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ponpoko
Posts: 23
Joined: May 20th, 2008, 1:07 am
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### What are the stupidest things people have said about risk neutrality?

Thanks list for quick comment. So far I am following Hulls book. Hull's book says that 'expected return on all securities is the risk free intereat rate in risk-neutral-world'. This will coincide to my experience that to verify BS by MCSimuilation, I have to use risk free rate as expected return. This also link to the fact that spot-future is in risk free rate relationship. In option market, we have market bid/offer first hand. Then volatility is adjusted to make model fit to market. In risk neutral framework expected return is untouchable ( should be kept same as risk free rate ), so only vol will be the adjustment term that makes implied vol very much deviate from historical vol and also the source of SMILE I believe. ( Nevertheless I strongly feel that I need to understand more on measure conversion, Gilzanov, (Omega,F,P), Sigma-Algebra,etc. Then I may understand what you mean. )

list
Posts: 2041
Joined: October 26th, 2005, 2:08 pm

### What are the stupidest things people have said about risk neutrality?

You right that Hull's book suggests that 'all securities is the risk free interest rate in risk-neutral-world' and he teaches that " to use risk free rate as expected return." It stems of course from misunderstanding math and finance. The latter goes from BS interpretation of the option price. It contradicts formal logic according to which in theory to get stock at maturity with -100% expected return and +100% expected return is impossible for the same price. But BS introduce arbitrage free interpretation of the option price that in theory possible.

ponpoko
Posts: 23
Joined: May 20th, 2008, 1:07 am
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### What are the stupidest things people have said about risk neutrality?

Thanks list for reply again. I just bought 7th edition of Hull but it still has same line as before, i.e. 'expected return on all securities is the risk free intereat rate in risk-neutral-world'. If this line is not correct, somebody should tell him to correct this. In any case I think I need to study more to be a part of any further math based discussion. Thank you for all help. I will be back.

list
Posts: 2041
Joined: October 26th, 2005, 2:08 pm

### What are the stupidest things people have said about risk neutrality?

You could try to solve the BS puzzle yourself by asking yourself. I am afraid that no one with probably a few exceptions will not be interested either professors or officials. This based on my own experience.

joeyk
Posts: 19
Joined: October 10th, 2002, 1:40 pm

### What are the stupidest things people have said about risk neutrality?

Re the topic of this FAQ, I have heard:"Risk Neutral pricing underprice options because risk free rate is definitely lower than expected returns.""The BS formula and the dynamic hedging ensures that at every moment your portfolio has no risk"

Fermion
Posts: 4486
Joined: November 14th, 2002, 8:50 pm

### What are the stupidest things people have said about risk neutrality?

Last edited by Fermion on October 22nd, 2009, 10:00 pm, edited 1 time in total.

taneururer
Posts: 16
Joined: October 4th, 2005, 4:07 pm

### What are the stupidest things people have said about risk neutrality?

Hopefully my brain is working correctly, but isn't this statement incorrect?"If the current market underprices the underlying, then risk-neutrality will underprice the call and, by put-call parity it will also underprice the put."If the market is truly underpricing the underlying, wouldn't this make puts overpriced (forgetting RN pricing and pricing based on utility)? If the SP500 is at 1,000 and you knew that it worth 1,100 you would sell puts & buy calls.In other words, if the underlying is underpriced then the forward must be underpriced.

Fermion
Posts: 4486
Joined: November 14th, 2002, 8:50 pm

### What are the stupidest things people have said about risk neutrality?

QuoteOriginally posted by: taneururerHopefully my brain is working correctly, but isn't this statement incorrect?"If the current market underprices the underlying, then risk-neutrality will underprice the call and, by put-call parity it will also underprice the put."If the market is truly underpricing the underlying, wouldn't this make puts overpriced (forgetting RN pricing and pricing based on utility)? If the SP500 is at 1,000 and you knew that it worth 1,100 you would sell puts & buy calls.In other words, if the underlying is underpriced then the forward must be underpriced.Context. The above statement was assuming that the risk-neutral density used to price the call has the same higher moments as the "real" density. As you say, the over-priced put argument is just as valid, but then this violates put-call parity unless the call is also over-priced. In reality, of course, this demonstrates that the conversion real density --> risk-neutral density cannot be achieved merely by changing the first moment. It also demonstrates to me, yet again, how easy it is to tie myself up in knots with this stuff....

Gmike2000
Posts: 801
Joined: September 25th, 2003, 9:49 pm

### What are the stupidest things people have said about risk neutrality?

The stupidest thing i ever heard on risk-neutrality:A "strategist" from some stupid bank telling us (the clients) that "The drift in the stochastic model of the stock price is positive because stocks have historically tended to go up"

chaoticrambler
Posts: 60
Joined: September 29th, 2009, 7:56 pm

### What are the stupidest things people have said about risk neutrality?

QuoteOriginally posted by: Gmike2000The stupidest thing i ever heard on risk-neutrality:A "strategist" from some stupid bank telling us (the clients) that "The drift in the stochastic model of the stock price is positive because stocks have historically tended to go up"I think I have seen it written in more than one book (or something similar).So what is the reason ? Inflation must be one, right ?

Costeanu
Posts: 189
Joined: December 29th, 2008, 5:33 pm

### What are the stupidest things people have said about risk neutrality?

That's a good question. Some people think like this: all information about a company is already factored into today's price. If a company has better prospects than its competition, and it is likely to increase its market share, then the price should reflect that, and should not go up when the market share actually increases. So positive drift seems to be a conundrum. The answer is of course risk aversion. But isn't the risk itself already priced in? The simplest example is of a risky zero coupon bond. The riskless rate is zero. A company wants to sell you a bond which will pay $100 in one year, and the chance that the company goes under is 1%. Are you willing to buy this bond for$99? Of course not. You require compensation for your risk. You are willing to buy it for 89.5. So on average, one year from now you make some money. With equities it is the same. The company may have a good quarter, or a bad one. The dividend may go up or down, or the company may even go bust. The price of the stock will reflect that, but with a haircut for risk. When time actually passes, on average the price will go up. Best,V.