Forums > Basics > Backtesting Delta Hedged Options/Volatility Strategies

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 Jurassic Total Posts: 199 Joined: Mar 2018
 Posted: 2018-04-28 00:00 I was wondering how relative value options strategies are generally backtested? There seems to be many complications that wouldnt occur with linear products. So if you wanted to do DAX IV vs CAC IV, both ATM say, (like the VIX/V2X spread in vol futures) how would you go about it? I assuming this would come from a delta hedged dac 50d option vs delta hedged cac 50d option?
 day1pnl Total Posts: 53 Joined: Jun 2017
 Posted: 2018-04-29 15:19 Say your package's net present value NPV(spot, rates, vol, time) depends on underlying, rates, vol, and time. Suppose you want to evaluate the trade's profitability by holding it over N days.1. Estimate the historical joint distribution, P, of daily changes in (spot, rates, vol, time).2. At time point j (say some specific calendar day) you have a net present value NPV(spot, rates, vol, time) for the package. Draw from P a daily change in (spot, rates, vol, time).3. Evaluate now your mark-to-market P/L by means of your greeksSpot: delta x chg spot + (1/2) gamma x (chg spot)^2Rates: rho x chg ratesVolatility: vega x chg volTime: theta x chg timeNonlinear: NPV(spot + chg, rates + chg, vol + chg, time + chg) - (spot PL) - (rates PL) - (vol PL) - (time PL) - NPV(spot, rates, vol, time)4. Recalculate your new greeks at (spot + chg, rates + chg, vol + chg, time + chg).5. Redraw from P a daily change in (spot, rates, vol, time).Repeat (2-5) N times and sum up the total MTM P/Ls. This gives you one realization of trading the package and holding for N days. If you want to subtract delta risk at some cost according to some specific method, you can just add a subroutine.The N-time-steps procedure can then be repeated 999 times or until you reach desired level of confidence.Not sure this method is too brute force, but at least is a 0th order approximation...
 day1pnl Total Posts: 53 Joined: Jun 2017
 Posted: 2018-04-29 15:40 Ok that was the pretty noobish part. I guess the tricky part is to point towards some workaround that makes sure that the vols slide down correctly in your estimated distribution of daily changes (when the old 4 motnh contracts roll into the new active contract).I suppose that the "new volatility" post-roll should be the volatility corresponding to a strike having the same daily B/E as the old contracts had prior to the roll date. But correct me if wrong
 Jurassic Total Posts: 199 Joined: Mar 2018
 Posted: 2018-04-29 17:17 @day1pnl. That just seems too complicated, I keep thinking there must be something easier.The problem is that the strike that the option had will change with time. In research you probably want to use IV with sticky delta, but you cannot execute in this space. If you use IV by sticky strike I cannot see how your research is relevant in the future. For instance risk reversals would be particularly problematic.Is this problem easier with gamma or vega strategies?
 frolloos Total Posts: 66 Joined: Dec 2007
 Posted: 2018-05-01 02:59 Can you mark the positions to model or do you have to mark it market? Reason I ask this is that if you can mark the positions to model you can delta hedge the options *to maturity* at the *constant* implied volatility you initially purchased the options for, i.e. you don't update the implied vol when revaluing the positions and your delta hedge will be based off the initial implied vols.The final p/l of this strategy is then purely the daily (initial) implied variance - realized variance of both options weighted by their respective gammas.If you do have to mark to market then you'll need to use the running implied volatility of both options and that will be more messy.
 Jurassic Total Posts: 199 Joined: Mar 2018
 Posted: 2018-05-01 11:06 Im not sure why market to model or mark to market would be more difficult to the other?To be honest Im really confused now as to how options strategies are backtested
 frolloos Total Posts: 66 Joined: Dec 2007
 Posted: 2018-05-01 12:40 forgetting the mark to model or mark to market for now, I take it you understand that delta hedging the options till maturity using the initial implied volatility gives you gamma p/l?there are numerous option strategies. I am assuming you dont mean the more static strats such as call overwriting etc.
