18

I did some digging and found the following papers - most of them offering quite a distinct perspective compared to classical option pricing theory! Stock Options as Lotteries by Brian H. Boyer et al. (2011) The Efficiency of the Buy-Write Strategy: Evidence from Australia by Tafadzwa Mugwagwa et al. (2010) The following is my favorite: You could do some ...


15

Great question! I think the most useful starting point is Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options by Bakshi, Kapadia and Madan (2003). Their paper proposes a definition of model-free implied skewness (they originally called it risk-neutral skewness, but MFIS is more accurate), which they prove will ...


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) ...


11

Interesting question. Unfortunately for you, the answer is no, it cannot be done. The principal difference between a basket of options and an option on the basket (or index) is correlation risk. In fact, there is a systematic difference between the implied volatility of the basket and the (properly weighted) sum of implied volatilities on the components. ...


11

A good place to start learning about option market making using quantitative techniques is Euan Sinclair's Option Trading (chapter 10 is devoted to market making techniques). He also gives a decent introduction to a more sophisticated quantitative market making technique which he calls information-based market making. Specifically, he explains how to apply ...


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

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 ...


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

Since I, too, have been very interested in this question, I will share some of my findings in the dual hope of encouraging comments on the papers and eliciting more activity on this question. Ammann, Skovmand, and Verhofen (2008): Implied and Realized Volatility in the Cross-Section of Equity Options Ang, Bali, and Cakici (2010): The Joint Cross Section of ...


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

The paper "Do option markets correctly price the probabilities of movement of the underlying asset? " by Yacine Aït-Sahalia, Yubo Wang, and Francis Yared should in my opinion provide many very usefull elements for this question (look in particular at section 3). Regards


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 ...


8

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 ...


7

This depends a little bit on your definition of volatility arbitrage but in general what is meant is a strategy that takes advantage of the difference between implied volatility and realized volatility. Normally you receive implied variance and pay realized variance. This strategy is the classical example of picking up nickles in front of a steamroller ...


7

Option Traders Use (very) Sophisticated Heuristics, Never the Black–Scholes–Merton Formula Stock Price Clustering on Option Expiration Dates Option Returns and Volatility Mispricing


6

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 ...


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

For single stock options against index options, this may be of interest: Dispersion -- A Guide for the clueless


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 ...


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

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

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

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

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 ...


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