It seems to me that the proposed cameras are primarily to protect the cab driver against physical/verbal abuse (possibly racial abuse*), and false accusations from the passengers. It seems unlikely that there is much call to protect passengers from the drivers. London black cab drivers need to invest a massive amount of time and effort to get their licenses, and also need to pass a test on their conduct/demeanor as well as the knowledge. I imagine it's there's something similar in Oxford, and save for the odd demented rogue, they're not going to give up their license lightly by committing crimes against their passengers. Certainly, I've never had a hint of a problem from Oxford cab drivers.
*N.B. In my experience, the majority of black cab drivers in Oxford are from the Asian communities.
Of course, the whole proposition is non-falsifiable unless someone can come up with a testable definition of what "x 'is' mathematics/y 'is not' mathematics" actually means.
IMHO, quicksort is mathematics, whereas slide-to-unlock is not. So the border lies somewhere in between. But again IMHO neither of these should be patentable, even if there may be some justifiable software patents. So if the patent office agrees with my examples of which software aspects count as mathematics, then the "mathematics is not patentable" principle is not enough to prevent some inappropriate software patents.
Totally agree. There's a qualitative difference between hardware, indeed any physical product, and software. Namely, the economics of reproducing the product are different: The marginal cost to reproduce software is indistinguishable from zero, but the marginal cost to reproduce a physical product is at least as much as the cost of the raw materials.
Once the development costs are mostly sunk (likely by the time you are at patent-granting stage), a software developer has all they need to produce unlimited copies at effectively zero cost, and a software patent grants them this right exclusively for a limited time. On the other hand, for a physical product, even after the development costs are sunk, the manufacturer still has to play off the costs of production against the revenues.
Based on this, it certainly seems to me that a patent would distort the "natural" supply/demand-led price discovery when it pertains to a software product much more than when it pertains to a physical product. And no, I'm not a dyed-in-the-wool free-marketeer, it's just to point out how the pure economics mean this analogy with patents on physical products is certainly fallacious.
I don't think anyone seriously uses BS as a direct pricing model these days. The way I think of it is as a means for converting option prices into the more intuitive vol space in which it's easier to compare across different strikes, expiries etc., and can be the basis of a more sophisticated model which incorporates the smile.
In this sense it's similar to say, converting bond prices into yields: it's hard to compare bond prices directly but comparing yields one can get a feel for rich/cheapness. Yet there remains an inconsistency in using different yields for bonds from the same issuer but of differing maturity, since it means using different constant reinvestment rates along the curve.
You're right that models which only fit to one point on the smile (typically the ATM vol) have an inbuilt inconsistency, but smarter models try to incorporate information encoded in the whole smile. Witness local vol models or the CMS replication using the swaption smile.
There seems to be general confusion between general economic modelling and quantitative models for pricing derivatives etc. This is not least helped by the TFA which also seems to confuse the two. Quant pricing models are not predictive models, they are tools for pricing and risk-managing derivatives. As some famous quant once put it, all pricing models are just fancy interpolation schemes.
A pricing model starts from the position that you can't predict the future with certainty. Instead, the idea of the model is to describe the joint probability distribution of the relevant variables underlying the derivative. These are things like short-term interest rates, stock prices etc., and generally not macro variables like GDP or jobless rates.
The probability distribution produced by the model doesn't even have to match the real world probabilities of the events, it just has to match the probabilities which are implied by the market prices of instruments which can be used to hedge the relevant risks, the so-called "risk-neutral" distribution and its variants. Given enough reference prices, a complete picture of the risk-neutral distribution can be built up. The issue of calibration comes in because in practice, there aren't enough reference prices to build up the complete picture so you have to start making assumptions, i.e. specifying functional a form with some free parameters, and fitting those parameters to what you can observe. But this is still not about prediction, it's about getting a full description of "what the market thinks now about all possible futures".
Not crazy in the slightest. As you've pointed out, the market prices of options are known and Black-Scholes implied volatility is just a transformation of the price using a standard formula.
Any custom option pricing model will output prices as a function of its parameters, those prices can in turn be transformed into Black-Scholes implied volatilities, so we can think of the BS implied volatilities as outputs of the model. Then adjusting the custom model's parameters to fit market prices (which is necessary to avoid introducing arbitrage into the model) is the same thing as fitting the modelled BS implied volatilities to the market.
