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	<title>Comments on: Warren Buffett on the Black-Scholes Formula</title>
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	<link>http://www.aleablog.com/warren-buffett-on-the-black-scholes-formula/</link>
	<description>Alea Jacta Est</description>
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		<title>By: Ben</title>
		<link>http://www.aleablog.com/warren-buffett-on-the-black-scholes-formula/#comment-2619</link>
		<dc:creator>Ben</dc:creator>
		<pubDate>Mon, 09 Mar 2009 04:34:09 +0000</pubDate>
		<guid isPermaLink="false">http://www.aleablog.com/?p=2774#comment-2619</guid>
		<description>The games Buffett can play are based on how he&#039;s so big and has so much cash.  Since he&#039;s holding these things on his book to maturity the only thing he&#039;s got to do is make sure that collateral he&#039;s going to need to post is there.  It&#039;s as though the main point is that he&#039;s got a lot of assets to post if things should go bad midway through - and as long as there&#039;s discipline about not playing the game too hard he&#039;ll be fine.  The underlying assumption in part is that reinsurance losses from disasters and what-not aren&#039;t going to be correlated with lousy stock returns.

I don&#039;t know if the puts he&#039;s written can be sold to a third party or if they&#039;re indexed to inflation.</description>
		<content:encoded><![CDATA[<p>The games Buffett can play are based on how he&#8217;s so big and has so much cash.  Since he&#8217;s holding these things on his book to maturity the only thing he&#8217;s got to do is make sure that collateral he&#8217;s going to need to post is there.  It&#8217;s as though the main point is that he&#8217;s got a lot of assets to post if things should go bad midway through &#8211; and as long as there&#8217;s discipline about not playing the game too hard he&#8217;ll be fine.  The underlying assumption in part is that reinsurance losses from disasters and what-not aren&#8217;t going to be correlated with lousy stock returns.</p>
<p>I don&#8217;t know if the puts he&#8217;s written can be sold to a third party or if they&#8217;re indexed to inflation.</p>
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		<title>By: Amicus</title>
		<link>http://www.aleablog.com/warren-buffett-on-the-black-scholes-formula/#comment-2594</link>
		<dc:creator>Amicus</dc:creator>
		<pubDate>Wed, 04 Mar 2009 15:19:51 +0000</pubDate>
		<guid isPermaLink="false">http://www.aleablog.com/?p=2774#comment-2594</guid>
		<description>To &quot;blame&quot; B-S is so sophomoric, don&#039;t you think?

I mean the &#039;troubles&#039; he notes are well known to people who value options and for quite some time (like almost 20 years...).

I guess blaming &quot;model risk&quot; is complex enough to snow people with an explanation, other than that &#039;we doubled-down that there wouldn&#039;t be a downside this big and we were wrong&#039;.</description>
		<content:encoded><![CDATA[<p>To &#8220;blame&#8221; B-S is so sophomoric, don&#8217;t you think?</p>
<p>I mean the &#8216;troubles&#8217; he notes are well known to people who value options and for quite some time (like almost 20 years&#8230;).</p>
<p>I guess blaming &#8220;model risk&#8221; is complex enough to snow people with an explanation, other than that &#8216;we doubled-down that there wouldn&#8217;t be a downside this big and we were wrong&#8217;.</p>
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		<title>By: Chris</title>
		<link>http://www.aleablog.com/warren-buffett-on-the-black-scholes-formula/#comment-2576</link>
		<dc:creator>Chris</dc:creator>
		<pubDate>Mon, 02 Mar 2009 18:42:21 +0000</pubDate>
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		<description>I agree with Warren, have you ever looked at LEAPS prices two years out?  I think the puts he sold are pure market genius.  He found a glitch in the Matrix and now he is going to exploit it.</description>
		<content:encoded><![CDATA[<p>I agree with Warren, have you ever looked at LEAPS prices two years out?  I think the puts he sold are pure market genius.  He found a glitch in the Matrix and now he is going to exploit it.</p>
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		<title>By: Volkan</title>
		<link>http://www.aleablog.com/warren-buffett-on-the-black-scholes-formula/#comment-2575</link>
		<dc:creator>Volkan</dc:creator>
		<pubDate>Mon, 02 Mar 2009 15:32:53 +0000</pubDate>
		<guid isPermaLink="false">http://www.aleablog.com/?p=2774#comment-2575</guid>
		<description>Buffett&#039;s derivatives trades are the right trades for Berkshire.  Even though I took the opposite side of his type of derivatives trades when I could, my time horizon was very short.  Buffett is generally not beholden to mark to market.  Thus, over long term, his derivative positions should be profitable. 

