jump model vs. BS model

[BILEL]

Hi all,

We can consider that jumps models are more performance than Black Scholes model in option pricing?

What are the cases where the use of jump model is better than BS model?

Thanks.

 

[Tsotne]

BS generally is not very good approximation for long time to expiration. There are many articles about comparisons and limitations of option pricing models you can search.

 

[BILEL]

BS generally is not very good approximation for long time to expiration. There are many articles about comparisons and limitations of option pricing models you can search.

I don't understand ... is not very good approximation for long time to expiration?
I have this article but i want a new idea to do comparison, any proposal?

 

[Tsotne]

Yes for long time to maturity there are better numerical models (nonparametric within) but BS advantage over them is its practicality and simplicity. It requires less time to compute and shoot a bet. For traders having limited time to make decisions, the still prefer BS regardless of existence of some other models better approximating option price but requiring huge time to analyze.

 

[enthusiast]

Yes for long time to maturity there are better numerical models (nonparametric within) but BS advantage over them is its practicality and simplicity. It requires less time to compute and shoot a bet. For traders having limited time to make decisions, the still prefer BS regardless of existence of some other models better approximating option price but requiring huge time to analyze.

Also consider a simple jump model using Poisson Distrution. What λ and h are u going to use. You output will be as good as your input. The more complex stochastic volatility models als have additional parameters you need to input. These better models (Stochastic VOL etc) are better if you give it the right inputs. I'd selecting the advanced model does have its advantages (and some disadvs), but the selection depends on what you are doing. If you are seeking an edge, then you may have to implement advanced models with appropriate inputs.

 

[Tsotne]

Hi all,

We can consider that jumps models are more performance than Black Scholes model in option pricing?

What are the cases where the use of jump model is better than BS model?

Thanks.

We once had a "great-war" here on this issue which you might find interesting for comparisons and alternatives for BS and nonparametric models. Search the forum...

 

[Tsotne]

I recently discovered a very good article about the BS limitations. Will post it later too (with the other promises in other threads).

 

[Tsotne]

Here it is for interested readers:

 

[financeguy]

Yes for long time to maturity there are better numerical models (nonparametric within) but BS advantage over them is its practicality and simplicity. It requires less time to compute and shoot a bet. For traders having limited time to make decisions, the still prefer BS regardless of existence of some other models better approximating option price but requiring huge time to analyze.

I've noticed that a lot of people have come to believe that options traders use Black-Scholes as their principal method of pricing, for ease of computation, simplicity, etc. I'm honestly not really sure why people think this. In 2011, no major options trading desk uses this model for pricing. I'm not here to argue with Tsotne or anything as he's just the guy who's very quickly mentioned it here (and this isn't what this thread is about, I understand) - I've found this misconception in other forums, documentaries, and books, mainly post-crisis. For example, I recently read Michael Lewis' (yes, the guy who wrote Liar's Poker) "The Big Short", in which he writes "...the model used by Wall Street to price LEAPs [read: long-dated vanilla options], the Black-Scholes option pricing model, made some strange assumptions." He then goes onto describe the assumption of normality etc. This is just the first example that comes to mind. It struck me because it was disappointing to find this quote in the middle of an otherwise educational and intuitive read (I'm not an expert on credit derivatives trading so I'm just taking Lewis' word that the rest of the book is more or less accurate). And it's also disappointing because in such an intuitive text that's so accessible to readers outside of finance, it proliferates this idea that trading desks have no fking clue what they're doing - which is an idea people these days want more than ever to believe. To be clear, I'm not saying that all trading desks have a great handle on their risks, but what I am saying is that it troubles me that people make precise statements that aren't true about how exactly trading desks misprice options. It is certainly not clear to me that long-dated options in any asset class are priced correctly, but what is clear to me is that it isn't Black-Scholes in this day and age that is responsible for the mispricing, and any discussion of Black-Scholes' flaws truly misses the point and is most likely not a meaningful discussion. Perhaps why Black-Scholes is still discussed is because every desk generally has its own way of pricing options and it's too difficult to discuss each model in a broad sense. But if we're going to get to any truth about mispricing of options, we've got to let this idea that traders use Black-Scholes go.

 

[Andy Nguyen]

I've noticed that a lot of people have come to believe that options traders use Black-Scholes as their principal method of pricing, for ease of computation, simplicity, etc. I'm honestly not really sure why people think this. In 2011, no major options trading desk uses this model for pricing.

