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I noticed that for some securities, puts were more expensive than calls (with same expiration). For example, suppose the underlying security is trading at 50. A put with a strike of 45 is more expensive than a call with a strike of 55. A put with a strike of 40 is more expensive than a call with a strike of 60. And so on.

This means that the market thinks the security has a greater chance of falling than of rising. But if this were the case, shouldn't the underlying security simply fall immediately? Shouldn't this sentiment just be priced into the underlying security until a put-call equilibrium is reached?

I've read about put-call parity, but that seems to be addressing puts and calls with equal strike prices. Here, I'm talking about puts and calls with different strike prices that are equidistant from the current trading price.

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    $\begingroup$ It looks like what I'm talking about is a known phenomenon called "volatility skew". But it still seems like this should not exist in an efficient market and that it represents an arbitrage opportunity. $\endgroup$ – Nik I May 29 '15 at 16:49
  • $\begingroup$ Where is the arbitrage opportunity? $\endgroup$ – will Aug 6 '16 at 12:44
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Its a stylized fact in academia that put options are overpriced.

E.g., the monthly average return on S&P500 put options is around -40% for ATM options.

The most often quoted reason for this phenomenon are hedging costs: A put is more difficult to hedge from a market maker's perspective, hence the prices artificially go up.

An important paper on this issue with a good introduction can be found here: http://www.investps.com/images/Why_Are_Put_Options_So_Expensive.pdf

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    $\begingroup$ Very interesting paper, thanks. Looks like people will really pay a fat premium to quell their fears of a crash. $\endgroup$ – Nik I May 30 '15 at 0:34
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    $\begingroup$ Link is currently broken. Alternative: papers.ssrn.com/sol3/Papers.cfm?abstract_id=375784 $\endgroup$ – John Sep 5 '17 at 15:32
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The typical investor is long. To protect the portfolio, he buys puts, thus driving up the price. To generate income against his long position, he sells covered calls, thus driving down the price.

This is the most basic explanation for the difference in put call prices that are equidistant from the money. Obviously other factors are there as pointed out by Thomas Baert.

Last but not the least, it could be a temporary imbalance that will correct itself.

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  • $\begingroup$ Your answer is interesting, I suggest you can improve it by quoting the Put-Call-Parity principle and showing the replication. $\endgroup$ – emcor May 29 '15 at 21:03
  • $\begingroup$ I thought that put and call price come solely from mathematical models whose inputs are strike price, interest rates and volatility $\endgroup$ – duckduckgo Jul 30 '16 at 1:55
  • $\begingroup$ They do, but volatility is not a fixed variable - it is determined by supply and demand of the option. This is the reason why option prices are sometimes quoted in terms of vol rather than a monetary value. $\endgroup$ – Ana Aug 5 '16 at 9:21
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if put call parity seems to be violated there could be things you are ignoring like dividends or hard to borrow fees. Hard to borrow will make puts more expensive

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  • $\begingroup$ The fact that PCP does not hold explains only 1/4 of the story. PCP would also be violated if puts are underpriced or calls are over/underpriced. $\endgroup$ – emcor May 30 '15 at 6:12
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Because American style options allow early exercise, the put-call parity will not hold unless they are held to expiration. Early exercise will result in a departure in the present values of the two portfolios.

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It could be that the chances of a market falling falling are low, but the move will be large. Conversely , the market is quite likely to go up, but the move will be smaller. In other words, the market will either grind higher or fall precipitously. Thus, the market is in equilibrium , but out of the money puts cost more than out of the money calls.

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Puts and calls will always be exactly the same price, if not then you can take a synthetic position called a reversal, its an arbitrage opportunity and you would make free money.

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  • $\begingroup$ issue is they aren't always the exact same price. $\endgroup$ – FX_NINJA Aug 30 '16 at 1:05

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