Of course, one or more of the custom model's parameters may be labelled "volatility" but that doesn't mean it should be confused or equated with Black-Scholes implied volatility. That would be crazy.
In the KJV, the biblical "value" of 3 for pi is clearly indicated to be an approximation:
Also he made a molten sea of ten cubits from brim to brim, round in compass, and five cubits the height thereof; and a line of thirty cubits did compass it round about.
Is there a "Moore's Law" for the calculation of PI digits?
Yes.
Doing a quick calculation using this data, I'd say that, very roughly, the precision (number of decimal digits calculated) has doubled about once every two years since the start of the computer age.
There are various (infinite) formulas for computing pi to any given precision. You just have to be patient enough to compute to as many digits as you need.
So advances in computing pi boil down to one or more of the following:
1. Finding a better formula or algorithm
2. Finding a better implementation of a particular algorithm
3. Throwing more resources (computing power x time) at the problem
As far as I can tell, it's just a case of the latter in this particular instance, which isn't that exciting.
I calculated on October 10 2010 started, and a calculation stopped by the trouble of the hard disk many times,
I made completion (including verify calculation) on October 16. It was about 191 days at real calculation time.
I'm no longer a VM customer (not available in my part of Scotland for reasons unrelated to rodents), but you'd think, given that a lot of their recent marketing campaigns have focused on superior realised speeds, that good speed would be one of their USPs.
TFA says it affected "the Kirkcaldy, Glenrothes and Leven areas" which I'd guess covers about half of the urban population of Fife (Dunfermline being the only other town of any notable size). Virgin Media's also got a decent market share (22% nationally according to Wikipedia) This is not the most populous are of the UK by any means but certainly way over 100 people were affected and I could easily believe that multiple thousands of people were cut off.
OT but Princess Elizabeth was never heir apparent. As with all female heirs to the British throne, she was heir presumptive, as in theory she could have moved down the order of succession if a younger brother had come along. Notwithstanding that this would have been unlikely given her mother's age (52 at the time of QE2's succession).
In my A-Level in electronics we had to learn to program in machine code. Rather than teach us a real instruction set they made one up so as not to 'give unfair advantage to a student who might know an existing instruction set'... what crap.
Crap indeed. Why should knowledge gained off the course constitute an unfair advantage? Imagine applying that principle in other subjects.
I took A-level Music. Does the fact that I'd studied piano for ten years mean I had an unfair advantage? As part of the course we studied Mahler's first symphony. Does the fact that I already knew this symphony mean I had an unfair advantage? The performance directions in the score for this symphony are in German. Does the fact that I speak German mean I had an unfair advantage? If yes, then wouldn't it only be fair to translate the performance directions into an imaginary pseudo-language?
The exam should test your knowledge of the field, not your ability to learn the field as taught in this particular curriculum!
Perhaps a physicist can explain this to me, because there's something I've never quite understood about the "arrow of time" mystery. It's the claim that all the fundamental interactions of nature are time-symmetric (at least all the fundamental interactions that are believed to matter to the human scale).
But what about gravity? That's a fundamental interaction, and in the Newtonian model at least, gravity is always an attractive force, with respect to increasing time. Play the tape backwards and gravity turns into a repulsive force. That seems to be a time-orientation to me, so what am I missing here? Is it something particular to relativistic gravity (which I'm not familiar enough with)?
I am not a physicist (obviously), but I am a mathematician, so I don't mind if the explanation comes with some equations.
I'll get you started. Yes, whoosh, I know.
There's really nothing wrong with the phrase "could care less". Yes, if you deconstruct it, it describes an unremarkable situation, but the same can be said of many English expressions, e.g. "head over heels" or "cheap at half the price". Nonetheless these are all established phrases in the language with commonly understood meanings, without requiring deconstruction. Language usage is based on "common understanding", not prescriptionism or a logical gold-standard.
Pfft Newton: A 15th century theologian who claimed that Jesus was sent to Earth to "operate the levers of gravity", stuck pins in his eyes to figure out the "nature of light", wrote close to million words on the numerology of 666, and snorted mercury fumes on the weekends.
Utter rubbish. Newton lived in the 17th & 18th Centuries.