Because none of these people have worked on a real trading desk, let alone an option desk?
Black-Scholes model is everywhere, from Hull to every other text book used in undergrad course up to MFE programs. You don't hear the guys trading options tell you their third party vendor's stuff they use. To read those stuff, you have to be up to date with trade magazines like Wall Street & Tech, etc.
I used to sit next to the option arbitrage guys and they don't even mention the stuff they have in their real time pricing engine which took up a huge GPU server. But I bet they aren't using BS on an Excel sheet like many people love to believe

 

[Tsotne]

I've noticed that a lot of people have come to believe that options traders use Black-Scholes as their principal method of pricing, for ease of computation, simplicity, etc. I'm honestly not really sure why people think this. In 2011, no major options trading desk uses this model for pricing. I'm not here to argue with Tsotne or anything as he's just the guy who's very quickly mentioned it here (and this isn't what this thread is about, I understand) - I've found this misconception in other forums, documentaries, and books, mainly post-crisis. For example, I recently read Michael Lewis' (yes, the guy who wrote Liar's Poker) "The Big Short", in which he writes "...the model used by Wall Street to price LEAPs [read: long-dated vanilla options], the Black-Scholes option pricing model, made some strange assumptions." He then goes onto describe the assumption of normality etc. This is just the first example that comes to mind. It struck me because it was disappointing to find this quote in the middle of an otherwise educational and intuitive read (I'm not an expert on credit derivatives trading so I'm just taking Lewis' word that the rest of the book is more or less accurate). And it's also disappointing because in such an intuitive text that's so accessible to readers outside of finance, it proliferates this idea that trading desks have no fking clue what they're doing - which is an idea people these days want more than ever to believe. To be clear, I'm not saying that all trading desks have a great handle on their risks, but what I am saying is that it troubles me that people make precise statements that aren't true about how exactly trading desks misprice options. It is certainly not clear to me that long-dated options in any asset class are priced correctly, but what is clear to me is that it isn't Black-Scholes in this day and age that is responsible for the mispricing, and any discussion of Black-Scholes' flaws truly misses the point and is most likely not a meaningful discussion. Perhaps why Black-Scholes is still discussed is because every desk generally has its own way of pricing options and it's too difficult to discuss each model in a broad sense. But if we're going to get to any truth about mispricing of options, we've got to let this idea that traders use Black-Scholes go.

I haven't had a practical touch with option pricing yet, but have written 2 diplom research papers on BS and have quite good theoretical understanding of the model. I don't want to argue too, but some points deserve to be noticed. First, BS model was not the first model giving an option price - what made it popular was the rationale of assumptions which at first seemed to be quite reasonable => so I have to disagree with you

the Black-Scholes option pricing model, made some strange assumptions."

Assumptions were not strange at first, and it increased the derivatives trading volume by hundreds of trillions of dollars. Yes, it's true, exactly after (1973) Black - Scholes model in 1970s and later. But then, something unexpected happened, 1987 crash revealing the dark sides of assumptions: normality assumption proved to be incorrect. Also the full martingale limit assumption where the model assumes you can construct the replicating portfolio (which may not always be correct). Then again, LTCM crisis and Russian default in 1998 harmed the robustness of the model reinforcing people's believes about the incorrectness of the model assumptions. I might agree with you when you say you see that you come across similar information in textbooks, other forums...again, I don't have touch to options but have read and know many traders have programmed BS model as a shortcut. We are talking about the usage of BS, it might be decreasing as time goes by and it should be so, it dramatically increased the importance of derivatives and can be said squeezed out itself. But as for precision and robustness, nobody argues that it is not unbeaten. (though the assumptions whether correct or not, makes sense and gives the good understanding of the option pricing idea)

 

[financeguy]

I haven't had a practical touch with option pricing yet, but have written 2 diplom research papers on BS and have quite good theoretical understanding of the model. I don't want to argue too, but some points deserve to be noticed. First, BS model was not the first model giving an option price - what made it popular was the rationale of assumptions which at first seemed to be quite reasonable => so I have to disagree with you

Assumptions were not strange at first, and it increased the derivatives trading volume by hundreds of trillions of dollars. Yes, it's true, exactly after (1973) Black - Scholes model in 1970s and later. But then, something unexpected happened, 1987 crash revealing the dark sides of assumptions: normality assumption proved to be incorrect. Also the full martingale limit assumption where the model assumes you can construct the replicating portfolio (which may not always be correct). Then again, LTCM crisis and Russian default in 1998 harmed the robustness of the model reinforcing people's believes about the incorrectness of the model assumptions. I might agree with you when you say you see that you come across similar information in textbooks, other forums...again, I don't have touch to options but have read and know many traders have programmed BS model as a shortcut. We are talking about the usage of BS, it might be decreasing as time goes by and it should be so, it dramatically increased the importance of derivatives and can be said squeezed out itself. But as for precision and robustness, nobody argues that it is not unbeaten. (though the assumptions whether correct or not, makes sense and gives the good understanding of the option pricing idea)

I think you've missed my point. First, I'm not saying that Black-Scholes wasn't a big step in the right direction at the time. I'm also not saying that the assumptions underlying Black-Scholes are ridiculous. What I am saying is that it's been almost 40 years since it came out and no major trading shop uses it for pricing an option anymore. Further I am saying that outside of trading desks, the public seems to believe that it is in fact the primary model used for pricing, and still traders continue to be criticized for using this model that they don't even really use that is so obviously flawed to manage trillions of dollars. I hope you see what I mean.

