SKEW STRATEGIES FOR INDEX OPTIONS
Updated November 30, 2022
By Andres Talero
Understanding the Volatility Skew of Index Options.
Option premiums for different strikes with the same expiration are a function of underlying market prices and the implied volatility curve. The implied volatility can be observed by applying backwards the Black and Scholes formula to find the volatility level consistent with each market traded option premium.
The shape of the resulting curve for different strikes can be used as a measure of their relative prices. Volatility skews are the biases present in the implied volatility curve. There is no volatility skew if all options for a given expiration date have the same implied volatility.
Using their implied volatility as a relative measure, out of the money low strike options on US equity indexes usually have high premiums, compared to at the money and above the money struck options.
The relative high price of low strikes is due to the high speed at which generalized market selloffs occur, risk aversion among market participants, and supply and demand for options with different strikes.
Counter-intuitively, the high relative premium of low strike options, creates a relative low cost for put spreads around the same strikes.
When out of the money low strike puts have a high relative price, the difference between at the money and out of the money put prices is smaller. This results in a low price for put spreads.
High strike index calls are usually inexpensive when compared to low strike puts. As a result of the low relative price of high strike calls, call spreads tend to be expensive, when compared to put spreads with strikes located at a similar distance to the at the money strike.
Below is a hypothetical table of SPY option prices and spreads:
SPY Market Price: $300
6 Month Option Premiums:
360 Call = $2, Put = $62
340 Call = $6; Put = $46
320 Call = $13; Put = $33
300 Call = $26; Put = $26 (At the Money)
280 Call = $40; Put = $20
260 Call = $55; Put = $15
240 Call = $71; Put = $11
In the table, at the money call and put options have the same premium – but low strike puts are more expensive than high strike calls.
Resulting Option Spreads Net Premiums:
340 to 360 Call Spread = $4; Put Spread $16
320 to 340 Call Spread = $7; Put Spread $13
300 to 320 Call Spread = $13; Put Spread $7
300 to 280 Call Spread = $14 ; Put Spread $6
280 to 260 Call Spread = $15 ; Put Spread $5
260 to 240 Call Spread = $16; Put Spread $4
Note the price difference between call spreads around the at the money strike and similarly positioned put spreads. Call spreads are more expensive than the similarly postioned - in terms of distance to at the money strikes - put spreads.
A number of strategies - bearish and bullish - take advantage of Index skews by using option spreads. Most of these strategies tend to work better when held to expiration, as in the short term spread prices sometimes may move in counter-intuitive ways, or exhibit little short term sensitivity to the underlying (low delta), and have bad convexity – as the relative price of low strike options tends to increase in accelerated index sell-offs.
The remainder of this article explores different strategy variations using the same underlying relative price concept. We outline the following strategies:
IN THE MONEY TO AT THE MONEY PUT SPREAD.
OUT OF THE MONEY TO AT THE MONEY PUT SPREAD.
BULLISH CALL SPREAD OVERLAYS.
IN THE MONEY TO AT THE MONEY PUT SPREAD.
This is a useful top of the range strategy. The spread cost usually is about 50% of the in the money range price, and can be set up with a wide range, and a breakeven located above the current Index price.
If the range is broken (when the bearish view is not realized), there is some protection from the increasing optionality (time value) of the high strike Put.
In our price example, a 340 to 300 put spread costs $20, with the underlying index trading at $300. The maximum payout of the strategy is double the net premium, or $40.
Breaking down the cost of the strategy, an in the money 340 Put costs $46; and an at the money Put can be sold for $26 – netting a cost of $20 for the spread. Below is a chart with the payout for different SPY prices at expiration for the combined strategy.
340 to 300 Put Spread Payout – $20 Net Cost – 6 month expiration:
The break-even at expiration for the strategy is at an SPY price of SPY $320, compared to the initial price of $300.
Mark to market evolution prior to expiration.
As a result of market moves, the intrinsic value of the strategy moves in opposite direction than the time value of the two options (their pure time value), creating some counterbalancing to market moves.
If SPY prices rise, the position will decrease in value. As the low strike looses value the combined position will have some protection from the time value of the high strike.
If SPY prices decrease, both options loose time value, and the position makes money from the directional move. If the combined position becomes deep in the money but has not fully appreciated, it becomes a high carry position.
At inception, the position has positive carry – as it makes money over time if the market does not move. Because the low strike put decreases in premium over time, the break-even of the strategy tends to improve over time, even if the Index price has not moved.
OUT OF THE MONEY PUT SPREADS:
This strategy can be used as a hedge, or as an outright short. In volatile markets, when the Index sells off, same expiration out of the money puts may converge to similar prices, compressing the spread between their premiums.
In our example price table, an out of the money put spread corresponds to paying $9 for a 280 to 240 Put Spread.
Breaking down the cost of the strategy, the 280 Put costs $20; the 240 Put can be sold for $11.
The net a cost of the spread is $9.
Below is a chart with the payout for different SPY prices at expiration with a Net Premium of $9.
280 to 240 Put Spread Payout – $9 Net Cost:
Note the higher leverage of the position in comparison to in the money put spreads (the previous example). The maximum payout for this example is about 4 times the net premium of the spread.
When used as hedges, the main drawback of out of the money index put spreads is the stickiness of their mark to market. The combined spread price might remain mostly unchanged in a continued selloff.
The position is most effective if held to expiration, and is usually a poor mark to market hedge.
BULLISH CALL SPREAD OVERLAY.
The Strategy is created by selling a call spread on top of a long index position.
Recalling 6 Month Option Premiums:
360 Call = $2; Put = $62
340 Call = $6; Put = $46
320 Call = $13; Put = $33
300 Call = $26; Put = $26 (At the Money)
280 Call = $40; Put = $20
260 Call = $55; Put = $15
240 Call = $71; Put = $11
The strategy is composed of: SPY purchase at 300
Selling an In the Money Call - 260 strike, $55 premium (15 time value)
Buying a 320 strike Out of the Money Call for a $13 premium.
Net Cost $258
The options strategy produces an absolute premium of $42, and a net premium of $2.
The net premium would be the strategy payout if the options expired with no change in the underlying Index price.
This strategy uses the skew to reduce risk, and create an attractive risk reward profile.
The position creates a wide range where it expires with no volatility, as from 260 to 320 the combined payout remains unchanged.
SPY (long at $300) and 260 to 320 Call Spread (short) Payout – 258 Net Cost:
The low strike call is $40 away from the current SPY price, but the high strike call is only $20 away. The downside of the position is reduced more than the upside that is given up, by a factor of 2.
The strategy produces a positive payout above the 320 strike, which is set $20 above the initial value of the SPY, but has downside below the 260 Strike, $40 below the initial value of the SPY.