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helix
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Joined: May 23rd, 2005, 3:07 pm

Transaction Costs

November 25th, 2008, 8:57 pm

Does anyone know any tricks for accounting for transaction costs in option pricing (vanillas, equity underlying)?
 
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crmorcom
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Transaction Costs

November 25th, 2008, 9:41 pm

The earliest reference is Leland (1985), "Option pricing and replication with transaction costs". Beyond a case that simple, you will often have to do simulation, as things tend to get messy pretty fast.
 
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Paul
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Joined: July 20th, 2001, 3:28 pm

Transaction Costs

November 26th, 2008, 11:23 am

See PWOQF2, of course! Yes, you can do simulations of various hedging strategies. But how do you know which hedging strategies are best?!P
 
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helix
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Transaction Costs

November 26th, 2008, 3:48 pm

I'm familiar with Leland and its limitations. In practice a trader is unlikely to run an optimal strategy, or religiously follow the optimal strategy that is produced from a model. So the question then becomes, what is the safest way to adjust pricing for transaction costs in a conservative manner (assuming the trader hedges as if there were no transaction costs)? A simple rule-of-thumb might be to use the Leland vol adjustment, with an additional factor of safety... (but how big?).Does anyone know what the hedging P&L distribution looks like when you add transaction costs (is it still Chi-Squared)?
 
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crmorcom
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Transaction Costs

November 26th, 2008, 4:03 pm

In practice, you don't want to go much further than Leland in closed-form or something similarly simple. Otherwise, you run the risk of thinking you know more about the price process than you do, which can be extremely dangerous. Any result about an optimal hedging strategy (and so transactions costs), even if you can find one, is likely to be quite sensitive to your payoff as well as the underlying process. "Keep it simple" is best.That's why, if you know roughly how your trader is hedging, you're probably best off simulating this, as it should give you a result which is close to the actual outcome. If you can find a better hedging strategy, of course, your trader will thank you! The problem with optimal hedging strategies (with imperfect replication or transactions costs) is that they will depend on your risk-aversion as well as things like your cost of capital and margin costs. These things are brutally difficult to model so, again, simple is best.In particular, worrying about whether your PL distribution is chi-squared or not is probably a bad idea: empirically, your price process probably doesn't even have a finite (or stable) second moment. This is one of those cases where overmodeling is probably not a good idea.
 
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Paul
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Joined: July 20th, 2001, 3:28 pm

Transaction Costs

November 29th, 2008, 11:01 am

I agree with half of what crmorcom says! I agree about the over modelling, especially on this topic. Worrying about whether hedging error is chi-squared or not does matter, but precisely for the reason that crmorcom mentions: the empirical distribution is not normal (personally, I worry about this less than most people!) but the hedging error is then the square of whatever that distribution is. And that makes hedging error potentially really horribly skewed in practice, far worse than in theory. (And this I do worry about!) Again see PWOQF2 for details about this (details that are neither too basic nor over modelled!)Other points worth mentioning:1. Leland only works for options with single-signed gamma. If you have a portfolio of options then you will probably be overestimating costs if you use Leland. And since Leland is not optimal then you will be way too conservative. (I'm all in favour of being conservative but this might be going too far!)2. Some traders hedge when the stock or the delta moves by some amount. The maths of even this simple strategy is quite complicated.3. Some people care a lot about costs, some not at all. It depends on the markets they are in.P