His logic is that of an insurer, using actuarial type probabilities rather than market indications. He is also correct in his criticism of Black Scholes for long tenor options.  In fact, he mentions just a few of the problems among many.  

Still, these options may be more valuable for some than Black Scholes value.  For example, a quant should start valuing them not as plain vanilla options, rather path dependent, knock-in options.  In the end, the correct value depends on the assumptions you make, just like everything.</description>
		<content:encoded><![CDATA[<p>Buffett&#8217;s derivatives trades are the right trades for Berkshire.  Even though I took the opposite side of his type of derivatives trades when I could, my time horizon was very short.  Buffett is generally not beholden to mark to market.  Thus, over long term, his derivative positions should be profitable. </p>
<p>His logic is that of an insurer, using actuarial type probabilities rather than market indications. He is also correct in his criticism of Black Scholes for long tenor options.  In fact, he mentions just a few of the problems among many.  </p>
<p>Still, these options may be more valuable for some than Black Scholes value.  For example, a quant should start valuing them not as plain vanilla options, rather path dependent, knock-in options.  In the end, the correct value depends on the assumptions you make, just like everything.</p>
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		<title>By: Brian Shriver</title>
		<link>http://www.aleablog.com/warren-buffett-on-the-black-scholes-formula/#comment-2574</link>
		<dc:creator>Brian Shriver</dc:creator>
		<pubDate>Mon, 02 Mar 2009 15:13:24 +0000</pubDate>
		<guid isPermaLink="false">http://www.aleablog.com/?p=2774#comment-2574</guid>
		<description>You guys are nuts and Buffett is right.  You have to use common sense in applying any mathematical model to the real world.  Buffett walks through the example of a 100-year put in his annual letter.

Buffett knows his stuff.  From his perspective, these puts are little different from other insurance policies he writes.  He may not win them all, but the odds are tilted in his favor.</description>
		<content:encoded><![CDATA[<p>You guys are nuts and Buffett is right.  You have to use common sense in applying any mathematical model to the real world.  Buffett walks through the example of a 100-year put in his annual letter.</p>
<p>Buffett knows his stuff.  From his perspective, these puts are little different from other insurance policies he writes.  He may not win them all, but the odds are tilted in his favor.</p>
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		<title>By: BrantW</title>
		<link>http://www.aleablog.com/warren-buffett-on-the-black-scholes-formula/#comment-2572</link>
		<dc:creator>BrantW</dc:creator>
		<pubDate>Mon, 02 Mar 2009 10:14:50 +0000</pubDate>
		<guid isPermaLink="false">http://www.aleablog.com/?p=2774#comment-2572</guid>
		<description>I am beginning to think that WB too is has been collecting quarters in front of a bulldozer.  

I wonder if Taleb thinks those puts are &#039;too expensive&#039;.</description>
		<content:encoded><![CDATA[<p>I am beginning to think that WB too is has been collecting quarters in front of a bulldozer.  </p>
<p>I wonder if Taleb thinks those puts are &#8216;too expensive&#8217;.</p>
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		<title>By: Innocent bystander</title>
		<link>http://www.aleablog.com/warren-buffett-on-the-black-scholes-formula/#comment-2571</link>
		<dc:creator>Innocent bystander</dc:creator>
		<pubDate>Mon, 02 Mar 2009 01:39:33 +0000</pubDate>
		<guid isPermaLink="false">http://www.aleablog.com/?p=2774#comment-2571</guid>
		<description>He&#039;s right and he&#039;s wrong. The BS method assumes continuous returns - no jumps - and zero transaction costs. If you make those two &#039;small&#039; assumptions you can hedge your sold options and make the BS formula come true. In the real world you are lucky if you can hedge 70% of the risk. So real world option prices do not match the BS model, especially for way of the money options.

