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Besides obvious extreme examples (ie volatility going to infinity, infinite time, zero time, or zero volatility, deep OTM/ITM ) how does one gauge if an option is 'correct' or at least in the ballpark when priced with an option pricing formula? Unlike physics, results in quant. finance seem to have more of a subjective nature to them. Are quoted options prices the benckmark of accuracy, so option pricing should strive to match them?

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up vote 5 down vote accepted

While the translation between implied volatility (iVol) and options prices is of a strictly mathematical nature (when you feed 10 market makers with the same iVol you most likely get 10 identical or close to identical option prices in vanilla structures).

What is on the other side more of an art than science is how to assess whether iVols/prices trade fairly, whether an option is fairly valued or whether implied volatility fairly represents the future underlying expected price variations.

So it comes down to what you believe about market dynamics. If you make the assumption that quoted options prices ARE the market and hence represent fair value then you take it from there and generate your vol surface and price other non-quoted structures. If you have your own model that derives prices and volatility measures that divert from your model prices then you obviously believe that the prices and volatility measures of your model have some sort of validity.

Hence the topic of calibration is a touchy one: When do you calibrate and at what point can you be reasonably certain that the data points you take into consideration for calibration represent fair value. Obviously you do not want to calibrate gold option vol surface right when the market pushed down gold prices and its futures by almost 10% intraday; admittedly a very rare move (though we just witnessed it last night) and hence nobody in their right mind would calibrate a volatility surface at a time when the market is showing very abnormal dynamics.

So, take it for what its worth, as much as the academic world likes to make options pricing and valuation a hard science, having traded volatility for many years I can tell you that I do find a number very unscientific aspects in pricing options accurately in order to make a long-term living out of this endeavor.

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good answer. thank you –  April Crenshaw Apr 16 '13 at 2:06
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@AprilCrenshaw, you do not need to mark an answer correct right away, take your time, wait for other answers to come in...just my 2c –  Matt Wolf Apr 16 '13 at 2:26
    
That was an excellent, nuanced answer. It motivates me to wonder whether historically, options prices have been fair compensation for the risk of expiring in the money. –  experquisite Apr 16 '13 at 14:03
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The most important road markings are given by the fact that the price has to be arbitrage-free.

A good introduction to the concept is given in this article by Schachermayer:
http://www.mat.univie.ac.at/~schachermayer/pubs/preprnts/prpr0118a.pdf

Another helpful concept in this context is put-call parity, which has to hold for combinations of prices:
http://en.wikipedia.org/wiki/Put%E2%80%93call_parity

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