Why Bartlett’s SABR Delta Can Differ in Sign from Black Delta
Summary
The document explains why a Bartlett delta calculated by bumping a forward and repricing under SABR can have the opposite sign from a conventional Black delta. Black delta holds implied volatility constant, while the finite-difference calculation in the question changes both the forward and the implied volatility as it moves along the SABR surface. The resulting sensitivity therefore includes the option’s exposure to volatility changes as well as the direct forward effect.
The accepted response illustrates this with the supplied call example: the SABR implied volatility falls when the forward is bumped up and rises when it is bumped down. Repricing with those changing volatilities produces a negative finite-difference delta, even though the fixed-volatility Black delta is positive. The response also shows that adding Black vega times the volatility change gives a close approximation to the repriced value, and notes that delta-and-vega hedging can make the two Greek approaches align more closely. Results depend on the volatility surface and bump setup; the document does not establish that Bartlett delta should always have a particular sign.
Key ideas
- Black delta holds implied volatility fixed, while Bartlett-style bump-and-reprice delta reflects movement along the SABR volatility surface.
- A changing implied volatility can outweigh the direct forward sensitivity and reverse the sign of the total finite-difference result.
- The example’s negative call delta follows from lower implied volatility at the upward forward bump.
- Combining Black delta and vega captures much of the repricing effect in the example.
- Delta-and-vega hedging can reduce differences between the two Greek approaches.
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# Systematic credit "liquidity provider" strategy # Systematic credit "liquidity provider" strategy I was reading a piece published by Bloomberg today, where it says the following: > “A systematic process lends itself to providing liquidity rather than taking it because our models have views on effectively every single security in the credit index thanks to the broad set of systematic signals that we use,” according to Gould. I am familiar with liquidity providers wearing the market maker hat in capital markets. However, I think AQR is doing something more than market making. Can anybody explain how AQR's factor based systematic credit/fixed income strategy can be labeled as "liquidity providing"? Also, how do you understand ## Answer by Dimitri Vulis (score 3, accepted) https://quant.stackexchange.com/a/47496 I think I understand what Gould means, (but maybe I'm mistaken, in which case all errors are mine). A market participant is usually acting in one of two modes: A market market provides liquidity. He knows where the asset is trading. He publishes the bid and ask quotes that normally don't include any view on whether the asset is rich or cheap. When he sells an asset, he might not have it in the inventory, but expects to know where to source it An axed proprietary trader consumes liquidity. He wants to buy or sell certain assets at whatever price is dictated by the market makers. Usually such a trader is motivated by his view that some assets are rich or cheap (but could also be motivated by asset inclusion in / deletion from some index, etc). As far as I understand, the HF not only knows where every asset trades, but also has a computer model that predicts whether the asset is rich or cheap. His bid and ask quotes reflect not just where the asset is now, but also whether he is a better buyer or better seller. This way, on one hand he gets paid for providing liquidity, as a market maker. But on the other hand he also gets paid for his prop trading, provided that his computer model correctly predicts rich/cheap. ## Answer by AK88 (score 0) https://quant.stackexchange.com/a/47508 While we cannot rule out pure market making, having discussed this further with a friend, I got some more color: Since factor investing (AQR framework) involves both buying and selling fixed income instruments (govies, corporates) to create value, momentum, carry, defensive, etc. styles, they will act as a seller. When they engage in selling, they can incorporate their views and expertise. So, I can imagine when they are doing value style investing, they will be selling the expensive fixed income. Assuming that most people will be after better performing (lower implied default by the market?) securities, AQR will enable transaction for these securities. At the same time, they will buy beaten up securities (higher implied default by the market?) that they believe will turn out profitable. Or is it vice versa, as stated in BBG article: > Quants say factor styles exploit time-honored behavioral quirks, while arguing vanilla credit managers tend to outperform by simply bidding up higher-yielding obligations often without being compensated for the liquidity risk. Similar arguments could be made for other styles, I guess. Thoughts? Resources: Systematic Fixed Income Investing, Systematic Fixed Income A Closer Look ## Answer by ontic (score 0) https://quant.stackexchange.com/a/47515 AQR and most factor driven style funds are low turnover, which means they do not have to use aggressive liquidity-taking execution. They can wait to be passively executed, which will decrease transaction costs and potentially (at least in the case of equities, not sure about bonds) receive exchange rebates from liquidity provision. So the core strategy is factor betting, but liquidity provision is icing on the cake, or more likely, a partial offset to market impact transaction costs.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.