### Calendar Spreads

Calendar spreads, also known as horizontal spreads or time spreads, compose of 2 same class options with the same strike (vertical) but a different expiration cycle (horizontal). Yes, naturally, a diagonal spread means two same class option with both different strikes and different expiration cycles. Herein, we refer them as time spreads. That is, when one is long a time/calendar/horizontal spread, it is buying time, or in other words, buying the long dated, selling the near dated option. Time spreads are complex option strategy since the way the spread is structured can position one for a number of different market scenarios – that is, a bullish/bearish/sideways/large movement biases.

A long time spread pays more premium in terms of IV since more time means more risk is possible, hence it is debiting and its maximum loss, if both options are held to the further expiry, is limited to the net premium paid for the long time spread. However, since nearer dated option sold have unlimited loss, the maximum profit cannot be determined. Best case scenario would be near dated option expires worthless so you credit the premium, and the time between the options expiration cycle, will the underlying move the long further dated option ITM, and profit is unlimitd. Worst case scenario would be underlying moves against option sold and near dated option expires deep ITM, and from there on, the time remaining to the further dated expiry, underlying moves OTM and long dated option expires worthless. Vice versa, a short time spread receives more premium selling longer dated option than paying for the premium for buying the shorter dated option, hence it is crediting and its maximum profit is limited to the net premium earned for the short time spread. Again, the maximum loss cannot be determined. However, in this case since longer dated option is sold and has unlimited loss, closing the long-dated option on the short-dated option expiration would mean that the maximum loss can be set at the difference in price of the 2 options, and the maximum profit would be the net positive theta earned everyday till the short-dated option expiry. This cannot be quantified at the outset of the trade as while both delta move synchronously, IV for both expiration cycle can be different in the term structure.

Since theta (daily) and vega (per 1% IV) is largest when strike is the close to underlying price, its P/L over strikes would be largest when ATM. Long time spreads can be used as a positioning strategy for **bullish/bearish/sideways**. That is, buying a time spread with **strike above current underlying price implies a bullish forecast at the expiry of the short-dated option, given that the point of maximum profitability is reached when the long-dated option is near ATM on the short-dated expiration**, and the short option theta is most positive when ATM – that is, the spread value expands. It is **a price and time target**. Likewise, when strike selected is below (bearish) or around current underlying price (forecasting sideways underlying price).

Selling a time spread with the strike price at current underlying price implies a strategy positioning for **large move in underlying**, in either direction – that is for the spread value to contract since the bid price you sold the long dated ATM option will be higher than the ask price when you are buying it back when its OTM.

Initially, it would seem **counterintuitive** to think in terms of spread value rather then the moneyness of the options. Here, **time spread value = long dated option value – short dated option value**

**Bidirectional large move in underlying causes time spread value to contract**

- For instance, you are short a
**put**time spread. Underlying price**rise**after short initiation. Short-dated put bought will be OTM, long-dated put sold will be OTM too, but because delta is smoother with more time left to expiration, the**short-dated put will be more OTM****and its intrinsic (delta) value falls by a smaller extent since delta is less negative**. Net change in spread value is**negative**. - For instance, you are short a
**call**time spread. Underlying price**rise**after short initiation. Short-dated call bought will be ITM, long-dated call sold will be ITM too, but because delta is smoother with more time left to expiration, the**short-dated call will be more ITM and its intrinsic (delta) value rises by a larger extent since delta is more positive**. Net change in spread value is**negative**. - For instance, you are short a
**put**time spread. Underlying price**fall**after short initiation. Short-dated put bought will be ITM, long-dated put sold will be ITM too, but because delta is smoother with more time left to expiration, the**short-dated put will be more ITM and its intrinsic (delta) value rises by a larger extent since delta is more negative**. Net change in spread value is**negative**. - For instance, you are short a
**call**time spread. Underlying price**fall**after short initiation. Short-dated call bought will be OTM, long-dated call sold will be OTM too, but because delta is smoother with more time left to expiration, the**short-dated call will be more OTM as its intrinsic (delta) value****falls by a smaller extent since delta is less positive**. Net change in spread value is**negative**.

