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

Market makers, obviously, have to be willing to short an option. They will delta hedge their positions to limit risk. As for investors, they can aim for a buy-write strategy to collect extra income in lieu of unlimited upside. And lastly, someone who owns a stock he can't sell right away (such as an entrepreneur still under a vesting period after his firm ...


11

Theta decay doesn't depend on the in the moneyness. A 70 delta call and a 30 delta call have very close theta decay at any given moment. They are slightly different because of skew with 70 delta put having slightly bigger theta. Theta is the decay of extrinsic value. In practical trading, you can assume your decay distribution (using your graph is fine) ...


10

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 ...


9

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 ...


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 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

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

When testing your strategy, what you need to pay particular attention to is performance attribution, in other words why did you see the returns you did? Let me give you a simple example to illustrate what I mean. Suppose I have an algorithm to pick stocks and you have a testing database of stock prices for one year. Suppose also that in that year the market ...


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

I suggest you avoid using the VIX for implied vols. Why? One has to consider that the VIX is not simply solely dependant on the dynamics on the S&P 500 anymore because the VIX can be traded via options, etc. Thus many more parameters affect the trajectory of the VIX. The VIX has to equal the ATM option vol because this is where arbitrage assumption ...


5

As a complement to chrisaycock's answer, I would also say that shorting options is useful when you want to create option strategies. Buying and shorting options on the same underlying with different strike prices allows the investor to create products with elaborate payoff which allows them to be more on a range of the underlying's price rather than on its ...


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 ...


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 best solution in most cases where one is backtesting from a non-standard universe is to construct your own index. I believe that to also be true in your case, as there is no standard index tracking the returns of a particular basket of options. VIX, in particular, is more accurately thought of as a price index, not a return index, in the options world. ...


4

In kamikaze_pilot's defense, the question is not that naive or simple. First of all, you need to define what options you are talking about. Consider a digital option for example (which is really fairly vanilla since you can proxy it as a combination of two European calls), which pays 1 of the stock is beyond a certain level at maturity and nothing otherwise....


4

While the time decay on the time value component of an option does not depend on how much the option is in the money, theta is the change in total option value not just the time value due to the passage of time. Time decay is higher for options that are out of the money assuming volatility and the risk free rate are held constant. This is because a greater ...


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. ...


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