Black-Scholes was a very important stepping stone to other better, more sophisticated models. What troubles me is when you see movies like "Inside Job" and when you read books like "The Big Short", traders are made out to look like retarded monkeys as the narrator says "this is the stupid model these Wall Street traders use, and anyone can see it's wrong - so then what value do these people have", etc. Coming out of this recession, I think this is an idea people seem to want to believe - that rich traders are all morons and that their irresponsibility has been the cause of everyone's misfortunes. Now to a certain extent people may be justified in believing this, but I feel like it has gotten out of hand to the point that people really believe that options traders truly trade off the assumption that asset returns are lognormally distributed and use a model that cranks out numbers based on that, which is plain wrong.

There are a few reasons you may find Black-Scholes on a trading desk. First, it's useful to train junior traders in the logic of options theory, and as a base case to which to compare the desks' more sophisticated models. Second, in the pricing of exotic options, it's common for customers/sales/traders and brokers/traders to confirm an option's Black-Scholes theoretical value (TV) to make sure everyone is talking about the same thing. After the TV is confirmed, the trader will go and get the real price for the client or broker. Third, sometimes it's useful to examine an options skew from the Black-Scholes price. The reason for that is because some models under some circumstances can skew prices too much or too little depending on parameters, and traders can generally have a feel for what is obviously too much or too little from TV. However, when it comes to making a real price on an option, no trader today at a major sell side operation uses Black-Scholes even as a shortcut to making a price - the price is made off of a more sophisticated model used by that trading desk. Desks have put a lot of time and money into optimizing and speeding up their models so that using these models is just as fast as getting a Black-Scholes number. It's not like when you build a toy model at home and the code takes forever to run. These desks have made their models fast and accurate and Black-Scholes is no shortcut anymore.

 

[BILEL]

Here it is for interested readers:

thanks very interesting.

 

[Tsotne]

I think you've missed my point. First, I'm not saying that Black-Scholes wasn't a big step in the right direction at the time. I'm also not saying that the assumptions underlying Black-Scholes are ridiculous. What I am saying is that it's been almost 40 years since it came out and no major trading shop uses it for pricing an option anymore. Further I am saying that outside of trading desks, the public seems to believe that it is in fact the primary model used for pricing, and still traders continue to be criticized for using this model that they don't even really use that is so obviously flawed to manage trillions of dollars. I hope you see what I mean.

Black-Scholes was a very important stepping stone to other better, more sophisticated models. What troubles me is when you see movies like "Inside Job" and when you read books like "The Big Short", traders are made out to look like retarded monkeys as the narrator says "this is the stupid model these Wall Street traders use, and anyone can see it's wrong - so then what value do these people have", etc. Coming out of this recession, I think this is an idea people seem to want to believe - that rich traders are all morons and that their irresponsibility has been the cause of everyone's misfortunes. Now to a certain extent people may be justified in believing this, but I feel like it has gotten out of hand to the point that people really believe that options traders truly trade off the assumption that asset returns are lognormally distributed and use a model that cranks out numbers based on that, which is plain wrong.

There are a few reasons you may find Black-Scholes on a trading desk. First, it's useful to train junior traders in the logic of options theory, and as a base case to which to compare the desks' more sophisticated models. Second, in the pricing of exotic options, it's common for customers/sales/traders and brokers/traders to confirm an option's Black-Scholes theoretical value (TV) to make sure everyone is talking about the same thing. After the TV is confirmed, the trader will go and get the real price for the client or broker. Third, sometimes it's useful to examine an options skew from the Black-Scholes price. The reason for that is because some models under some circumstances can skew prices too much or too little depending on parameters, and traders can generally have a feel for what is obviously too much or too little from TV. However, when it comes to making a real price on an option, no trader today at a major sell side operation uses Black-Scholes even as a shortcut to making a price - the price is made off of a more sophisticated model used by that trading desk. Desks have put a lot of time and money into optimizing and speeding up their models so that using these models is just as fast as getting a Black-Scholes number. It's not like when you build a toy model at home and the code takes forever to run. These desks have made their models fast and accurate and Black-Scholes is no shortcut anymore.

Good. You are more aware of practical issues. I agree with the whole opinion. Got your point.

 

[quotes]

Well, some criticisers on jump-diffusion models simply don't calculate them at all.
It is useless when I don't have it.