In summary,

- when
**OTM (fall in intrinsic value)**, delta change is**smaller**for near-dated compared to further-dated - when
**ITM****(rise in intrinsic value)**, delta change is**larger**for near-dated compared to further-dated

Greeks exposures of time spread

Netting the delta above, +further dated delta – nearer dated delta results in the delta of a put or call time spread below. Delta exposure tallies with the calculation in the table above i.e. as underlying price falls, delta change is positive.

Note that put or call time spread delta are **synthetically equivalent** except that call is between 1 (ITM) to 0 (OTM), while put is between 0 (OTM) to -1 (ITM). Much like vertical spreads that are linked by a market-neutral interest rate driven structure (**Box**), put and call time spreads are linked by the **jelly roll**.

That said, for other greeks, both PTS and CTS have the same greek exposures.

Remember that gamma is more sensitive to moneyness when the remaining time to expiry is shorter, and as a result, a long time spread that is long the further dated option with a positive gamma, and short the nearer dated option with a negative gamma, will have a net negative gamma because the nearer dated option gamma is higher when near ATM. However, long time spread has a positive gamma when underlying is far away from the strike price of the time spread, as seen below that the nearer dated long option gamma is lower then the further dated long option when option is deep ITM or OTM.

As the nearer dated option approaches expiry, gamma is more pronounced i.e. Refer above and derive 9m-6m and fast forward to 6m-3m.

Remember that vega of a long option is positive and is higher across all moneyness when its time to expiration is longer. Since vega of an option generally falls across moneyness as it approaches expiry, vega of a long time spread generally rises across moneyness approaching the nearer dated option expiry.

Theta is the the exact opposite of gamma and is positive, yes positive, when the underlying is around the long time spread strike, but falls to negative when underlying is far away from the strike. This is intuitive as you are buying time by buying the time spread, which makes sense for theta to be positive.

As the nearer dated option approaches expiry, theta is more pronounced as may fall to negative if underlying is far away from strike.

The uniqueness of a time spread greeks allow time spread to be versatile in its use for multiple strategies. In the table below, we see that the uniqueness is because the netted greek of buying a further dated and selling a nearer dated option (long time spread) is able to **have both positive theta and positive vega**, which if its a single option i.e. short option that has a positive theta cannot have a positive vega at the same time! The only shortfall is that a long time spread has a negative gamma and that means the underlying is against the trader i.e. underlying falls, delta becomes more positive, vice versa. The silver lining to its negative gamma is that its negative only when underlying is close to the strike price. Approaching shorter dated option expiry, net gamma exposure becomes more pronounced and if the underlying moved far away from strike, gamma becomes positive.

Because a long time spread has both positive theta and positve vega, its a strategy to employ when **underlying is sideways with a low IV (longer dated) that will only rise later (That is, downward sloping term structure since longer dated option bought at lower IV than IV of nearer dated option sold)**.

Positioning the strike not at current underlying price implies a directional move **towards targeted price at the nearer dated expiration date**.

A short time spread with positive gamma to accelerate the favourable delta, but with negative vega and theta, positions for a **sharp movement away from strike followed by falling IV from a higher IV after a sharp move (downward sloping IV term structure), since vega becomes more negative approaching the expiration of nearer dated option**.

Either long or short time spread can address a large IV differential, seen as a kink resulting in a higher than average IV at front end of the term structure. Usually, the longer dated options will trade in line with the historical long-term volatility, and spiking typically occurs at nearer dated expiration cycles. Main consideration for a time spread still remains at one’s forecasted price, and IV differentials from history remains a secondary consideration.

