$, per interval is:
$$N = Δ(S+dS,t+dt)- Δ(S,t)≈ Γ*dS$$
...
- 877
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, ...
- 17.5k
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:
...
- 27.6k
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 ...
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 ...
- 395
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 ...
- 6,652
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 ...
- 2,506
4
votes
Accepted
Are there any books/articles on how to use options to be long volatility (implied or realized)?
The simplest long vol strategy is to be long an ATM straddle and delta hedge it, the problem is that when it is no longer ATM the exposure to vol weakens. You could then sell that straddle and enter ...
- 11.6k
4
votes
How to normalise options? Normalise strike price, premium, tenors
Given a certain market environment, option quotes are impacted by at least the following factors: moneyness (distance from spot/forward to strike) and tenor (time to maturity). This makes it difficult ...
- 628
4
votes
Accepted
Calculating a Covered Call Strike with N% Probability that Shares Won't be Called Away
Using an option's delta could be a quick and easy way to back into the probability that you are seeking. For example, if you are looking for an option that has a 70% chance of expiring worthless, you ...
- 4,368
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 ...
- 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 $$
$$...
- 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 ...
- 14.7k
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 ...
- 31
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 ...
- 101
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