Forums > Basics > Stupid Q about Pricing Models

 Page 1 of 1
Display using:
 rp6 Total Posts: 14 Joined: Jun 2012
 Posted: 2012-06-16 23:08 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?
 dgn2 Total Posts: 1906 Joined: May 2004
 Posted: 2012-06-17 03:48 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
 rp6 Total Posts: 14 Joined: Jun 2012
 Posted: 2012-06-17 18:21 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.
 dgn2 Total Posts: 1906 Joined: May 2004
 Posted: 2012-06-17 19:32 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
 rp6 Total Posts: 14 Joined: Jun 2012
 Posted: 2012-07-06 12:53 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
 granchio Total Posts: 1415 Joined: Apr 2004
 Posted: 2012-07-06 16:14 <<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. >>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?<<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?>>I don't think you need r at all in this case "Deserve got nothing to do with it" - Clint
 gc Total Posts: 44 Joined: Jul 2004