That said, **if the current term structure of IV is not in alignment with one’s price/time forecast for the underlying, it might favor another strategy besides a time spread i.e. vertical spreads, instead of horizontal spread at strikes away from current underlying price as a limited-risk bullish/bearish strategy. For instance, buying a 100/110 call spread is favored over buying a 110 time spread if IV term structure is downward sloping. **

Call time spread or Put time spread?

Options prices are derived from a model that uses the underlying forward price as its input. That is, if there is a forwards market for the underlying its used, else a theoretical fair-value forward price is computed with its financing cost, rate differential, storage cost, dividends, etc, basically S*(1+debit-credit) i.e. debit that applies to all instrument is the interest rate that you could earned if invested in money market. Remember that for FX, the forward points from forward market is different from the (for <=1y) OIS implied rate differential model theoretical price minus current spot price, and that difference can be explained by the CCBS plug in. That is, CCBS is a component that make up the FX forward points. Since CCBS are quoted against USD, CCBS curve (within 1y tenor) flatenning, whether its negative or positive, means the forward points (where USD is base e.g. USDCHF) will be flatten to more backwardation and in the future, you need less CHF for 1 USD. That is, a flattening CCBS implies more future demand for USD with a more positive carry if you are long USDCHF, and a negative CCBS means lenders of USD pay less rate for the collateral currency accepted. Either way, a positve CCBS in backwardation or a negative CCBS in backwardation means less future demand for USD, only difference is a negative CCBS means forward points from forward market demand and supply is lower than the OIS implied theoretical rate differential model, resulting in a negative plug in, that is market is pricing in a better than expected positive carry for holding USD. This hints on a strong demand, or shortage, of USD.

That said, given the forward pricing curve embodied into the options pricing of different expiration cycle, with the same strike price locked in, the cost of carry (interest rate) differential from one expiration month to the next is captured in a **market-neutral** structure called **Jelly Roll**.

To reiterate the concept of a Jelly Roll from the previous part I post, jelly roll is composed of a long time spread and a short time spread, both have the same strike price and same near and further expiration cycles, and either one is of calls, the other is of puts. That is, its 2 synthetic equivalent offsetting time spreads, where either call or put is long, the other is short. This structure isolates the difference in pricing between call and put time spreads.

Jelly Roll Value = Strike * (d2 – d1) * (rate/360), approx if d2-d1 is small with no rate convexity, should always equal the cost of carry differential of the expiration, adjusted by the strike price.

**No arbitrage relationship: CTS – PTS = JR > 0**

Since rate > 0 and jelly roll value > 0, that explains why call time spread is more expensive than put time spread i.e. long call time spread – long put time spread = jelly roll value > 0 has upward slope forward curve, that is, debiting carry, since you for buying time and paying for the time value of money.

Remember: Put-Call Parity, P+S = C + Ke^-rt of cash.

- Column wise: its 2 offsetting time spreads
- Row wise: its a market neutral JR structure composed of 2 market-neutral put-call parity equation, which explains why JR = Strike * (d2 – d1) * (rate/360)
- earning or + Ke^-r(nearer T d1) = P+S-C
- paying or – Ke^-r(further T d2) = -P-S+C

Vice versa, one can earn the time value of money between the time differentials with a short jelly roll.

Likewise, if one is confident of their JR calculation methodology, they can benchmark theirs against the market prices and find relative opportunities. Here, JR can be opportunities of mere milli-cents, so be sure that your method has been tested to be the method that the market have been and is using. Besides arbitraging relative value opportunities, cost saving on entry or exit is another reason on checking market value against theoretical JR value.

Simple rules to consider when considering between CTS or PTS:

- Favor buying the cheaper time spread, shorting the more expensive time spread.
- Compare bids when you are shorting, or asks when you are buying.