Slashdot Mirror
It seems to me that the proposed cameras are primarily to protect the cab driver against physical/verbal abuse (possibly racial abuse*), and false accusations from the passengers. It seems unlikely that there is much call to protect passengers from the drivers. London black cab drivers need to invest a massive amount of time and effort to get their licenses, and also need to pass a test on their conduct/demeanor as well as the knowledge. I imagine it's there's something similar in Oxford, and save for the odd demented rogue, they're not going to give up their license lightly by committing crimes against their passengers. Certainly, I've never had a hint of a problem from Oxford cab drivers.
*N.B. In my experience, the majority of black cab drivers in Oxford are from the Asian communities.
Of course, the whole proposition is non-falsifiable unless someone can come up with a testable definition of what "x 'is' mathematics/y 'is not' mathematics" actually means.
IMHO, quicksort is mathematics, whereas slide-to-unlock is not. So the border lies somewhere in between. But again IMHO neither of these should be patentable, even if there may be some justifiable software patents. So if the patent office agrees with my examples of which software aspects count as mathematics, then the "mathematics is not patentable" principle is not enough to prevent some inappropriate software patents.
Totally agree. There's a qualitative difference between hardware, indeed any physical product, and software. Namely, the economics of reproducing the product are different: The marginal cost to reproduce software is indistinguishable from zero, but the marginal cost to reproduce a physical product is at least as much as the cost of the raw materials.
Once the development costs are mostly sunk (likely by the time you are at patent-granting stage), a software developer has all they need to produce unlimited copies at effectively zero cost, and a software patent grants them this right exclusively for a limited time. On the other hand, for a physical product, even after the development costs are sunk, the manufacturer still has to play off the costs of production against the revenues.
Based on this, it certainly seems to me that a patent would distort the "natural" supply/demand-led price discovery when it pertains to a software product much more than when it pertains to a physical product. And no, I'm not a dyed-in-the-wool free-marketeer, it's just to point out how the pure economics mean this analogy with patents on physical products is certainly fallacious.
I don't think anyone seriously uses BS as a direct pricing model these days. The way I think of it is as a means for converting option prices into the more intuitive vol space in which it's easier to compare across different strikes, expiries etc., and can be the basis of a more sophisticated model which incorporates the smile.
In this sense it's similar to say, converting bond prices into yields: it's hard to compare bond prices directly but comparing yields one can get a feel for rich/cheapness. Yet there remains an inconsistency in using different yields for bonds from the same issuer but of differing maturity, since it means using different constant reinvestment rates along the curve.
You're right that models which only fit to one point on the smile (typically the ATM vol) have an inbuilt inconsistency, but smarter models try to incorporate information encoded in the whole smile. Witness local vol models or the CMS replication using the swaption smile.
There seems to be general confusion between general economic modelling and quantitative models for pricing derivatives etc. This is not least helped by the TFA which also seems to confuse the two. Quant pricing models are not predictive models, they are tools for pricing and risk-managing derivatives. As some famous quant once put it, all pricing models are just fancy interpolation schemes.
A pricing model starts from the position that you can't predict the future with certainty. Instead, the idea of the model is to describe the joint probability distribution of the relevant variables underlying the derivative. These are things like short-term interest rates, stock prices etc., and generally not macro variables like GDP or jobless rates.
The probability distribution produced by the model doesn't even have to match the real world probabilities of the events, it just has to match the probabilities which are implied by the market prices of instruments which can be used to hedge the relevant risks, the so-called "risk-neutral" distribution and its variants. Given enough reference prices, a complete picture of the risk-neutral distribution can be built up. The issue of calibration comes in because in practice, there aren't enough reference prices to build up the complete picture so you have to start making assumptions, i.e. specifying functional a form with some free parameters, and fitting those parameters to what you can observe. But this is still not about prediction, it's about getting a full description of "what the market thinks now about all possible futures".
Not crazy in the slightest. As you've pointed out, the market prices of options are known and Black-Scholes implied volatility is just a transformation of the price using a standard formula.
Any custom option pricing model will output prices as a function of its parameters, those prices can in turn be transformed into Black-Scholes implied volatilities, so we can think of the BS implied volatilities as outputs of the model. Then adjusting the custom model's parameters to fit market prices (which is necessary to avoid introducing arbitrage into the model) is the same thing as fitting the modelled BS implied volatilities to the market.
Of course, one or more of the custom model's parameters may be labelled "volatility" but that doesn't mean it should be confused or equated with Black-Scholes implied volatility. That would be crazy.
obvious attempt at jury disqualification is obvious.