 ronin Total Posts: 435 Joined: May 2006
 Jurassic Total Posts: 199 Joined: Mar 2018
 Posted: 2018-05-01 23:50 Ok had a think about this.The problem with backtesting using prices, that I can see, is that for a given price there can be two implied vol, which is what options are usually quoted in. This should cause problems as it will be hard to say these options would evolve into the future in the same way
 ronin Total Posts: 435 Joined: May 2006
 Posted: 2018-05-03 11:04 @Jurassic,Stop making stuff up. Try doing it instead. Start simple. Open an excel spreadsheet. Assume Black Scholes, single vol that does not change with time, strike or maturity. Download the history for the underlying from Yahoo finance. Buy or sell an option on day 1, and buy or sell some delta to make it flat. Then evolve it every day to maturity, and at every day reprice the option, calculate the delta, and adjust the delta hedge to keep delta within some limits. You should be tracking the size of the option position, size of the delta hedge, and the amount of cash.A long, long time ago, when I was a junior quant, that was an actual exercise they made me do on my second day.Once you have done that, you can try some real options. They are also on Yahoo finance. Btw, they are not quoted in implied vol.This is from Yahoo finance this morning, some puts on AAPL.PutsforSeptember 21, 2018Contract Name Last Trade Date Strike Last Price Bid Ask Change % Change Volume Open Interest Implied VolatilityAAPL180921P00075000 2018-05-02 11:20AM EDT 75.00 0.01 0.00 0.00 0.00 - 4 0 25.00%AAPL180921P00080000 2018-04-23 10:54AM EDT 80.00 0.06 0.02 0.11 0.00 - 20 346 50.00%AAPL180921P00085000 2018-03-07 2:27PM EDT 85.00 0.08 0.06 0.14 -0.07 -46.67% 1 555 50.88%AAPL180921P00090000 2018-04-23 9:41AM EDT 90.00 0.09 0.04 0.15 0.00 - 15 689 47.66%AAPL180921P00095000 2018-03-12 9:34AM EDT 95.00 0.05 0.07 0.18 0.00 - 10 3,749 45.31%AAPL180921P00100000 2018-05-02 12:43PM EDT 100.00 0.07 0.05 0.11 -0.14 -66.67% 61 1,679 39.26%AAPL180921P00105000 2018-04-24 12:46PM EDT 105.00 0.29 0.22 0.36 0.00 - 25 859 42.94%Take it from there. At one point, you'll probably move from Excel to something else. Good luck. "There is a SIX am?" -- Arthur
 Jurassic Total Posts: 199 Joined: Mar 2018
 Posted: 2018-05-03 14:50 Ok I have done that in Excel.I think Im still struggling to understand what options strategies aim to predict. With equities its whether the stock goes up or down. With options every option at a different strike for a given vol is different.
 frolloos Total Posts: 66 Joined: Dec 2007
 Posted: 2018-05-04 04:48 Delta-hedged option strategies do not necessarily aim to predict, but they aim to monetize a view / expectation of how the volatility of the underlying will behave in the future.An unhedged option strategy, i.e. buying a call spread and holding it until maturity, aims to monetize the view that the underlying will move up but not beyond a certain level.Have you followed ronin's suggestion? I suspect, but correct me if I'm wrong, that you might need to understand fully the mechanics of delta hedging just 1 option first, before you start adding more options and getting totally lost in the maze.
 ronin Total Posts: 435 Joined: May 2006
 Posted: 2018-05-04 14:35 > I think Im still struggling to understand what options strategies aim to predict.Good going.Are you making money or losing money with that?Start changing the (flat, constant) implied vol of the option. Where is the breakeven? At what implied vols do you make money, and at what implied vols do you lose money? How does that compare to the realised vol of the underlying? What happens when you consistently overhedge by some factor, and what happens when you consistently underhedge?Once you know that, you have the basic element of trading gamma and vega.The next step would be to separate gamma from vega. Make your original option longer dated (1y plus, so it has some vega), and start hedging the gamma. That is, take a short dated option (say 1m or so, so it has no vega and lots of gamma) and use it to flatten the gamma of your long dated option. Delta hedge the net option position. When the short dated option expires, roll it to next month.Again, you want to understand how this makes money and how it loses money. Now you can start changing the implied vol of the short dated options vs the implied vol of the long dated option (introduce some term structure) and see what that does.Then you can start playing with smile and skew. Take two options with different strikes and different implied vols, see how your pnl does for either of them.That, in a nutshell, would be what vanilla options are for - gamma and vega. Forget delta. You want delta, trade the underlying.Once you get there, you can start looking at a vol surface. Which options are mispriced in absolute terms (so they are worth running naked), and which options are mispriced in relative terms (so it makes sense to put up a spread)? The only way you can understand that is if you know how to make money from gamma and vega, hence your excel exercise. "There is a SIX am?" -- Arthur
 Jurassic Total Posts: 199 Joined: Mar 2018
 Posted: 2018-05-04 19:37 Worryingly, in my excel spreadsheet, realised vol = implied vol does not breakeven (for the flat vol, delta hedging case)....
 day1pnl Total Posts: 53 Joined: Jun 2017
 Posted: 2018-05-04 20:21 Did you simulate geometric brownian underlying? Think a sample of real data would almost always have a breakeven vol for each strike K (i.e. a breakeven skew).
 Jurassic Total Posts: 199 Joined: Mar 2018
 Posted: 2018-05-04 20:45 No I took AAPL from last month (a couple of days ago). Took the option ATM at 168Ok this delta problem is fixed now and the breakeven is implied vol = realised vol
 Strange Total Posts: 1532 Joined: Jun 2004
 Jurassic Total Posts: 199 Joined: Mar 2018
 Posted: 2018-05-05 20:44 I get that from a delta hedged option, the gamma pnl is IV-RV and the vega pnl comes from the IV. (Not sure how this is derived though).But I still dont see how you backtest these...Lets say you have a short term option ~30days (lots of gamma, little vega) would you look to predict the option implied vol - realised vol spread?
 day1pnl Total Posts: 53 Joined: Jun 2017
 Posted: 2018-05-05 21:12 would look to predict quadratic variation of underlyingGamma pnl comes from gamma. Vega pnl comes from vega. your vega risk can be calculated by brute force, e.g. by "bumping" the implied vol 1 pts in your model and recalculating the all-upfront value for the derivativeEDIT: but since your delta hedged pnl is going to be path dependent would look into that too - doesn't matter if you get the quadratic variation you asked for if it happens in a range outside of where your derivs have gamma, and vice versa you can get smoked selling if all the variation happens where you have the most negative gamma but in any other range stays still
 ronin Total Posts: 435 Joined: May 2006