Understanding the synthetic long put option
A long put - you have a small initial cost (the option premium) but profit as the stock goes down. You have no additional risk if the shock rises, even a lot. Short a stock - you gain if the stock drops, but have unlimited risk if it rises, the call mitigates this, by capping that rising stock risk. The profit/loss graph looks similar to the long put when you hold both the short position and the long call.  You might consider producing a graph or spreadsheet to compare positions. You can easily sketch put, call, long stock, short stock, and study how combinations of positions can synthetically look like other positions. Often, when a stock has no shares to short, the synthetic short can help you put your stock position in place.
Yes. There are levels of option trading permission. For example, I've never set myself up for naked put writing.  But, if you already have the call spread, buying back the shorted call will leave you with a long call. This wouldn't be an issue. As long as you have the cash/margin to buy back that higher strike call. The short answer is that it depends on the taxation laws in your country. The long answer is that there are usually tax avoidance mechanisms that you can use which may make it more economically feasible for you to go one way or the other. Consider the following: The long term average growth rate of the stock market in Australia is around 7%.  The average interest on a mortgage is 4.75%.  Assuming you have money left over from a 20% deposit, you have a few options.  You could: 1) Put that money into an index fund for the long term, understanding that the market may not move for a decade, or even move downwards; 2) Dump that money straight into the mortgage; 3) Put that money in an offset account Option 1 will get you (over the course of 30-40 years) around 7% return.  If and when that profit is realised it will be taxed at a minimum of half your marginal tax rate (probably around 20%, netting you around 5.25%) Option 2 will effectively earn you 4.75% pa tax free Option 3 will effectively earn you 4.75% pa tax free with the added bonus that the money is ready for you to draw upon on short notice. Of the three options, until you have a good 3+ months of living expenses covered, I'd go with the offset account every single time. Once you have a few months worth of living expenses covered, I would the adopt a policy of spreading your risk.  In Australia, that would mean extra contributions to my Super (401k in the US) and possibly purchasing an investment property as well (once I had the capital to positively gear it). Of course, you should find out more about the tax laws in your country and do your own maths. Thanks. Just to clarify I am looking for a more value-neutral answer in terms of things like Sharpe ratios. I think it's an oversimplification to say that on average you lose money because of put options - even if they expire uselessly 90% of the time, they still have some expected payoff that kicks in 10% of the time, and if the price is less than the expected payoff you will earn money in the long term by investing in put options (I am sure you know this as a PhD student I just wanted to get it out there.)I guess more formally my question would be are there studies on whether options prices correspond well to the diversification benefits they offer from an MPT point of view. "As already noted, options contain inherent leverage (a multiplier on the profit or loss). The amount of ""leverage"" is dictated primarily by both the options strike relative to the current share price and the time remaining to expiration. Options are a far more difficult investment than stocks because they require that you are right on both the direction and the timing of the future price movement. With a stock, you could choose to buy and hold forever (Buffett style), and even if you are wrong for 5 years, your unrealized losses can suddenly become realized profits if the shares finally start to rise 6 years later. But with options, the profits and losses become very final very quickly. As a professional options trader, the single best piece of advice I can give to investors dabbling in options for the first time is to only purchase significantly ITM (in-the-money) options, for both calls and puts. Do a web search on ""in-the-money options"" to see what calls or puts qualify.  With ITM options, the leverage is still noticeably better than buying/selling the shares outright, but you have a much less chance of losing all your premium. Also, by being fairly deep in-the-money, you reduce the constant bleed in value as you wait for the expected move to happen (the market moves sideways more than people usually expect). Fairly- to deeply-ITM options are the ones that options market-makers like least to trade in, because they offer neither large nor ""easy"" premiums. And options market-makers make their living by selling options to retail investors and other people that want them like you, so connect the dots. By trading only ITM options until you become quite experienced, you are minimizing your chances of being the average sucker (all else equal). Some amateur options investors believe that similar benefits could be obtained by purchasing long-expiration options (like LEAPS for 1+ years) that are not ITM (like ATM or OTM options). The problem here is that your significant time value is bleeding away slowly every day you wait.  