When considering to** long** a time spread,

- favor
**cheaper**CTS when CTS**ask**– PTS**ask**< JR (market is pricing a cheaper CTS ask) - favor
**cheaper**PTS when CTS**ask**– PTS**ask**> JR

When considering **shorting** a time spread (or exiting a long time spread),

- favor
**rich**CTS when CTS**bid**– PTS**bid**> JR - favor
**rich**PTS when CTS**bid**– PTS**bid**< JR (market is pricing a more expensive PTS bid)

As the saying goes, plan for the worst and hope for the best, there needs to be active trade management of the time spread position. In both long and short time spreads, the risk is limited to the debit paid when you are long time, but the risk of early exercise of a short deep ITM (further dated) leg of a time spread exists if you are short time.

Questions to consider:

- At nearer dated option expiration, what to do?
- cheapest way to take profit or loss? Liquidate original positions or offset with synthetic equivalent?
- Underlying reaches target price ahead of schedule before option’s expiration?
- Say you long a time spread with a biases based on strike selected, what to do if forecasted direction is completely wrong or underlying environment has changed?
- Say you are short a time spread to position for a bidirectional breakout, what to do when a breakout fails to materialise and you are paying theta?

In the case when one’s forecast have been met, there should be P/L targets to liquidate the original positions. Are there any synthetic equivalents, that could be cheaper, as a TP exit strategy? Yes, there is, but you have to carry a jelly roll structure as a residual position. Note that, more modifications or strategy transformation means more commissions and bid-ask options spreads to pay. Another alternative to take profit, is taking partial profit and scaling out of the original size. This allows taking money off the table, limiting risk and staying on course with one’s forecast (in the case with time spreads, since eventual profit is not locked in at initiation, its a good strategy to handle the unlimited loss with the further dated option). In the case when market have changed course and one’s forecast is absolutely on wrong foot, there needs to be liquidation, or at least, a modification of strategy.

As mentioned, there are 2 factors deciding on how to liquidate the original positions: Price and Liquidity. Price is straightforward as we apply the jelly roll no-arbitrage pricing principle and favor the most advantageously priced time spread to use (call or put). Liquidity can take cue from the moneyness of the inidividual options leg that compose the time spread. Generally, options that move ITM acquire a larger delta and that makes hedging them riskier to market makers, and accordingly, market makers typically widen the bid-ask spread of ITM options to compensate them for this risk. That is, for every ITM put time spread, you have a synthetic equivalent OTM call time spread that is cheaper to use to liquidate, vice versa. **Given that CTS is more expensive than a PTS, any jelly roll that compose of a long PTS (with short CTS) will make that back by earning a credit from a backwardation jelly roll forward curve.**

A dilemma a long time spreader face is, when he got the direction right but the timing was too conservative, with too much time left to expiration and time decay have not act on the shorted nearer dated option, **should he hold on a while more to earn some theta or simply exit?** If the trader believes that underlying move is a reaction that will fade with a medium term change of direction, an immediate exit is favorable least the underlying moves out of favor and you loss the change to take the only profit. If the trader believes that the underlying is going to move sideways at the current level, then by all means, he should hold the position. However, if the trader believe that the **underlying will remain sideways but strategy needs an adjustment as the target price is slightly off, then the time spread can be “rolled” to a new target price**. Rolling to a new target price is achieved by initiating 2 vertical spreads in both the near and further expiration months. This involves 4 legs and bears costly commission.

Early arrival at target price

Say you own a **long call** time spread and you wish to **adjust the target price upwards**, the **shorted nearer dated** call have to net with the long call leg of lower strike in a call vertical spread, hence it requires buying a call vertical spread (**bull** **call** spread). If it involves **adjusting the target price lower**, it requires selling a call vertical spread (**bear** spread) for the shorted nearer expiration month. Vice versa, for a short time spread, the same vertical spread of equal strikes **at the further out month is sold if the nearer month is bought**. In summary, whether a long or short time spread, the shorted option (nearer month if long time spread, further month if short time spread) will be adjusted with a bull spread (call or put) to adjust target price upwards, likewise, with a bear spread if you desire to adjust the target price downwards.

Say the underlying movement does not move (or you might think, arrive late), then its best not to be lazy and close the further dated option on expiration of the nearer dated option, otherwise, you will have a directional position from the residual further dated option.