The hedging fails of course just when you need it most - when there are big jumps in the market.  Older readers may recall the 1987 crash which was in large part caused by failed attempts to hedge against market declines. In those days it was called portfolio insurance.

Of course one might suspect that WB is making excuses for his losses selling options. One thing he doesn&#039;t seem to have acknowledged is that the &quot;investment returns&quot; he is expecting to make from the premiums are going to be highly correlated with what he insuring. If the market tanks long term - as other markets have eg Japan - and he has to pay up on the puts, his investment returns are also likely to be lousy. Correlated risk is bad. Also note that WB is not a young man so the returns will have to be achieved by his successor who may not be as good an investor.</description>
		<content:encoded><![CDATA[<p>He&#8217;s right and he&#8217;s wrong. The BS method assumes continuous returns &#8211; no jumps &#8211; and zero transaction costs. If you make those two &#8217;small&#8217; assumptions you can hedge your sold options and make the BS formula come true. In the real world you are lucky if you can hedge 70% of the risk. So real world option prices do not match the BS model, especially for way of the money options.</p>
<p>The hedging fails of course just when you need it most &#8211; when there are big jumps in the market.  Older readers may recall the 1987 crash which was in large part caused by failed attempts to hedge against market declines. In those days it was called portfolio insurance.</p>
<p>Of course one might suspect that WB is making excuses for his losses selling options. One thing he doesn&#8217;t seem to have acknowledged is that the &#8220;investment returns&#8221; he is expecting to make from the premiums are going to be highly correlated with what he insuring. If the market tanks long term &#8211; as other markets have eg Japan &#8211; and he has to pay up on the puts, his investment returns are also likely to be lousy. Correlated risk is bad. Also note that WB is not a young man so the returns will have to be achieved by his successor who may not be as good an investor.</p>
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		<title>By: Martin.Ho</title>
		<link>http://www.aleablog.com/warren-buffett-on-the-black-scholes-formula/#comment-2570</link>
		<dc:creator>Martin.Ho</dc:creator>
		<pubDate>Sun, 01 Mar 2009 21:14:20 +0000</pubDate>
		<guid isPermaLink="false">http://www.aleablog.com/?p=2774#comment-2570</guid>
		<description>If my memory serves me well, Sigma (volatility) and T (time to exercise) are two separate parameters in the BS equation. [T] is a very well defined number but the true [Sigma] is an unknown and thus requires an estimate from what we observed.</description>
		<content:encoded><![CDATA[<p>If my memory serves me well, Sigma (volatility) and T (time to exercise) are two separate parameters in the BS equation. [T] is a very well defined number but the true [Sigma] is an unknown and thus requires an estimate from what we observed.</p>
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		<title>By: DancesWithVols</title>
		<link>http://www.aleablog.com/warren-buffett-on-the-black-scholes-formula/#comment-2569</link>
		<dc:creator>DancesWithVols</dc:creator>
		<pubDate>Sun, 01 Mar 2009 20:28:39 +0000</pubDate>
		<guid isPermaLink="false">http://www.aleablog.com/?p=2774#comment-2569</guid>
		<description>Hey...! I was thinking the very same thing....! Whenever I&#039;m short index puts, and the market takes a dump, I feel like switching-off the screens and declaring &quot;It&#039;s all a bunch of nonsense!&quot;

Just too bad none of the brokers, counter-parties or clearling-firms buy such an argument (even if any were possibly stupid enough to do so, their own CDS would blow-up, fatally-damaging their own financing arrangements: thus winning themselves the Darwin Award).....

Well, if he *truly* believes that Black-Scholes &quot;overstates&quot; long-dated options values, then he should just go all-in: Sell an infinite number of puts on an infinite number of indices what&#039;s the worst that could *possibly* happen...? 

