Paradigm Insights | Save The Date: A Comprehensive Overview of the Calendar Spread Options Strategy

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December 7, 2022



In our previous article, we explored butterfly spreads and their various applications. Butterflies are a versatile way to take a stance on both directionality and volatility in a manner that is significantly less risky than strategies like straddles or strangles. While the lower risk imposes a cap on the potential payout, note that reducing risk often entails sacrificing some upside optionality in multi-legged structures.

Similar to butterflies, calendar spreads also can be multifaceted structures allowing for dynamic implementation within a portfolio for potential profits from a wide range of market conditions. This versatility can be enhanced by modifying the structure, such as altering the strike which transforms the spread into a diagonal.

What is a Calendar Spread?

Calendar spreads, also known as horizontal spreads or time spreads, are a multi-legged option strategy that differs from most structures in several ways, with the most salient distinction of this structure is the utilization of two distinct expiry dates. In contrast to the butterfly strategy previously discussed, calendar spreads involve options that expire on different dates. These spreads are constructed by incorporating opposing positions in two options of the same type (both puts or both calls) with the same strike price and different expiries. For example, one may sell the December 30th 20K strike BTC call and purchase the January 27th 20K strike BTC call and be considered “long” a calendar spread.

Traders are considered "long" the structure when the longer-dated (back-month) option is bought and the short-term (front-month) option is sold, resulting in a debit. Conversely, traders are "short" the structure when the longer-dated option is sold and the short-term option is bought, resulting in a credit. Calendar spreads are typically executed in a 1:1 fashion, but they can also be implemented in a ratio-like manner. For the purpose of this article, we will exclusively focus on 1:1 calendar spreads consisting of the same strike..

Why would someone use a calendar spread?

Traders may use a calendar spread for a variety of reasons. The calendar spread is unique in that it implements two of the same options and strikes across different expiries, which allows for a few other use cases. Some of the most popular use cases include generating income, trading volatility term structure, and even taking a slight view on direction. In more detail:

1. Generating Income

Generating income is a popular use of calendar spreads among retail and professional traders. The income-generating potential of a long ATM calendar spread stems from the inherent positive theta of the position. Traders who enter a short position in a front-month ATM call and a long position in a back-month ATM call initially pay a debit, which may seem counterintuitive for traders seeking to generate income. Why would someone pay to enter a position in order to generate income, instead of simply receiving an initial credit by selling something like a covered call?

If you think about it, that’s essentially what this strategy is doing, but without the need to own the underlying to protect yourself. By holding a long position in the back-month ATM call and keeping the strikes constant, if the underlying were to reach the strike price and be exercised, the trader would be theoretically long the underlying shares at the strike price. This would enable the trader to pay back the short position if necessary, or at least ensure that the value of the long option is always greater than the value of the short option. In this way, a calendar spread allows the trader to take a similar stance to a covered call seller without owning the underlying asset.

The effectiveness of this approach in a calendar spread is due to the properties of theta. The shorter-dated ATM option decays faster than the longer-term ATM option. The optimal outcome occurs when the underlying is at the short strike when the short-term option expires. At this point, the long option has its highest value, while the short option expires without the trader being assigned.

The diagram below shows an ATM Calendar P/L chart with the red line at expiry and the green at inception. Essentially what happens is at expiry if spot trades at the strike level, the short option expires worthless and your spread value is whatever the value of the remaining naked long option is. After expiry, traders will typically roll/short a new option expiring before the long strike to continue to earn credit.

It’s challenging to interpret a P/L diagram at expiration of a calendar spread because of the staggered expiration months. As an example, for the long calendar spread, the maximum loss will always be the debit paid for the spread. If the underlying is below the short front-month strike, the call becomes worthless, and the long back-month option may or may not retain some residual value. If the underlying is above the strike at expiration, the front-month call will be equivalent to a short underlying position, and the long call will be equivalent to a long underlying position. The final P/L will depend on interest rates and borrowing costs, but will be slightly less than the maximum loss.

2. Trading Term Structure

Example Term Structure

The term structure of the implied volatility surface often exhibits abnormalities and tradable opportunities. Volatility trading, at its core, is no different from directional trading. Traders aim to "buy low, sell high," but instead of focusing on price, they are more interested in implied volatility. The idea is to buy the cheap month in terms of implied volatility and sell the expensive month. While this strategy may sound simple, as with most seemingly straightforward trades, the devil is in the details.

Backwardation and contango are two descriptors of term structure that are essential to understand. Backwardation is when the front-month implied volatility is higher than long-dated volatility, and typically indicates a market in distress, as market participants position themselves for short-term moves in the underlying. In contrast, contango is when short-dated implied volatility is lower than that of longer-dated implied vols, and in such a scenario market participants may be complacent and sell short-dated options for additional yield.  This drives down demand for short-dated options and causes longer-dated options of the same strike to trade at higher levels of implied volatility due to increased uncertainty between the time of inception and the longer-dated options.

In an environment where the term structure of volatility is steeply downward-sloping, traders may engage in a volatility trade known as a "calendar spread" by selling front-month options and buying longer-dated options, effectively selling expensive (ie. high volatility) short-dated options while buying cheap (ie. low volatility) long-dated options. Alternatively, if the term structure is upward-sloping, traders may enter into a calendar spread by buying front-month options and selling longer-dated options. This trade sounds like a straightforward way to take a view on volatility, but we will cover the specific view and actual risks shortly.