### Ratio Spreads

Generally, any structure that involves the purchase of an option that is underwritten by the sale of a greater number of further OTM options of same class and expiration cycle is a ratio spread (buy 1 : sell >1). The ratio can be any, depending on the moneyness of the options sold and IV level. Depending on how it is structured, ratio spread can be debit, credit or breakeven. Given that ratio spreads are net short of options, they **generally are short vega and long theta**. For those reasons, ratio spreads is more effective when one is expecting **a low-magnitude directional move (upwards use calls, downwards use puts) alongside a declining IV or sideways underlying movement to capture positive theta**. Typically, this situation happens when the underlying has traded higher (lower) and the trader is forecasting a mild correction lower (higher) while IV declines.

**The silver lining is that, ratio spread as a strategy for counter-trend trades is expecting a mild correction but is also protected if the underlying trend prevails, that is, if the trend resumes, the ratio spread position in that direction has its risk capped**. However, a net short options structure have open ended risk in the direction of the short options, and loss is unlimited when a mild correction actually evolves into a reversal. Counter intuitively, a call ratio spread expecting a mild upward movement in underlying has a declining profit as the underlying moves upward. That said, because they are counter-trend trading vehicles, that is, with little profit potential, ratio spreads are constructed with minimal debit or a credit.

Call/Put Ratio Spread Payoff

- Max Profit = (K2 – K1) + credit or – debit (to initiate spread)
- Call Max Loss = Unlimited on upside, limited to initiation debit on underlying downside (None if credit on initiation)
- Put Max Loss = Unlimited on downside, limited to initiation debit on underlying upside (None if credit on initiation)
- Call Breakeven
- downside: K1 + initiation debit (certainty ITM if credit on initiation)
- upside: ([#shorts * short call strike] – [#longs * long call strike]) / (#shorts – #longs) + credit – debit

- Put Breakeven
- downside: ([#shorts * short put strike] – [#longs * long put strike]) / (#shorts – #longs) – credit + debit
- upside: K2 – initiation debit (certainty ITM if credit on initiation)

Of course, one can liken a call vertical spread (+1 -1) with 1 or 2 extra shorts at the call of higher strike to make it equivalents to a (+1 -2) or (+1 -3) call ratio spread. A butterfly (+1 -2 +1) with an extra short at the highest strike call also evolves into a (+1 -2) call ratio spread. That said, both call (bull) vertical spread and butterfly is limited risk positions that address mild upward movement (call spread) and declining IV (butterfly is long theta, short gamma, short vega at the middle strike) and a call ratio spread do inherit these behaviour. Selling additional call options at higher strike simply reduces the risk to the downside (debit to credit) at the expense of increasing the risk to the upside.

Likewise, put ratio spread inherits the behavior of a butterfly and a put (bear) vertical spread, and the additional sales of put options at lower strike reduces the risk to the upside, in the event that the up trend resumes, at the expense of increasing the risk to the downside, counterintuitive to put downside bias.

Greeks of ratio spread

We can think delta of an option as the odds that the option will finish In-The-Money. That said, ITM options would have higher delta (odds) than the long shot OTM options, and as the race to expiration gets closer, ITM delta will increase to 100 (or fall to -100 for Put) as its odd to finish In-The-Money rises, whereas the OTM options delta will fall (or rise) to 0 as expiration approaches.

Another concept to help visualise greeks is the idea that a declining volatility reduces the odds of OTM options ending ITM before expiration, and increases the odds of ITM options ending ITM before expiration. This effect is similar to the effect on delta when there is less time to expiration, as shown above. That said, **a declining volatility mimics the passing of time**. Remember, long option is long delta, long gamma, long vega, short theta. **Falling IV likens to a fall in extrinsic value, given a positive vega, as do passing of time with a negative theta.**

As IV rises for the particular expiration cycle, given that more options are sold than bought, call ratio gamma quickly becomes negative. As underlying rises to and beyond the strike price of of the sold options (actually could turn negative before the strike if there is more time to expiration) , call ratio gamma will turn negative. Remember that negative gamma is always against the trader favor. inheriting the same behavior from delta, a declining volatility mimics the passing of time.