After all, AIG is getting yet another free $30bil from the US Gov&#039;t for it&#039;s negative-convexity-bet gone wild, so why not do the same and pick pick-up some free cash from a  negative-gamma dice-throw....?

In all seroiusness, If someone can come along with a &quot;better&quot; formula that prints money and doesn&#039;t blow you up, then, hey, I&#039;ll take it; I just find it awfully convenient that he&#039;s cryyyying a river now that his &quot;free money&quot; bet (short the options, collect the premia for 20 years, and like, there&#039;s *no* penalty to pay until the very end) is beginning to do a Nick Leeson on him, and his CDS premia are exploding, counter-parties are easing-back and it&#039;s all hitting the Bloomberg screen at an inopportune time...</description>
		<content:encoded><![CDATA[<p>Hey&#8230;! I was thinking the very same thing&#8230;.! Whenever I&#8217;m short index puts, and the market takes a dump, I feel like switching-off the screens and declaring &#8220;It&#8217;s all a bunch of nonsense!&#8221;</p>
<p>Just too bad none of the brokers, counter-parties or clearling-firms buy such an argument (even if any were possibly stupid enough to do so, their own CDS would blow-up, fatally-damaging their own financing arrangements: thus winning themselves the Darwin Award)&#8230;..</p>
<p>Well, if he *truly* believes that Black-Scholes &#8220;overstates&#8221; long-dated options values, then he should just go all-in: Sell an infinite number of puts on an infinite number of indices what&#8217;s the worst that could *possibly* happen&#8230;? </p>
<p>After all, AIG is getting yet another free $30bil from the US Gov&#8217;t for it&#8217;s negative-convexity-bet gone wild, so why not do the same and pick pick-up some free cash from a  negative-gamma dice-throw&#8230;.?</p>
<p>In all seroiusness, If someone can come along with a &#8220;better&#8221; formula that prints money and doesn&#8217;t blow you up, then, hey, I&#8217;ll take it; I just find it awfully convenient that he&#8217;s cryyyying a river now that his &#8220;free money&#8221; bet (short the options, collect the premia for 20 years, and like, there&#8217;s *no* penalty to pay until the very end) is beginning to do a Nick Leeson on him, and his CDS premia are exploding, counter-parties are easing-back and it&#8217;s all hitting the Bloomberg screen at an inopportune time&#8230;</p>
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		<title>By: ss</title>
		<link>http://www.aleablog.com/warren-buffett-on-the-black-scholes-formula/#comment-2568</link>
		<dc:creator>ss</dc:creator>
		<pubDate>Sun, 01 Mar 2009 17:02:31 +0000</pubDate>
		<guid isPermaLink="false">http://www.aleablog.com/?p=2774#comment-2568</guid>
		<description>I found the part about selling his derivatives portfolio to some unknown buyer -- with recourse back to BH -- most illuminating. Why would I not be surprised to find that GS was the buyer here and this was an &quot;unmentioned&quot; part of that particular deal. 

With regard to BS,  &quot;absurd&quot; values are generated in times of extreme risk as uncertainty grows. How else are traders supposed to manage risk? It&#039;s not like there&#039;s a crystal ball out there that says &quot;this low and no lower.&quot; Unless of course you believe, like Bill Gross, that the government will set a floor to values...</description>
		<content:encoded><![CDATA[<p>I found the part about selling his derivatives portfolio to some unknown buyer &#8212; with recourse back to BH &#8212; most illuminating. Why would I not be surprised to find that GS was the buyer here and this was an &#8220;unmentioned&#8221; part of that particular deal. </p>
<p>With regard to BS,  &#8220;absurd&#8221; values are generated in times of extreme risk as uncertainty grows. How else are traders supposed to manage risk? It&#8217;s not like there&#8217;s a crystal ball out there that says &#8220;this low and no lower.&#8221; Unless of course you believe, like Bill Gross, that the government will set a floor to values&#8230;</p>
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