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This is a question about why options prices do not take volume into account. The popular option valuation formula "black-scholes" certainly does not account for this and I don't suggest that it does.

But one could hold a large option position while the underlying asset's price walks up or down on very low volume, allowing the option to gain more and more value and be liquidated without affecting the market for the underlying asset. This seems strange to me, since it would seem to me that the option's value/price should have a liquidity premium for exercising the option and closing the position on the underlying asset, despite the fact that most options are not exercised.

I like the inefficiencies in option pricing, as a speculative tool and the predictability in calculating intrinsic value as an in the money option moves deeper in the money. But it seems that volume weighted price nearer expiration should determine the price of an option's intrinsic value in the black-scholes formula

Thoughts and insight appreciated

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1 Answer 1

As you correctly pointed out volume has no place in the pricing models of most any option(Unless of course you create an option whose underlying or is volume in some way or if volume is used as some sort of barrier). The reason is simple: The contingent payoff and hence the probability of ending up in the money is not a function of volume.

Why the market is perfectly comfortable with that fact, including those who hedge the option with underlying assets is because liquidity is priced into the implied volatility directly to some degree but it is especially priced into the implied vol spread. Should the underlying be highly illiquid or should, for example a highly uncertain dividend declaration loom, then spreads in the quoted implied vols will widen. This can easily be seen when you compare options on underlying assets that are highly liquid with much turnover vs options whose underlying rarely trades.

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It is also worth noting that cash-settled futures options make some people nervous about financial system stability, since they worry that these liquidity considerations are not properly "priced in". It was a topic of much discussion back in the 70s and 80s. –  Brian B Jul 29 '13 at 16:49
    
@BrianB, thanks for mentioning that. Do you have couple products in mind where that was the case? I have traded JGB futures options in the past and felt liquidity was well reflected in the iVol spreads at most times. –  Matt Wolf Jul 30 '13 at 0:19
    
I've never personally perceived it as a problem in modern markets, but it was considered an important point in the aftermath of the '87 crash. Some papers argued the liquidity only came to be priced in properly after that crash. These days the only concerns I have seen have been on the part of the maniacs at ZeroHedge. –  Brian B Jul 30 '13 at 15:59
    
@BrianB, ah now I see what you meant. Yes, agree, and even in 2008 people hugely underpriced the value of liquidity, especially when the CP market went seismic and a number money market funds broke the buck. Or I bet ex Lehman upper management would have paid a much higher price for liquidity in retrospect. –  Matt Wolf Jul 31 '13 at 5:13

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