Every spread so far used one expiration. A calendar spread uses two, at the same strike: sell the nearer expiration, called the front, and buy the further one, the back. Same strike, same type, different dates.
What you pay and why
At the same strike the back month always costs more than the front, because it has more time. So a long calendar is a debit. With a stock at $150, the 30-day $150 call at $4.00 and the 60-day $150 call at $5.80, the calendar costs $1.80. That is the most you can lose if you hold it to the front expiration.
The trade makes money if, when the front expires, the back option is worth more than $1.80. That happens when the stock is near $150: the front expires worthless and the back still carries good time value. It loses if the stock runs far either way, because then both legs are deep in or deep out of the money, the difference between them shrinks toward zero, and the debit is gone. Plot the value at the front expiration and it is a tent like a butterfly, peaking at the strike. Unlike the butterfly, its height is not fixed. It depends on what the back month's volatility is at the time.
What you are long and short
The front option decays faster per day than the back one, because theta is steepest near expiration. So a long calendar collects time decay: it is long theta. It is also long vega, because the back option has more vega than the front. Both facts come from one chart.
One at-the-money $100 call against days to expiry. Hover at 30 and 60 days for the two legs of a calendar: the back has more vega, the front has more theta. Switch between vega and theta to read both.
Read the vega line at 30 days and at 60 days: the 60-day option has more, so owning it and selling the 30-day leaves you long vega. Switch to theta and read the same two points: the 30-day option loses more per day, so selling it and owning the 60-day leaves you collecting decay. That is the volatility view inside a calendar. You want the front to decay quickly, and you want the back month's implied volatility to hold or rise. If the whole term structure drops, the back leg you own loses more than the front leg you sold gains, and the position loses even with the stock pinned at the strike.
The front-to-back ratio
Plot at-the-money implied volatility against days to expiry and you get the term structure. Divide the front expiration's at-the-money implied volatility by the back's. Below 1.0 is the normal shape, an upward term structure: the market charges more vol for more time. Above 1.0 the front is priced higher than the back, an inverted term structure, which happens when a near-term event is expected or after a shock. A long calendar sells the front, so it likes a high ratio: sell the expensive near vol, own the cheaper far vol.
At-the-money implied volatility by days to expiry. It starts upward, front below the long-run level. Drag front-month volatility above the long-run level to invert it: that is the shape a long calendar wants to sell into.
The same ratio tells you the calendar's risk. If the front is high because of earnings, the front vol collapses after the event and the calendar usually wins. If the front is high because the stock is in free fall, the move itself can blow through the strike, and no amount of front decay makes up for a back option that has gone deep out of the money.
Earnings inside the front month
An earnings date is a known day on which the stock is likely to jump. Every expiration after that date has to price the jump, but the jump is one day's move spread over the option's whole life. For a short-dated option that is a big share of its total movement, so its implied volatility rises a lot. For a long-dated one it is a small share, so its implied volatility barely moves. The result is a bump in the term structure just after the event, largest in the first expiration that includes it.
Earnings on day 20, pricing a 6% one-day move. Expirations just after it jump; later ones barely move. Drag the earnings move to zero to see the bump vanish, which is what happens to the front leg the morning after the report.
The classic earnings calendar sells the first expiration after the report and buys a later one. The day after the report the event is gone, the front vol drops back to the grey line, and the back vol drops only a little. The risk is the move itself: a jump larger than the market priced sends the stock away from the strike and flattens the tent.
The maths: a calendar's vega and theta, worked through
At the money, with little in rates, an option is worth about 0.4 × S × v × √T, its vega per vol point is about 0.4 × S × √T / 100, and its theta per day is about -0.4 × S × v / (2 × √T) / 365. Take a $100 stock, 30% vol, a 30-day front and a 60-day back. √T is 0.287 and 0.405.
Prices: front 0.4 × 100 × 0.30 × 0.287 = $3.44, back 12 × 0.405 = $4.86, debit $1.42. Vega: front 0.115, back 0.162, so the calendar is long 0.047 per vol point. Theta: front 12 / 0.574 / 365 = $0.057 a day, back 12 / 0.810 / 365 = $0.041, so the calendar collects about $0.016 a day. If both months drop 2 vol points the position loses 2 × 0.047, about $0.09, which is nearly six days of net theta. If only the front drops, as it does after earnings, the short leg gets cheaper and the calendar gains. At the front expiry with the stock still at $100, the back has 30 days left and is worth about $3.44 at an unchanged 30% vol, against the $1.42 paid.
The earnings bump works on variance, vol squared times time, which adds up across days. An event with a one-day standard move of e lifts an option expiring T years later from base vol b to √(b² + e² / T). With b = 30% and e = 6%, a 20-day option (T = 0.055) goes to √(0.09 + 0.0036 / 0.055), about 39%, while a 120-day option goes only to about 32%.
Your turn
Open MSFT. Read the at-the-money IV on the monthly chain, then on the following monthly. Divide them for the ratio and check it against the Calendar Spread panel. Then price the calendar itself: the back call mid minus the front call mid at the shared at-the-money strike.