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Yesterday, 7:44 pm
Forum: Book And Research Paper Forum
Topic: "Option Pricing, Risk Premium, and Arbitrage: An Argument for Volatility-Modified Risk-Neutral Prices."
Replies: 51
Views: 4883

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

My abbreviated version of my "over time" and "into the tails" comment omits the "over time" part, in case that wasn't clear.
Yesterday, 12:44 pm
Forum: Book And Research Paper Forum
Topic: "Option Pricing, Risk Premium, and Arbitrage: An Argument for Volatility-Modified Risk-Neutral Prices."
Replies: 51
Views: 4883

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

Tightened up:

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 P0(S,X,T).
August 6th, 2022, 12:34 pm
Forum: Book And Research Paper Forum
Topic: "Option Pricing, Risk Premium, and Arbitrage: An Argument for Volatility-Modified Risk-Neutral Prices."
Replies: 51
Views: 4883

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

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.)
August 5th, 2022, 11:50 am
Forum: Book And Research Paper Forum
Topic: "Option Pricing, Risk Premium, and Arbitrage: An Argument for Volatility-Modified Risk-Neutral Prices."
Replies: 51
Views: 4883

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

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."
August 5th, 2022, 1:11 am
Forum: Book And Research Paper Forum
Topic: "Option Pricing, Risk Premium, and Arbitrage: An Argument for Volatility-Modified Risk-Neutral Prices."
Replies: 51
Views: 4883

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

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.
August 5th, 2022, 12:21 am
Forum: Book And Research Paper Forum
Topic: "Option Pricing, Risk Premium, and Arbitrage: An Argument for Volatility-Modified Risk-Neutral Prices."
Replies: 51
Views: 4883

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

My response is that µ > r is not relevant to two-dimensional Markowitz criterion.
August 4th, 2022, 8:05 pm
Forum: Book And Research Paper Forum
Topic: "Option Pricing, Risk Premium, and Arbitrage: An Argument for Volatility-Modified Risk-Neutral Prices."
Replies: 51
Views: 4883

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

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...
August 4th, 2022, 7:58 pm
Forum: Book And Research Paper Forum
Topic: "Option Pricing, Risk Premium, and Arbitrage: An Argument for Volatility-Modified Risk-Neutral Prices."
Replies: 51
Views: 4883

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

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 "med...
August 4th, 2022, 4:56 pm
Forum: Book And Research Paper Forum
Topic: "Option Pricing, Risk Premium, and Arbitrage: An Argument for Volatility-Modified Risk-Neutral Prices."
Replies: 51
Views: 4883

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

To be clear,  µ in this context is the drift of the normal distribution that the log normal 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 sto...
August 4th, 2022, 1:56 pm
Forum: Book And Research Paper Forum
Topic: "Option Pricing, Risk Premium, and Arbitrage: An Argument for Volatility-Modified Risk-Neutral Prices."
Replies: 51
Views: 4883

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

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 t...
August 2nd, 2022, 11:51 am
Forum: Off Topic
Topic: Stupid question of the day
Replies: 2747
Views: 246918

### Re: Stupid question of the day

Maybe you read too much into things and think too little.
August 1st, 2022, 5:48 pm
Forum: Off Topic
Topic: Stupid question of the day
Replies: 2747
Views: 246918

### Re: Stupid question of the day

Are all (mostly left-leaning) supporters of Putin Special Ops closet Trotskyites? ? Maybe it's different in Europe, but in America the only people who support Putin, from all I have seen, are Trumpists. I don't know if there's anything more to it than that their Dear Leader got along with him, and ...
July 31st, 2022, 4:26 pm
Forum: Off Topic
Topic: Stupid question of the day
Replies: 2747
Views: 246918

### Re: Stupid question of the day

Pickleball. Why?
So old, out-of-shape people can get a little exercise.
July 31st, 2022, 4:24 pm
Forum: Politics Forum
Topic: Trump -- the last 100 days
Replies: 4515
Views: 347034

### Re: Trump -- the last 100 days

This one, I think, is a slam dunk based on the former President's pressuring of the Department of Justice to send letters to various state legislatures and governors claiming (falsely) that it has identified massive election fraud, and suggesting that legislatures be convened to replace the legitima...
July 21st, 2022, 10:17 am
Forum: Politics Forum
Topic: What is Borisism?
Replies: 360
Views: 52227

### Re: What is Borisism?

"Conservatism consists of exactly one proposition, to wit: There must be in-groups whom the law protects but does not bind, alongside out-groups whom the law binds but does not protect." -- Frank Wilhoit, musical composer