3. Taking a directional bet

OTM Calendar Spread P/L (Red Expiry, Green Inception)

The previous two examples have leveraged ATM options as the contract of choice for their use cases. These structures may have a slight delta, but there’s a way to significantly shift the bet to be more directional rather than range bound. One can use an OTM strike, and due to the properties of time to expiry and delta, the delta, and hence directional bias, will become more prevalent. 

An OTM strike for shorter-dated options will have a lower delta, while the same OTM strike for a longer-dated option will have a much higher delta. Entering a long OTM calendar spread will thus create a more directionally biased position than a long ATM calendar spread more typically utilized for generating income.

What view are traders taking?

It is  difficult to look at the Greeks associated with a calendar spread and reasonably assume what someone may want to happen in the underlying market, especially relative to other strategies ​​such as butterflies. This ambiguity makes calendar spreads more involved when attempting to discern the underlying thesis, as it can contradict the Greek profile upon first glance.

To further explain, we recap the three examples we discussed and analyze what market conditions may be optimal for implementing this strategy.

Generating Income

Traders hoping to generate income through a long calendar spread are hoping for range-bound, minimal movement around the current ATM strike price. As time passes, the delta will flatten out for an ATM spread as the front-month, and back-month deltas start to converge to +0.5 and -0.5. Gamma and theta both begin to rise as the underlying stays around the strike – as expiration approaches, there is greater risk if there is movement and a greater reward paid through theta if not. 

Traders who utilize this strategy will typically continue to roll their short front-month call multiple times and will continue to reap the rewards of theta if the underlying remains the same over a more extended period. At some point, rolling calendar spreads can eventually lead to free optionality – although it is not necessarily “free,” as it represents compensation for the monthly risk taken on the short leg. An example of this is a trader may be long a six-month to a one-year option and continuously shorting one-month options, as theta decay for an ATM option is greatest with the shorter-dated options.

Trading Volatility Term Structure

Traders wanting a pure way to trade the differences in implied volatility between expiries (term structure) can put on a similar trade depending on the current shape of the term structure, whether in contango or backwardation. Traders looking to take advantage of one-off event volatility may implement these trades as well. 

One may think that an increase in volatility may lead to sharp increases in profit; however, the constructed short-gamma position would prefer very little or no movement until expiry to collect theta. Additionally, the way the time-volatility dynamic typically plays out means that one may see an increase in longer-dated volatility, but it would also typically be followed by a much more significant volatility increase in the front-month option, leading to potential losses on the short front-month call that are greater than the profit on the long back-month call.

Traders who trade term structure through strategies like long calendar spreads are hoping that near-term volatility declines while longer-dated volatility is stickier, allowing them to make more on the short Vega from the front-month call than they lose on a drop in volatility in the back-month.

When trading volatility through a calendar spread, keep in mind the relationship to time and the underlying market dynamics that occur. For example, a scenario in which the back-month trades at a premium may represent a collective sense of complacency in the short term, leading traders to sell front-month options in bulk and pushing down IV in the front-month options more than in the back. Another scenario in which back-month volatility could trade higher is when the market expects higher movement after the front-month expiration but before the back-month expiration. A crypto-specific example would be during the Ethereum merge in which September 23/30th calls traded at a significant volatility premium to the September 9th calls, where the same weekly/bi-weekly expiration difference in the September 23/30th and October 7th/14th expiries were much smaller.

This graph shows the current Forward IV of the 12/16 expiry options that include the FOMC and CPI print. The weekly expiry shortly after show a decline. Kinks like this are opportunities term-structure traders would look for, but need to be aware the kink exists in this case for a reason - the events.

Pre-Merge options showing significantly lower IV than directly post-merge options.

Taking a directional bet

Traders taking a directional bet through a long OTM calendar spread should be aware of the risks previously described and note that negative gamma will be important to strategically position around. Those placing a directional bet via a long OTM calendar spread want some directional price movement, but not too much. It’s also important to note that directional bets can be positioned through ITM or OTM strikes, but deeper ITM options may tend to have wider bid-ask spreads. This bid-ask width can be a guiding factor for choosing between implementing a call or put calendar on the underlying based on the moneyness of the strike selected. ITM calendars also face assignment risk for American-style options and can impact and complicate their implementation as dividends and interest come into play in other asset classes.


Since the overall Greek portfolio may be misleading for understanding how these positions profit, it is more insightful to understand the underlying market conditions and how implied volatility can be impacted.

The Greeks of a Long Calendar Spread are shown below; however, the intuition established earlier is much more critical to understand. 

*In the graphs below, solid lines represent at inception, and dotted lines represent in the future (as time to expiry decreases) with the center of the X axis representing an ATM option.

Long ATM Calendar Spread: Delta vs Price

Long ATM Calendar Spread: Gamma vs Price
Long ATM Calendar Spread: Theta vs Price

Long ATM Calendar Spread: Vega vs Price


In summary, calendar spreads allow traders to take positions oriented around directional movement, realized volatility expectations, and implied volatility, and involve two expirations to allow bets on the volatility spread between different months – making calendar spreads an efficient and unique way to trade volatility term structure.

Because calendars are two-legged spreads, giving up edge by legging into two positions separately should be heavily considered. Paradigm allows spread trading through a Global RFQ platform, minimizing the execution risk and maximizing the ease and efficiency of implementing spread trading.

Article by
Chris Newhouse @CryptoDeFiGuy
Chris Newhouse is an OTC Trader at GSR, a crypto native market-maker that specializes in providing liquidity across spot and derivatives markets. He is interested in the growth and development of the crypto options market, and stays up to date with trends and projects related to DeFi derivatives. Additionally, he is a recent graduate from Georgia Tech and is the Founder of their Quantitative Trading Club and a Co-Founder of their Blockchain organization.

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