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Marsden
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Re: "Option Pricing, Risk Premium, and Arbitrage: An Argument for Volatility-Modified Risk-Neutral Prices."

July 4th, 2022, 4:58 pm

Oldrich Vasicek had figured it out by the mid 70’s. Look for it around equation 20 in his classic “An equilibrium characterization of the term structure”, JFE 1977. There is a lot more to that paper than an OU short rate model…
At http://citeseerx.ist.psu.edu/viewdoc/do ... 1&type=pdf, by the way.
 
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Gamal
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Re: "Option Pricing, Risk Premium, and Arbitrage: An Argument for Volatility-Modified Risk-Neutral Prices."

August 4th, 2022, 12:48 pm

Is there that volatility adjustment formula or was I not careful enough? I've got problems with understanding plain English (and other languages), only formulas are sufficiently clear for me.
 
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Marsden
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Re: "Option Pricing, Risk Premium, and Arbitrage: An Argument for Volatility-Modified Risk-Neutral Prices."

August 4th, 2022, 1:56 pm

Is there that volatility adjustment formula or was I not careful enough? I've got problems with understanding plain English (and other languages), only formulas are sufficiently clear for me.
No volatility adjustment formula as such. From the appendix, there is σ’=sqrt[2(r−µ)], but this refers to the real world drift coefficient µ, for which there is no readily available market value.

Quants I guess like to base everything off of market prices and exercise no input from their own judgment ... which is good work if it pays well.

But also ultimately equivalent to working in library stacks, returning books to their proper places. Which really shouldn't pay terribly well.

;-)
 
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Gamal
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Re: "Option Pricing, Risk Premium, and Arbitrage: An Argument for Volatility-Modified Risk-Neutral Prices."

August 4th, 2022, 3:47 pm

And what if µ > r? This is the usual situation.
 
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Marsden
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Re: "Option Pricing, Risk Premium, and Arbitrage: An Argument for Volatility-Modified Risk-Neutral Prices."

August 4th, 2022, 4:56 pm

To be clear, µ in this context is the drift of the normal distribution that the lognormal distribution of future stock price is based on in the stock price model.

The expected rate of return on the stock is µ+½σ².

To my thinking, µ>r should not happen; this would imply (per the model) that a stock investment will almost surely (in the technical meaning of that phrase) be more profitable than a riskless investment, if you just wait long enough.

Although note that the model assumes no debt for the company underlying the stock. Debt changes expected rates of return, even within the model as modified to address debt, A LOT.
 
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Paul
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Re: "Option Pricing, Risk Premium, and Arbitrage: An Argument for Volatility-Modified Risk-Neutral Prices."

August 4th, 2022, 4:59 pm

But also ultimately equivalent to working in library stacks, returning books to their proper places. Which really shouldn't pay terribly well.

;-)
A wonderful analogy. I am jealous!

Good man!
 
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Gamal
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Re: "Option Pricing, Risk Premium, and Arbitrage: An Argument for Volatility-Modified Risk-Neutral Prices."

August 4th, 2022, 7:04 pm

To my thinking, µ>r should not happen; this would imply (per the model) that a stock investment will almost surely (in the technical meaning of that phrase) be more profitable than a riskless investment, if you just wait long enough.
Right. If µ < r, then the stock investment is more risky and less profitable  than the riskless investment, hence it is dominated according to the two-dimensional Markowitz criterion. This investment has no sense.
 
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Marsden
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Re: "Option Pricing, Risk Premium, and Arbitrage: An Argument for Volatility-Modified Risk-Neutral Prices."

August 4th, 2022, 7:58 pm

Right. If µ < r, then the stock investment is more risky and less profitable  than the riskless investment, hence it is dominated according to the two-dimensional Markowitz criterion. This investment has no sense.
And if µ+½σ²>r?

Is it "mean-variance efficiency" we demand, or "median-variance efficiency?"
 
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Marsden
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Re: "Option Pricing, Risk Premium, and Arbitrage: An Argument for Volatility-Modified Risk-Neutral Prices."

August 4th, 2022, 8:05 pm

But also ultimately equivalent to working in library stacks, returning books to their proper places. Which really shouldn't pay terribly well.

;-)
A wonderful analogy. I am jealous!

Good man!
Having done stints in the stacks in college, it's good, relaxing, unchallenging work. Engages little enough of the brain that more important matters can be addressed ... which in college was of course mainly sexual fantasies.

Didn't pay terribly well.
 
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Gamal
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Re: "Option Pricing, Risk Premium, and Arbitrage: An Argument for Volatility-Modified Risk-Neutral Prices."

August 4th, 2022, 9:05 pm

Right. If µ < r, then the stock investment is more risky and less profitable  than the riskless investment, hence it is dominated according to the two-dimensional Markowitz criterion. This investment has no sense.
And if µ+½σ²>r?

Is it "mean-variance efficiency" we demand, or "median-variance efficiency?"
What do you think about finishing the previous subject before passing to this one? 

So once again: what if  µ > r what is the usual situation according to Markowitz?
 
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Marsden
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Re: "Option Pricing, Risk Premium, and Arbitrage: An Argument for Volatility-Modified Risk-Neutral Prices."

August 5th, 2022, 12:21 am

My response is that µ > r is not relevant to two-dimensional Markowitz criterion.
 
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Marsden
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Re: "Option Pricing, Risk Premium, and Arbitrage: An Argument for Volatility-Modified Risk-Neutral Prices."

August 5th, 2022, 1:11 am

I read your last comment incorrectly, and responded incorrectly.

I would say that µ < r is not relevant to two-dimensional Markowitz criterion, which is not what you asked.

If µ > r, buy the stock all day long, at least within the parameters of the model.
 
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Gamal
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Re: "Option Pricing, Risk Premium, and Arbitrage: An Argument for Volatility-Modified Risk-Neutral Prices."

August 5th, 2022, 8:41 am

If µ > r, buy the stock all day long, at least within the parameters of the model.
The question was about your research and not trading in general. So once again: what if µ > r?
 
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Marsden
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Re: "Option Pricing, Risk Premium, and Arbitrage: An Argument for Volatility-Modified Risk-Neutral Prices."

August 5th, 2022, 11:50 am

Then there are all manner of trading strategies that are almost surely profitable beyond the riskless interest rate, with some combination of "over time" and "into the tails."
 
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Marsden
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Re: "Option Pricing, Risk Premium, and Arbitrage: An Argument for Volatility-Modified Risk-Neutral Prices."

August 6th, 2022, 12:34 pm

An abbreviated version of the same statement, mostly in formulas:

If μ > r, then for any {ε > 0, ζ > 0} there exists a put option Pt(S,X,T) such that Pr{PT(S,X,T) > 0} < ε and E{PT(S,X,T)} < ζ and P0(S,X,T) > e-rTE{PT(S,X,T)}.

(This within Black-Scholes assumptions.)