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Steilermeier
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Optimal Hedging with Transaction Costs

October 7th, 2015, 12:36 pm

Hi guys,what do you guys use in practice to determine whether to hedge or not? Time? Price? Delta? Do you have a corridor? Do you look at some quantitative measure?I have read a bit in the literature but haven't found anything yet to put to practice. Any tips?CheersSteilermeier
 
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mtsm
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Optimal Hedging with Transaction Costs

October 7th, 2015, 2:52 pm

This is an invitation to my usual rant, which is to say that most of the work out there considers a single option pricing problem in some silly idealized model, so that doesn't even come close to the real problem. Of course, the excuse is that not everybody able to address the problem quantitatively has access to or is involved with a legacy options book with 10,000 positions, etc... It's the curve of finance, as opposed to science or engineering, in finance as a quant you do not necessarily have an easy access to experimental data (ie traders). I don't think it is possible to answer that question in general terms. It depends on a lot of things. Buy- or sell-side? Asset class? Book type? And so on. Typically you have some risk limits, so if you blow these out and want to come to work tomorrow, you hedge back to within the limit. Then it's all about views. If your book has a direction you like and you think the market is going into the right direction, then keep it. Otherwise for gamma, you could hedge on breaking even day to day. That would be a conservative strategy for a junior trader who wants to come to work tomorrow. Anyway, it's such a vague topic. What you are really asking is "how do I make f***ing money?"
 
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Steilermeier
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Optimal Hedging with Transaction Costs

October 7th, 2015, 3:29 pm

Hi mtsm,it is for prop trading on gas standard options, as well as swings and storages. For the two latter the problem becomes even more complex because these are path-dependent options, so I would like to understand the process first for standard options.I want to benchmark historical decisions to a rule based hedging strategy with transaction costs in order to backtest whether gut or rules are better.Does that make it less vague enough?CheersSteilermeier
 
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mtsm
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Optimal Hedging with Transaction Costs

October 7th, 2015, 4:18 pm

It sure does and I am totally incompetent to say anything more here. I could only make some general remarks.
 
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DavidJN
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Optimal Hedging with Transaction Costs

October 7th, 2015, 7:18 pm

Gut feel conditioned by experience has proven pretty useful over the years. Try to find that in a book!
 
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Steilermeier
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Optimal Hedging with Transaction Costs

October 8th, 2015, 7:17 am

So gut feel is assumed to easily beat some quantitative strategy? But still I would like to prove that. Isn't there any standard algorithm I could let race against the gut?One other idea would be to just try some rule based strategies in a backtesting and identify some worthwhile schemes to look at. The best can then compete against the gut.
 
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crmorcom
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Optimal Hedging with Transaction Costs

October 8th, 2015, 1:24 pm

It is definitely worth trying rules-based hedges in backtests, though you will need tick-data if you're going to look at intraday problems, which complicates things a bit, particularly for swing and storage instruments. For exotics, you have to model the instrument price-change, and that means you've rather cooked your results: you need to treat any conclusions with extreme care.Even given that, there also are not very many clean, prescriptive answers. What you will get is a trade-off between (somewhat model dependent) variance reduction and a cost. You need to think quite hard about how much a given portfolio variance reduction is worth to you, in addition to whether you believe in it or not.When you actually do careful hedge strategy back-testing, for delta-hedging at least, you tend to find that excessive fussiness beyond keeping your delta within sensible limits is not worth it: you will burn too much in transaction costs, your deltas are model-dependent anyway, and it won't affect your main risks significantly if you have decent amounts of vega or e.g. storage/listed option basis risk. But you should definitely do this for yourself: you will learn quite a lot from the exercise.
 
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Traden4Alpha
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Optimal Hedging with Transaction Costs

October 8th, 2015, 2:21 pm

Hedging under transactions costs seems like a recursive options problem. A hedge is like an option protecting against certain price movement scenarios and the transaction cost is the premium for that option. However, unlike a standard option in which most of the price of the option (except for deep OTM options) is derived from market expectations on the underlying, the price of the hedge (the transaction costs) arise from fixed costs plus some variable costs linked to liquidity (which, itself, is tied to optionality to the extent that an illiquid market obligates the transacting party to hold their position and a liquid market gives transaction parties the right to unwind their trade in the future).
 
