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# Minyan Mailbag - Math Help

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Note: Our goal in Minyanville is to remove intimidation from the financial markets and encourage an interactive dialogue among the Minyanship. We share this next discussion with that very intent.

John,

With the vols sinking like they are, I started thinking about the story of Simon. I went back and searched the archives and in that story,
written on November 18, 2003 you stated:

"Simon recommended to accounts and friends and family alike to buy six month 10%
out of the money puts and wait. In today's market this would cost around 1% of the price of the index. In 1987 the cost was a mere .02%."

So, I take the S&P at 1185.00 x .9 gives us 1065.00. I don't see a quote on a June 1065, but there are quotes for the 1075 and 1050. So I checked the price on a SPM5 1050P, 10.50 bid at 12.00. For the sake of simplicity, let's call it 11.00.

11 / 1184 = .01

So, if my math is correct, it costs 1% to buy a 6 month, 10+% out of the money, put today. The same price, perhaps a little more, than it did in November of 2003. I don't know what vols were in November 2003, but I think it is safe to say they were higher than they are here, no?

So my question is several fold? Why, with lower vols, is the cost the same? I assume it must be a steeper skew, but I'm not sure. Second, does this not portend fear in the market place? If complacency was rampant, wouldn't the price be cheaper? Finally, are there no bargains like Simon got? I want to live and ski in the mountains. ;-)

Minyan JK

Minyan JK,

By my calculations a 1065 six month put at the correct implied volatility of around 16.8% (for that strike) would cost \$9.70 or .82% of the index. So the prices of these index options have become slightly cheaper since I published that piece.

But of course, not anywhere as cheap as they were before 1987. 1987 was caused by an anomoly called portfolio insurance which drove the prices of most options to levels never seen before since (and probably never will).

This does not mean that options are relatively cheap. And further, index options (which price systemic risk) are normally over-priced (people love their stocks but hate the markets). Where I see the real cheapness of options is in individual equity options. We normally sell index options and buy individual options; not consistently but opportunistically. For example, we do not see index options rich enough to have this trade on; we are simply long individual stock options of various sorts (long convexity but delta neutral).

The bottom line is that the skew is still prevalent in index options but not in individual stock options. For this reason I have stated that in a market decline it is not likely to occur like it did in 1987 where the huge negative gamma forced a crash. A decline would act much more fitfully.

Regards,
Prof. Succo

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