Since a ratio spread structure have more shorts than longs option, it is generally short vega, and this is more pronounced when underlying price is nearer the strike price of short options. Since vega is much higher with more time to expiration, when the underlying is even before the strike, vega starts turning negative because there is more short options. Remember that as time passes, the holder of an option pays theta and is less long volatility as vega fades lower. That said, the vega profile of the long option and short options in a ratio spread will fade to 0 approaching expiration.

Remember that theta of ATM option increases as time to expiration decreases, whereas the theta of OTM and ITM options decreases as time to expiration decreases.

That said, as the underlying price increases from the strike of the option bought (negative theta) to the strike of the options sold (positive theta), options sold will be less OTM appproaching ATM and hence the swing of theta from negative to positive will be more dramatic.

Greek profiles are vice versa for a put ratio spread. For easy visualisation for the readers, find the greek exposures of the put ratio spread below. Again, a declining volatility when vega is positive mimics the passing of time or paying of theta.

**Put ratio spread greeks**

When to use ratio spreads?

- Counter trend moves – The greeks explain why ratio spreads are best suited as a counter trend strategy. Expecting a mild correction in an up trend, directional wise, you have the trend support to avoid the asymmetrical risk-reward properties (unlimited risk if correction extends, limited if trend continues) so that strategy is executed at a credit. Greeks wise, as trend resumes, volatility picks up and vega is favourably positive, though u pay theta. If corrective fall slowly plays out, value of the put ratio spread expands as theta is positive as days pass and extrinsic value rises as volatility declines on negative vega.
- Trend decelerations – When the market is trending, it will enter areas of previous price congestion. Price movements typically, but not necessarily, slows at this area because of overheard resistance from past inventory levels. If its a bullish rally and reentry into a previous congestion zone, we can take hints from positioning reports
- Positioning is net long: Are they real money that sticks to their long term view (especially if its a positive carry and they are chasing yield) or hot money that chases where the short term opportunities is? If its mainly speculative money, they would preferably breakeven and sell to close their longs, especially if its negative carry to reduce the pain from time decay. When price broke out of previous congestion zone, was net position reduced accordingly? If no, then there is still past inventory bought at the congested zone that will likely sell to close their longs at breakeven. If positioning is at historically extreme net long, it depends on the conviction of the participants to hold through the congestion zone, that is, the current circumstances is in favor of longs than before.
- Positioning is net short: That means the shorts are holding a painful drawdown. Will they continue holding their shorts? Likely if its a positive carry, very unlikely if its a negative carry. Price movement would slow down if sellers are would add on their shorts on reentry into previous congestion zone, that is, their conviction that price is going lower in the long run.

- Meltups / meltdowns – typically driven by good or bad news and underlying price explodes to the upside or downside with IV rising sharply. In these scenarios, going against the trend is very risky, however, if a correction does occur, IV typically backs off and this plays to the strengths of ratio spreads. Likewise, if trend resumes, risk is limited to initial investment.
- Volatility
**skew**plays – (*Note: IV is always secondary consideration and price direction is primary, since delta is always more than vega*) Sometimes, there can be large IV differentials between the strikes, which prompts a “sell high IV strike, buy low IV strike”. Similar to vertical spreads, ratio spreads have a more aggressive stance that the high IV strike will experience a IV normalisation.