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Engy
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Optimal Hedging with Transaction Costs

October 9th, 2015, 9:20 am

QuoteOriginally posted by: SteilermeierSo gut feel is assumed to easily beat some quantitative strategy? But still I would like to prove that. Isn't there any standard algorithm I could let race against the gut?One other idea would be to just try some rule based strategies in a backtesting and identify some worthwhile schemes to look at. The best can then compete against the gut.You can find some rule based strategies to compute the optimal delta with respect to the volatility of P&L and transaction costs here: When You Hedge Discretely: Optimization of Sharpe Ratio for Delta-Hedging Strategy under Discrete Hedging and Transaction Costs
 
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crmorcom
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Optimal Hedging with Transaction Costs

October 9th, 2015, 1:15 pm

This is a fairly useful exercise, but is still simulated. Worth also looking at actual backtests - particularly because it looks like this paper has fixed vols and no vega effects, which are rather important.You'll notice that, if you cast a quick eye over the time-based hedging tables at the end, that once a day is not far from optimal for all the models and, within a range of hedging frequencies near optimal, most of the time you don't make a huge difference to your SR.
 
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Engy
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Optimal Hedging with Transaction Costs

October 10th, 2015, 6:50 am

QuoteOriginally posted by: crmorcomThis is a fairly useful exercise, but is still simulated. Worth also looking at actual backtests - particularly because it looks like this paper has fixed vols and no vega effects, which are rather important.The paper provides analytical (approximate) formulas for the expected P&L, transaction costs, and P&L volatility for the log-normal price dynamics which may include jumps and stochastic volatility. The hedging can be deterministic at fixed time steps or range based with triggers from either changes in price or delta. Monte-Carlo simulations are only applied to verify these approximate formulas and show that these formulas are indeed accurate. An assumption is made that the option is delta-hedged to maturity so that the vega, while important for day-to-day P&L, has no impact on the terminal P&L from the delta-hedge.QuoteOriginally posted by: crmorcomYou'll notice that, if you cast a quick eye over the time-based hedging tables at the end, that once a day is not far from optimal for all the models and, within a range of hedging frequencies near optimal, most of the time you don't make a huge difference to your SR.If you look at Figures 1 and 2 in the paper above, you can see that the Sharpe ratio of the delta-hedging strategy has a humped shape as a function of the hedging frequency. On the one hand, when you hedge infrequently, you save in transaction costs but the P&L volatility will be high. On the other hand, when you hedge frequently, your P&L volatility will be small (still when jumps or stochastic volatility present you cannot hedge all the risk by the delta-hedging) but transaction costs will be prohibitive. The analytical results in the paper help to find the optimal hedging frequency to trade-off between transcation costs and the P&L volatiliy and, as a result, to maximize the Sharpe ratio.If you look at the Figure 7 for the Sharpe ratio under the simple log-normal model, you can see that the range for the Sharpe ratio is from 1.5 to -1.0 as a function of the hedging frequency. There IS a huge difference to the Sharpe ratio coming from the choice of the hedging frequency.
Last edited by Engy on October 9th, 2015, 10:00 pm, edited 1 time in total.
 
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crmorcom
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Optimal Hedging with Transaction Costs

October 10th, 2015, 3:13 pm

Thank you, Engy, I did read the paper.Most of us don't have the luxury of only being judged on terminal PL; all too often, vega effects are terminal in quite another sense. By all means, do have this conversation with your boss and you risk-manager next time you have a large drawdown :)Yes, there is a huge difference in PL from the hedging frequency - if you read my comment carefully, you'd realise that I didn't claim otherwise. But, because the response curve is indeed hump-shaped that means that, near the optimum, it is quite flat. As a consequence, once you include model mis-specification and vega effects, it's very hard to conclude that hedging, say, once a day is worse than, say, hedging every other day or twice a day.
 
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Engy
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Optimal Hedging with Transaction Costs

October 11th, 2015, 11:23 am

Thank you for your feedback, crmorcom There are two main sources of risk-taking in the volatility:1) The flow in structured products. Profit margins in these products must include some premium to hedge first-order risks, including delta and vega risks. The risk limits may be tight here and the hedge rebalancing takes place at least at the end of day. There is still some discretion on how to adjust the delta, how frequently to hedge intra-day, etc. 2) Proprietary view on the volatility dynamics coming from either systematic strategies or discretionary views. The questions here are the following: 1) given a certain spread between expected realized vol and current implied vol, say of 2%, what is the expected P&L that can be generated at the option maturity by delta-hedging with transaction costs, 2) what is the volatility of this P&L, 3) how to optimize the Sharpe ratio for the delta-hedging strategy.The results in the paper provide a quantitative insight and answer to these questions. Finally, there is a big difference in the realized Sharpe ratio when, say, one year option is delta-hedged daily, by-daily, every week etc.