With an ITM option, your intrinsic value is not bleeding out at all. Only the relatively smaller time value of the option is at risk. Thus my recommendation to initially deal only in fairly- to deeply-ITM options with expirations of 1-4 months out, depending on how daring you wish to be with your move timing." Intuitive? I doubt it. Derivatives are not the simplest thing to understand.  The price is either in the money or it isn't. (by the way, exactly 'at the money' is not 'in the money.') An option that's not in the money has time value only. As the price rises, and the option is more and more in the money, the time value drops. We have a $40 stock. It makes sense to me that a $40 strike price is all just a bet the stock will rise, there's no intrinsic value. The option prices at about $4.00 for one year out, with 25% volatility. But the strike of $30 is at $10.68, with $10 in the money and only .68 in time premium. There's a great calculator on line to tinker with.  Volatility is a key component of options trading. Think about it. If a stock rises 5%/yr but rarely goes up any more or less, just steady up, why would you even buy an option that was even 10% out of the money? The only way I can describe this is to look at a bell curve and how there's a 1/6 chance the event will be above one standard deviation. If that standard deviation is small, the chance of hitting the higher strikes is also small.  I wrote an article Betting on Apple at 9 to 2 in which I describe how a pair of option trades was set up so that a 35% rise in Apple stock would return 354% and Apple had two years to reach its target. I offer this as an example of options trading not being theory, but something that many are engaged in. What I found curious about the trade was that Apple's volatility was high enough that a 35% move didn't seem like the 4.5 to 1 risk the market said it was. As of today, Apple needs to rise 13% in the next 10 months for the trade to pay off. (Disclosure - the long time to expiration was both good and bad, two years to recover 35% seemed reasonable, but 2 years could bring anything in the macro sense. Another recession, some worldwide event that would impact Apple's market, etc. The average investor will not have the patience for these long term option trades.) Yes, and there's a good reason they might. (I'm gonna use equity options for the example; FX options are my thing, but they typically trade European style). The catch is dividends.  Imagine you're long a deep-ITM call on a stock that's about to pay a dividend. If that dividend is larger than the time value remaining on the option, you'd prefer to exercise early - giving you the stock and the dividend payment - rather than hanging on to the time value of the option.  You can get a similar situation in FX options when you're long a deep-ITM American call on a positive-carry currency (say AUDJPY); you might find yourself so deep in the money, with so little time value left on the option, that you'd rather exercise the option and give up the remaining time value in return for the additional carry from getting the spot position early. In the money puts and calls are subject to automatic execution at expiration. Each broker has its own rules and process for this.  For example, I am long a put. The strike is $100. The stock trades at the close, that final friday for $90. I am out to lunch that day. Figuratively, of course. I wake up Saturday and am short 100 shares. I can only be short in a margin account. And similarly, if I own calls, I either need the full value of the stock (i.e. 100*strike price) or a margin account.  I am going to repeat the key point. Each broker has its own process for auto execution. But, yes, you really don't want a deep in the money option to expire with no transaction.  On the flip side, you don't want to wake up Monday to find they were bought out by Apple for $150. "I'm far from certain, but I'll take a swing at it.  Equilibrium term structure models ""predict"" a term structure that we don't observe, and no-arbitrage models ""correct"" prediction to match reality.  An analogous place to look would be implied volatility surfaces.  Black-Scholes predicts a specific implied volatility surface (or rather, it assumes the surface is flat).  So I think a Hull-White-style no-arbitrage model might work by addressing the difference between predicted and actual surfaces.  Like term structure models, you'd take a set of observed volatilities and somehow plug them into BS so that the BS price didn't imply arbitrage opportunities within the observed set of options.  I'm not at all certain that I'm being clear, and there's a distinct possibility that I'm saying/thinking something stupid."