rp6
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Ola, I am not a quant nor good at quant stuff. But here goes.
So if standard BS models use assume a normal/lognormal distribution of returns, which we know to be slightly incorrect - fatter tails etc. Then is there a model which takes the past data for an asset, defines its distribution and uses that rather than ~N in the calculation. I guess computationally that's a lot harder, but is that thinking a part of some other model, or does it not make logical sense? |
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dgn2
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It is quite simple to resample the data and compute option prices - particularly European options - via Monte Carlo. Search for 'bootstrapping' and option pricing.
One of the problems with this approach is that the pricing of options is only a small part of what makes BS useful. Sensitivities are also very important and using the actual distribution doesn't help there.
In general, it is much easier to determine the impact of different assumptions on pricing when computing prices via Monte Carlo. Expanding to fatter tails isn't difficult, but what we know about the tails is limited, so how do you choose how fat they should be (or what form they should take)? Part of what makes BS useful is that there is really only one unknown parameter (i.e., volatility). Using a distribution with fatter tails adds more unknown parameters.
You might want to look at Heston and variance gamma models. |
...WARNING: I am an optimal f'er |
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rp6
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| Total Posts: 14 |
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| Excellent, thanks for your help i will try and look into these some more. I see your point wrt the simplicity of just having to change volatility. |
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dgn2
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| There are also works where a Kernal density smoothed estimate of the historical distribution is used to compute odds and price options, so you could search in that space as well. |
...WARNING: I am an optimal f'er |
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rp6
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| Total Posts: 14 |
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If it's OK i'm going to continue to ask stupid questions about pricing models here rather than starting a new thread. All my knowledge on options comes from practical books like Natenberg/Baird and i have no background in financial mathematics so i can't understand a lot of the language to do with modelling techniques.
Any info much appreciated:
1. Day Count. In Natenberg's book he says that actual days should be used for interest calculations but only trading days for vol, since a stock can only move on those days. But then he says that the pricing model will be OK with only using one input for time to maturity. Why is this?
2. Black 76 model. For an option on a future, where both the option and the future are subject to mark-to-market futures style margin, why is the interest rate a feature of the model at all. If there is no carry cost on the future or the option, then what is the r discounting?
more to follow |
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granchio
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<<
1. Day Count. In Natenberg's book he says that actual days should be used for interest calculations but only trading days for vol, since a stock can only move on those days.
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Natemberg is not holy scriptures. Think for yourself: is it true that stock prices don't move when the market is closed? e.g. is it true that the open price tomorrow morning will be same as close tonight? is it true that open on monday is same as close on friday?
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2. Black 76 model. For an option on a future, where both the option and the future are subject to mark-to-market futures style margin, why is the interest rate a feature of the model at all. If there is no carry cost on the future or the option, then what is the r discounting?
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I don't think you need r at all in this case
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"Deserve got nothing to do with it" - Clint |
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gc
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I don't know if it is as closely related to your question as it seems to me, but by chance I am reading an old issue of the Risk Magazine (January 2001) and there is an article that seem to answer your question: "A fair value for the skew" by Emanuel Derman and Joe Zou. The synopsys is: "Both investors and dealers want to know the fair value of options in their portfolios. But outside the one-volatility-fits-all Black-Scholes model, there is no consensus on how to do this for a range of strikes and maturities. Using risk-neutralised historical distributions, ED and JZ propose a fair valuation technique that incorporates the skew".
If you don't have access to the magazine I can probably email you a scanned version (hoping that I am not going to get in trouble with copyrights.
About the question on counting business days or calendar days for volatility, as granchio hinted, it's a matter of personal choice. Some people believe that for some assets there is little or no movement when the exchange is closed hence using business days makes sense. For other assets (e.g. USD swap rates and govt bonds that are practically traded 24x6) it makes more sense to count the week-ends but a little bit less than 2 days. Since realised volatility is strictly speaking not tradable, it's a quantity that doesn't really exist, so any number that you get makes sense if you find that helps you building an intuition for what you are trading and on average helps you to make more money than you lose.
For interest calculation it's a different matter. This is specified by the contract specification so you have to take it as a definition you start from. (A bond is a tradable entity and if the specs say that the interest accrues daily, that's what you have to consider). BTW: It really depends on the contract you are trading. For example Brasilian Denominated bonds use the Brasilian Bond Basis (B/252), where by the interest accures only on working days and not on Sat/Sundays |
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rp6
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| Total Posts: 14 |
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Thanks both of you, i see your point for the day count.
On the Black model, the formula i see for the call is something like
c=e^-rT [FN(d1)-KN(d2)]
r is not in the d1 and d2 terms as it is in the BSM equation which makes sense, but why is it in that main equation? It looks like the call is discounting any possible payoff at expiration [F-K], but why if it is margined like a future? Maybe this isn't the way it is used in practice anymore.
[I don't really know what a partial differential equation is, so that might have something to do with it]. |
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I think CME futures options tend to settle like equity options, w/cash premium paid up front and no daily MtM. The Black76 formula would apply in this case. But futures options in Europe and Asia tend to settle like futures with daily MtM, so cost of carry on the option premium is 0. |
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rp6
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| Total Posts: 14 |
| Joined: Jun 2012 |
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Not about pricing models, but still a basic question:
What's the most common way to store options data in a database. For example if i have options settlements in a csv file, 1 file for each day since sep 09 gives about 730 files, i need them in a database to ultimately look at the vol surfaces. I suppose the relational model gives it more flexibility - but does that necessarily mean 1 table for every day?
1 table would give the surface for that day, but then if i want to calculate time series stuff from the underlying, or atm iv wouldn't that be harder and slower? |
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