Tautolgical statement is tautological
Whoosh
2 Chronicles 4:2
In the KJV, the biblical "value" of 3 for pi is clearly indicated to be an approximation:
Also he made a molten sea of ten cubits from brim to brim, round in compass, and five cubits the height thereof; and a line of thirty cubits did compass it round about.
(Emphasis added)
Is there a "Moore's Law" for the calculation of PI digits?
Yes.
Doing a quick calculation using this data, I'd say that, very roughly, the precision (number of decimal digits calculated) has doubled about once every two years since the start of the computer age.
There are various (infinite) formulas for computing pi to any given precision. You just have to be patient enough to compute to as many digits as you need.
So advances in computing pi boil down to one or more of the following:
1. Finding a better formula or algorithm
2. Finding a better implementation of a particular algorithm
3. Throwing more resources (computing power x time) at the problem
As far as I can tell, it's just a case of the latter in this particular instance, which isn't that exciting.
I calculated on October 10 2010 started, and a calculation stopped by the trouble of the hard disk many times, I made completion (including verify calculation) on October 16. It was about 191 days at real calculation time.
Somebody set up us the bomb!
I'm no longer a VM customer (not available in my part of Scotland for reasons unrelated to rodents), but you'd think, given that a lot of their recent marketing campaigns have focused on superior realised speeds, that good speed would be one of their USPs.
TFA says it affected "the Kirkcaldy, Glenrothes and Leven areas" which I'd guess covers about half of the urban population of Fife (Dunfermline being the only other town of any notable size). Virgin Media's also got a decent market share (22% nationally according to Wikipedia) This is not the most populous are of the UK by any means but certainly way over 100 people were affected and I could easily believe that multiple thousands of people were cut off.
OT but Princess Elizabeth was never heir apparent. As with all female heirs to the British throne, she was heir presumptive, as in theory she could have moved down the order of succession if a younger brother had come along. Notwithstanding that this would have been unlikely given her mother's age (52 at the time of QE2's succession).
Isn't male-preference primogeniture wonderful?
In my A-Level in electronics we had to learn to program in machine code. Rather than teach us a real instruction set they made one up so as not to 'give unfair advantage to a student who might know an existing instruction set'... what crap.
Crap indeed. Why should knowledge gained off the course constitute an unfair advantage? Imagine applying that principle in other subjects.
I took A-level Music. Does the fact that I'd studied piano for ten years mean I had an unfair advantage? As part of the course we studied Mahler's first symphony. Does the fact that I already knew this symphony mean I had an unfair advantage? The performance directions in the score for this symphony are in German. Does the fact that I speak German mean I had an unfair advantage? If yes, then wouldn't it only be fair to translate the performance directions into an imaginary pseudo-language?
The exam should test your knowledge of the field, not your ability to learn the field as taught in this particular curriculum!
Perhaps a physicist can explain this to me, because there's something I've never quite understood about the "arrow of time" mystery. It's the claim that all the fundamental interactions of nature are time-symmetric (at least all the fundamental interactions that are believed to matter to the human scale).
But what about gravity? That's a fundamental interaction, and in the Newtonian model at least, gravity is always an attractive force, with respect to increasing time. Play the tape backwards and gravity turns into a repulsive force. That seems to be a time-orientation to me, so what am I missing here? Is it something particular to relativistic gravity (which I'm not familiar enough with)?
I am not a physicist (obviously), but I am a mathematician, so I don't mind if the explanation comes with some equations.
I'll get you started. Yes, whoosh, I know. There's really nothing wrong with the phrase "could care less". Yes, if you deconstruct it, it describes an unremarkable situation, but the same can be said of many English expressions, e.g. "head over heels" or "cheap at half the price". Nonetheless these are all established phrases in the language with commonly understood meanings, without requiring deconstruction. Language usage is based on "common understanding", not prescriptionism or a logical gold-standard.
Except that science only requires observation as a postulate and no other 'leaps of faith'.
Not really. How about:
All of which are (quite reasonably) taken for granted in the exercise of natural science.
Pfft Newton: A 15th century theologian who claimed that Jesus was sent to Earth to "operate the levers of gravity", stuck pins in his eyes to figure out the "nature of light", wrote close to million words on the numerology of 666, and snorted mercury fumes on the weekends.
Utter rubbish. Newton lived in the 17th & 18th Centuries.