That said, the congestion zone as well as support and resistance zones are needed for structuring the ratio spread higher and lower strikes selection. Similar to a two-winged butterfly, the maximum profitability is achieved at the short strike of the fly. However, ratio spread is a one-wing fly that is not delta neutral and has a directional bias. Slightly beyond the short strikes (body), or the missing clipped wing for initiation cost savings, must be backstopped by a key support or resistance level. On timing of initiation of strategy, the trader favors initiating the selling of ATM options, that is, you buy the 90/100 put ratio spread (sell 2x 90 puts, buy 1x 100 put) when the underlying is at the peak of its uptrend near its resistance at 100, and you are expecting a mild correction, but do not wish to take a delta 1 direction with underlying.

If the price correction or rebound is expected to be slow with a declining volatility for the next 1 month, then its favorable to use a 1 month expiration cycle that mirrors the forecast.

Given that there is an open ended risk beyond the clipped wing in a ratio spread, if the trader does not have enough capital to withstand a sharp gap through the body short strikes, then he might need to retreat to a more conservative (could be credit if its a iron) fly or condor strategy to trade decelerating price movements and declining IV situations. **When red flags are flying, being greedy to temptations to try to get “one more day” of time decay out of the position can be a trader’s undoing.** The trader can scale out a profitable ratio spread position, or place stop loss levels a few points away from the key support and resistance that is filling in as the missing clipped wing to ensure the risk plan is followed through. However the need for a stop loss need not necessarily be warranted, depending on the size of the initial investment size. If the underlying is falling in a call ratio spread, the trader is assured that the loss is limited to the credit/debit on initiation, likewise when the underlying is rising in a put ratio spread where the risk is limited too. In those scenarios, a stop loss is not required since position will be in positive carry with positive theta. Likewise, if the lines are not breached and underlying is behaving as expected near key levels or areas of congestion, there is no need to exit from or scale out the position.

Say a trader is expecting a mild correction at the top of an up trend and he thinks the price movement will be slow to play out, taking at most 1 month to arrive to the body strike. However, the underlying moved towards the short strikes faster than expected and the trader is unnerved as the odds of having the position profit dwindling into unlimited loss is higher than before if happens the underlying breaks through the key support or resistance acting as the clipped wing.

There are 2 ways to handle this scenario of a threatened short strike:

- Capping the clipped wing to modify it into a butterfly
- short strike “rolled” away from underlying price to give the trader more breathing room
- 1:1 with vertical spreads
- 1:k with ratio spreads

That said, it cost least to transform a ratio spread (i.e. 1:2) to a butterfly with buying an additional call. To maintain a 1:2 ratio spread with an extended short strike requires squaring original shorts closer to money than when its sold OTM on strategy initiation, that is, its a loss to buyback your 2x 95 shorts unless sufficient time has passed that the theta earned more than offsets the expanded intrinsic value (very unlikely), and repeat, selling 2x OTM calls, now at a further price 100. This has cost on buybacking and initiation of 4 legs (commission + spreads). To avoid the cost required to extend the 1:2 ratio spread short strikes with buying 2x of vertical spreads, some traders will sell more OTM options to cover the cost of transforming the position or increase its profitability. That is, they sell more OTM 100 call options to just or more than compensate the cost aforementioned. However, its a martingale that doubles the ultimate risk to the upside.

### BackSpreads

Also known as volatility spreads, they are the exact opposite of ratio spreads, used to capture high magnitude, high velocity directional moves occurring in a short period of time. Yes, instead of selling multiple OTM options, it involves purchasing multiple OTM options underwritten by the sale of an nearer the money or ATM option of the same class and expiration cycle. Likewise, the higher the gearing ratio, the more profit (and loss) potential there is. Since there is more long options, greeks exposure profile carry the characteristics of a long option position, that is, long delta, long gamma, long vega, short theta, however, only around the long strike. And because the asymmetrical risk is underwritten by the sales of option at the other side of the underlying movement, it can be executed at a credit. But again, more profit potential means more gearing ratio.

In this case, vice versa to ratio spread, it will be long 2x 105 call, short 1x 100 call (nearer in the money). Its equivalent to selling a 100/105 1:2 call ratio spread and inherits characteristics from selling a butterfly or selling a call spread.

