economics

How We Discovered Skew

August 18, 20237 min read
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TL;DR the right skew is where put spreads trade

How We Discovered Skew

London 2003

the birth of iTraxx Xover 3m payer+receiver markets
  • 3m refers to the quarterly roll. Liquidity moved to the next expiration about 2 weeks before. If you were not square before and the market sniffed out your position, implied vols got pushed in your mush. No position stayed on the books for more than 3 months. While the slate got wiped regularly, it was difficult to build sustainable intuition about vol market behavior across multiple seasons, different micro/macro regimes, etc.

  • payers are bearish options: pay a fixed strike to benefit when spreads are wider.

  • receivers are bullish options: receive fixed to benefit when spreads are tighter.

iTraxx XO

the most interesting option market

iTraxx Xover is an index of 50 names picked every 6 months (by a survey of dealers) of "fallen angel" credits which used to be investment grade and might return, or they might degrade further and be forced to refinance at high yield spreads. If this refinancing event was imminent, it would mean a change of business plan that would itself take several quarters to play out.

There is no US equivalent: in the US, the CDX HY trades at even wider spreads (i.e., points upfront), and those companies are already firmly high yield credits.

The 50-name universe also experiences significant turnover, making it difficult to predict the spread impact of the semi-annual roll. As options traders, we take the spread level as an exogenous input, while we have to assess the volatility impact. By construction, more uncertainty gets injected with each index composition rebalance event. However, implied vols don't go higher forever just because of construction — "trees don't grow to the sky".

Term structure and rolls (due to index rebalancing events) are relatively straightforward to reason about. A rule of thumb: reset the implied volatility on each roll to remove the impact of any technical dislocations from the prior index series. Add 2 vol points for each rebalance roll, while eyeballing the correlations for the second-order effect worth +/-2 vols.

Volatility skew by observation

Guidance from more mature asset classes

FX and rates options exhibit increased implied volatility for strikes away from at-the-money — an uncertainty premium for the possibility of the world changing over time.

Equity index options show an asymmetric volatility skew (a "smirk") — lower vols for better states of the world; higher vols in worse states of the world.

For out-of-the-money iTraxx Xover receivers, we would bid realized vol (which was generally lower than ATM vol) and offer +2 to the ATM vols. For out-of-the-money payers, we would try to show one-sided markets, bidding ATM vol and offering +10, and slowly inch tighter on both as we got price discovery.

Sometimes we'd bid or offer 2 vols more aggressively (exclusively in the voice broker market), in order to gauge the speed/aggressiveness of the response, and expect that other dealers were too timid to fully cross the market, but greedy enough to leak information as they engaged on a price that looked attractive relative to their sheets. We'd also keep our sheets updated, and engage with prices that looked mispriced without trusting entirely that our sheets were correct.

For upside payers (wider credit spread = weaker credit conditions), we would see bids at ATM vol+4; sometimes trades would print away from us around ATM vol+6.

Volatility skew from 1st principles

My boss had been involved early with cds markets, before pioneering the single name and index options markets. To better understand how/why the skew had settled into this apparently persistent shape, he had me solve for the break-even strikes on zero-premium 1x2, 1x3, 1x4 put spreads (payers) at ATM vol+4. This pricing assumed we would bid the skew at where we saw it quoted in the market.

To triangulate the other sectors of the volatility surface, we also looked at call spreads (receivers) and condor spreads.

He also observed that we couldn't bid at market—which represents the price for social size—for 4x the notional of downside puts. As soon as we got hit there, we wouldn't be able to hedge without moving the market against our position.

We priced the zero-premium put spreads at ATM vol+0, which was a level we could hold indefinitely by selling the ATM options (non-trivially, requiring dynamic adjustments to balance vega against theta). The goal was to build a long skew book, from a cost basis that would make us the strongest hands in the market.

Massive interest in zero-premium put spreads from the real-money community

Put spread economics appeared very appealing to experienced credit investors. They wanted tactical hedges against their long holdings, and knew structurally/strategically that they would be buyers of the credit at lower prices (wider spreads).

For real money, hedging with credit default swaps was tricky: cds have negative carry and MTM noise to balance sheets. On the other hand, put spreads require zero premium outlay, have lower delta, and align with their long-term intentions to buy more when spreads widen dramatically.

Since iTraxx Xover was a new product, very wide spreads had not appeared yet in the empirical history, and reasonable people could defensibly underweight the probabilities and reflexive market reactions to a sudden widening of credit spreads within a specific sub-universe of salient European credits.

options pricing magic == a useful mathematical tyranny

The human brain pattern-matches against history, and conflates probabilities and outcomes, especially low probabilities and extreme outcomes. It simplifies the continuous distribution by creating a handful of distinct regimes and mapping narratives to them.

Meanwhile, in an analytic options pricing model, math ensures that all probabilities add up to 100%. Outcomes near each other have smooth-ish transitions; the parameterization pushes against sharp dislocations by design.

Monetizing the skew

We built a long skew position, marked at ATM vol+1 while the market quoted ATM vol+4 at ATM vol+6. On any given day, we could crystallize 3 vols of positive PnL by hitting the market bid (also giving a competitor +1 vol of mark-to-market PnL).

Of course, we had a large inventory behind it, and did not want to collapse the market. Better to drip it out slowly, and reload the inventory if/when we were able to recycle the risk. If we had just sat on the long skew position, all that potential PnL would disappear—at each quarterly expiration, out-of-the-money payers decay to zero.

Some observations

  • the first way to answer "What is the right price" is to observe it in the market. "The market is always right", "it is what it is", and price is defined as the intersection of supply and demand

  • however, an un-curious market-maker can forever "know the price of everything, and the value of nothing". The market-maker who simply mirrors others is naively providing marginal liquidity, while it takes work, exploration, and risk to extract real value from the "differing opinions that make up a market"

  • if other market participants had sniffed the relatively easy +3 vols of PnL, anyone could:

    • smack bids ahead of us, and bid to buy back from us lower
    • pull their bids and offer more aggressively, also to induce us to spit out/transfer some of our gains to them
    • find our real money customers and pitch them more attractive put spreads (either directly, or indirectly through a broker). Maybe someone would be willing to take a 3 vol markup rather than our 5 vol markup (since we bid ATM vol when the market mid was ATM vol+5) to compensate for the cost/risk of hedging
  • if real money was very bullish, i.e., not worried about hedging against a minor downturn, they would not buy put spreads at any price. Dealers would not be able to make these same kinds of profits by packaging structures and intermediating between end users and market-makers

skewit is what it iscredit default swap index options
長話短說 (short + sweet):
Thanks for reading, anon!