A risk reversal buys one wing of the smile and sells the other. It is how a desk trades skew itself, rather than the stock or the level of volatility. Skew, from the first lesson in this module, is the extra volatility the market charges for puts below the stock over calls above it.
Two legs, one expiration
Both legs sit on one expiration. Buy the call whose delta is about 0.25 and sell the put whose delta is about minus 0.25, one strike above the stock and one below. At expiry nothing happens between the strikes; above the call you gain like a stock owner, below the put you lose like one. The reverse trade, long the 25-delta put and short the 25-delta call, is the mirror image.
Long the $104 call and short the $96 put, 30 days out. At expiry the line is flat between the strikes and moves like 100 shares outside them. The chart prices both legs at one flat volatility, so its entry cost is a small debit; on a real smile the put is dearer and the trade usually pays a credit. Drag days toward zero to watch today's line settle onto the expiry line.
Used on its own, the long risk reversal is a cheap bullish bet, because the put you sell pays for most or all of the call. Hedged with stock, what is left depends only on the two IVs, and that is the use here.
What its price says
Take a $100 stock with 30 days left, an at-the-money IV of 20% and a 4% interest rate. The 25-delta put is the $96 strike, at 24% IV. The 25-delta call is the $104 strike, at 18%. Priced off those vols, the put is worth about $1.06 and the call about $0.76, so buying the call and selling the put takes in about 30 cents a share. The market pays you to own the upside wing and carry the downside one, because it values the downside more.
A 20% stock with index-style skew. Hover near 96% and 104% of the stock price, roughly where the 25-delta put and call sit with a month to go: the gap between the two readings is the risk reversal in vol points. Drag skew to zero and the gap closes; drag it below zero and the calls become the dearer wing, which is call skew.
At one flat 20% the same two strikes are worth $0.94 for the call and $0.71 for the put. The call is now the dearer leg, because the interest rate lifts the forward, the carry from Module 2. Skew moved the trade more than 50 cents a share toward the put. Since the dollar price mixes skew with carry and the size of the stock, desks quote a risk reversal in vol points: call IV minus put IV, here 18 minus 24, or minus 6. On equities it is negative almost every day.
Trading skew as a view
The long risk reversal carries about 0.50 of delta, 0.25 from the call and 0.25 from the short put. Cancel it by delta hedging, short about 50 shares per contract, and the position is close to flat on the stock. The two vegas are similar and opposite, so it is close to flat on the overall level of volatility too. What is left is the tilt. The long risk reversal gains when put IV falls toward call IV, which is skew flattening; the short one gains when skew steepens.
So the view is about the price of protection, not the direction of the stock. A trader who thinks index put skew is stretched after a scare sells the 25-delta put, buys the 25-delta call and hedges the delta. One who thinks a calm market has left crash protection cheap does the reverse, a trade with the same shape as the collar that Module 12 covers.
What moves skew over time
- Sell-offs and demand for puts. When the market falls, funds rush for protection and the dealers who sell it charge more for each extra put. The whole surface rises and the put wing usually rises most, so index skew tends to steepen into a sell-off and ease as things calm.
- Overwriting. Funds sell upside calls against stock they own for income, the covered call run at size. That steady supply keeps call IV low on indexes and big stocks and holds skew steep even in quiet markets.
- Takeover and meme names. A stock that could be bought out at a premium, or one where a crowd buys short-dated calls, has buyers for the upside. Call IV can climb above put IV and the risk reversal turns positive. That is call skew, and it is rare on an index.
Skew against its own history
Four points of skew can be an ordinary day on SPY and loud on a stock that usually shows two. So traders rank skew against its own past, as IV percentile ranks IV. At the steep end of its one-year range the puts are dear and a skew seller has the better price; at the flat end protection is cheap. Skew in points also grows when all volatility is high, so the normalized skew from the first lesson in this module, skew divided by ATM IV, shows whether the tilt changed or only the level.
The maths: skew in a risk reversal's price
In volatility terms the quote is RR = IV(25Δ call) - IV(25Δ put), the put-minus-call skew with the sign flipped. In dollars the trade costs C(K_c, σ_c) - P(K_p, σ_p), each leg priced at its own IV.
Vega links the two. Against a flat smile at the ATM vol σ0, the dollar price moves by about vega_c × (σ_c - σ0) - vega_p × (σ_p - σ0). In the example both vegas are about 0.09 per vol point, the call sits 2 points under the middle and the put 4 points over it: 0.09 × (-2) - 0.09 × 4 = -0.54. Pricing both legs exactly gives -0.537, from a 23-cent debit at flat vol to a 30-cent credit on the smile.
The same arithmetic prices a change in skew. If the puts rise 1 point and the calls fall 1, the delta-hedged long risk reversal loses about 0.09 + 0.09 = 0.18 a share, $18 a contract. If every strike rises 2 points instead, the call gains about 0.18 and the short put loses about the same. A level move cancels; a tilt does not.
Your turn
Open the QQQ chain on the monthly expiration. Find the call nearest 0.25 delta and the put nearest minus 0.25, and price the risk reversal from their Mids. Then open the TSLA chain, measure its skew the way you did for SPY in the first lesson in this module, and set it beside the index.