Likewise, its payoff is the direct opposite since its a sale of a ratio spread.

Call/Put ~~ratio~~ backspread Payoff

- Max Loss
~~Profit~~= (K2 – K1) + credit or – debit (to initiate spread) - Call Max Profit
~~Loss~~= Unlimited on upside, limited to initiation debit on underlying downside (None if credit on initiation) - Put Max Profit
~~Loss~~= Unlimited on downside, limited to initiation debit on underlying upside (None if credit on initiation) - Call Breakeven
- downside: K1 + initiation credit
~~debit~~(certainty OTM if debit~~credit~~on initiation) - upside: ([#shorts * long
~~short~~call strike] – [#longs * short~~long~~call strike]) / (#longs~~shorts~~– #shorts~~longs~~) + credit – debit

- downside: K1 + initiation credit
- Put Breakeven
- downside: ([#shorts * short put strike] – [#longs * long put strike]) / (#shorts – #longs) – credit + debit
- upside: K2 + initiation credit
~~debit~~(certainty OTM if debit~~credit~~on initiation)

For reference, its greek profile is exactly opposite to buying a call ratio or put ratio spread.

Because its asymmetrical risk-reward profile, a backspread has substantial profit potential on a large move in the delta of the option bought, a risk limited to its strikes difference when underlying is in-between the strikes, and the overall strategy credit or debit on a trend reversal (ratio expires on initiaion debit/credit on a trend resumption). This makes backspread, unlike a straddle/strangle that is delta neutral, a strategy favorable for playing low-probability, high-reward scenarios where there is a delta bias. That is, breakout scenarios that is large enough to move through both strikes and beyond the OTM strike bought. So if you have reasons to believe that there will be a strong upside directional move, supported by key support levels, you will initiate a call backspread (-1 +2). This equates to selling an ITM call option in expectation that it remains ITM, but selling more OTM call options in expectation that they will also be ITM such that, based on a higher gearing ratio, you will end up profitable. Its equivalent to a selling call (bull) spread with buying an additional OTM call of higher strike. Its equivalent to selling a put (bear) spread with buying an additional OTM put of lower strike.

Given that the position is positive vega at prices above the strike sold, IV should be steady-to-rising. Because backspread’s theta is negative, forecast breakout should take place as short a time as possible. There are no hard rules in breakouts, but typically, breakouts follow from either 1) a consolidation, trendless market or 2) a continuation “flag” on trend resumption. It could also be used when a large reversal is impending, say, on a overcrowded positioning where there is too many longs and no new buyers when holders wish to sell.

Likewise as ratio spreads, backspreads are actively managed in the same way as ratio spreads. If the breakout magnitude happened faster than expected, you can either take profit or if you think your initial forecasted magnitude is not large enough, you can **“roll” the call upper (put lower) strike further OTM** with either selling **2**x vertical spreads, or doubling down by selling **2 **ATM: buying 4 OTM call ratio spreads.

Between backspreads and ratio spreads, a few differences are that, on rolling the bought option strike further OTM, consideration to favor selling 2:4 ratio spread (or buying 2:4 backspread) over selling 2x vertical spreads is **more on gearing up the profit potential than on covering the cost of rolling** because here, we are squaring (selling) the original position that was OTM and now ATM, and buying cheap OTM options. Moreover, given an unlimited upside, no one would cap their profit potential to earn the premium of an additional OTM option, hence it will not transformed into a butterfly sold. Given backspread rolling is opening one’s position to more profit potential on top of being crediting, the trader needs to decide if he should be tempted to roll further, that is, whether he believes the trend or reversal has more to run.

Secondary considerations such as the IV skew also is a factor, as in ratio spreads. In the case of backspreads, it favors initiation of call/put backspread when the OTM call/put has a lower IV than the ATM/ITM call/put. That is, call backspread favors a normal reverse IV skew, while a put backspread favors a forward IV skew. Its vice versa for ratio spreads.