14

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}\gamma (\Delta S)^2 + \nu \Delta \sigma, \end{align*} where $\delta$, $\gamma$, and $\nu$ are respectively the delta, gamma, and vega hedge ratios. Then it is clear ...


12

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 process had continuous sample paths of bounded variation, then the binary trading strategy is actually self-financing. In contrast, when these continuous sample ...


11

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 course. The below chart shows the drawdown profile of the PutWrite index - you would have lost nearly 40% of your investment at one point. So how did the ...


9

The option is a contract that gives you the right to buy the stock in one year for 18. Today people are trading the stock for 20, so you can sell the stock short for 20 today, meaning, someone gives you 20 cash today in return for a stock IOU, where you are obligated to deliver the stock to them on a later date. So you get 20 cash upfront but you need to ...


8

You can find an exact algorithm with a step-by-step explanation here: https://www.dropbox.com/s/t4fq067kzx26mhw/project_paper.pdf As you can see from the URL it is an archived document because the original site is unfortunately long gone and the tool referenced in the paper with it :-( But it should be helpful anyway to understand what is going on. Notice ...


8

Skew "arbitrage" is a pretty broad term. When you are trading the skew, there are 3 principal risks (or sources of P&L, if you will): (a) the actual change in the slope of the skew in the implied space. e.g. if you are trading 95% strike against 105% strike and your underlying stays in place, all of your instantaneous P&L would be due to the changes ...


8

You can find everything you want to know about this here (and in a very readable and easily reproducible form): How Students Can Backtest Madoff’s Claims by Michael J. Stutzer (2009) From the abstract: Markopolos’ writings neither described nor included any specific backtests of the strike conversion strategy. Fortunately, a backtest is relatively ...


6

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. The second part of the question you have answered yourself. Short dated options have more gamma exposure, long dated options have more vega exposure.


5

The main thing to keep in mind with all these different option combination strategies is that you are really trading option greeks! I think the answer to why the calender spread is so popular lies in the special combination of gamma and vega risk: Calendar spreads are the one type of trade where gamma can be negative while vega is positive (and vice versa ...


5

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 $i = 0, 1, \ldots, n$. Without loss of generality, we assume that $S_0 = 0$ and write $V_i$ as short-hand for $V \left( S_i \right)$. We assume that the slope of the ...


5

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 Trading, and he has another book out soon. Sinclair covers actual strategies, along with questions of liquidity and position sizing that I never see in other options ...


5

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 which prices are reasonable. Humans like round numbers so especially for deep OTM strikes you will see the bulk of open interest located at nice numbers. Deep ...


4

I just thought it is worth mentioning that the skew of the underlier implied by traded option prices and the options implied-volatility skew are indeed related by no-arb relation. The point is that you can integrate implied variance over the strike prices to get the unconditional implied variance (and hence volatility) of the underlier and the skewness of ...


4

There is one more solution available now to backtest option strategies: www.oscreener.com! This tool allows to screen and backtest bull put spreads, long calls, short puts, debit spreads etc and validate these strategies in seconds.


4

The first Google result seems clear enough: A seagull option is structured through the purchase of a call spread and the sale of a put option (or vice versa)....This structure is appropriate when volatility is high but expected to fall, and the price is expected to trade with a lack of certainty on direction. So, for example, you might buy the 105% call, ...


4

Assume $p_i(x)$ is a payoff of one particular option. You can try to reproduce the diagram using a bunch of options with strikes on the breakpoints (underlying is useless, because its payoff can always be modelled by buy&sell of a certain call and put). Then you can create a system of k equations with n unknowns (number of each kind of option). All other ...


4

The data has definitely not disappeared, it's a problem with your vendor. There has been a corporate action on 2014-02-27 and hence the strike prices have been adapted accordingly. According to Bloomberg bsym your P69 (composite ID BBG004L7P7L6) became P68.63, and P70 (BBG004L7P8C4) became P69.63.


4

When dividends are continuous, they are essentially negative interest rates, so you should price options w.r.t. new interest rate $\hat r := r-d$ where $r$ is the original interest rate and $d$ is the continuous dividend yield. If $\hat r>0$ then the price of the call is still a submartingale, so early exercise is not (strongly) optimal, however in a more ...


4

An Investment Bank earns a profit by selling you an option at a slightly higher price than the theoretical price, or buying it back from you at a slightly lower price. They call this "earning a spread". Then they hedge the option, so as not to make any [further] gains or losses on it (other than the risk free rate). Another way they could earn a profit is ...


4

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 price and a slow gradual increase over the same period, such that the final difference in the price of the underlying was largely unchanged. For multiple options ...


4

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 consider each leg as an independent trade which should be profitable by itself, without other legs.


4

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 not path dependent. This is all still in a hypothetical world of course with continuous trading. In reality when rehedging less frequently, pnl becomes random ...


4

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 delta hedged portfolio. For example: If you are long an at-the-money call option, you are long 0.5 Delta and long Gamma. If you hedge this position, you will ...


4

Using Taylor polynomials of 2nd order:$$V(r+h)\approx V(r) + \frac{\partial{V}}{\partial{r}}h +\frac{1}{2}\frac{\partial^2{V}}{\partial{r}^2}h^2$$ $$V(r-h)\approx V(r) - \frac{\partial{V}}{\partial{r}}h +\frac{1}{2}\frac{\partial^2{V}}{\partial{r}^2}h^2$$ The sum of the previous 2 equation will give us gamma as: $$Gamma = \frac{\partial^2{V}}{\partial{r}^2} ...


4

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 net price change of shares in the underlying due to exercise on expiration would be ~0. As @Emma mentioned, deep in the money options have a high delta. This ...


4

Having a position "tested" or "stressed" is trader jargon for "an assumption I made when entering the position is turning out wrong and I am losing money" or "the trade is going the wrong way at the moment". For example: you sell an OTM option with strike K, as the underlying S approaches (and goes beyond) K that option position is "tested" or stressed. You ...


4

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 $$OptionValue=Intrinsic Value+Time Value $$ $$OptionValue= (S-K)-Dividend$$ $$OptionValue=267x(1-0.02)-267x1.8\%x3=\\\$247$$


3

It depends on the exact structure. E.g., a butterfly can be bought or sold and every market participant understands which individual options are bought or sold given knowledge of the agreed spot level and distance of the wing from spot in regards to agreed strikes. Please note that a butterfly can be structured as a combination of calls but also through ...


3

You are right for delta but wrong for other greeks. Delta of stock is 1 so Covered call Delta = 1 - "long call delta" is correct However a stock doesn't have gamma , theta or vega. So these greeks of your covered call positions will be just that of short call. i.e Covered Call Gamma = - "Long Call gamma" Covered Call Theta = - "Long Call theta" ...


3

It might not work the way you think. Note first that nobody sells options for free so at least one of your integers ($a,b,c$) is negative, meaning you will have nonzero risk of losing money on your short option leg. More specifically, let's pretend $b \geq |c|$. Then since the value of a forward contract is the same as the call minus the put plus strike $...


Only top voted, non community-wiki answers of a minimum length are eligible