Calendar Spread Value at the Near-Dated Option’s Expiry
Summary
The document considers a calendar spread that is short a call expiring first and long a call with the same strike expiring later. At the first expiry, the short call’s payoff is determined by the stock price, while the remaining long call still has time value. Its value is therefore a function of the stock price at that date, rather than a payoff that can be fixed in advance from the current price alone.
The response characterizes the spread’s value as the remaining option’s time value: its market value less intrinsic value. It describes this value as greatest around the strike and lower when the stock is far below or above it, explaining why the spread’s expiry profile depends on where the stock finishes. The discussion also notes that a calendar spread can appear inexpensive when the volatility term structure is inverted, while its outcome remains sensitive to the stock ending near the strike. It offers conceptual guidance, not a full pricing formula or treatment of rates, dividends, and volatility dynamics.
Key ideas
- At the short call’s expiry, the longer-dated call still has time value.
- The remaining call’s value depends on the stock price at the near expiry and cannot be known beforehand.
- The spread’s value reflects the remaining option’s value after accounting for intrinsic value.
- The described profile is strongest near the strike and weaker when the stock is far from it.
- An inverted volatility term structure may make the spread appear inexpensive, but does not remove its price-path sensitivity.
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# Calendar spread pricing: how find the final value of call long
# Calendar spread pricing: how find the final value of call long
Consider a calendar spread: short a call expiring at $T_1$ and long a call expiring at $T_2$ ($T_2>T_1$).
I didn't understand how estimate the price of the long call option at $T_1$. With a payoff like this $\left( c_1 - \max \left\{ S_{T_1} - K, 0 \right\} \right) + \left( -c_2 + Z \right)$, how can i find $Z$ as I don't know the future spot price?
Updated
$Z$ should represent the value of the call long but i don't understand how determine it if at $T_1$ (expiry of the short call) we don't know the future stock price yet.
From Hull-Treepongkaruna: "To understand the profile pattern from a calendar spread, first consider what happens if the stock price is very low when the short-maturity option expires. The short-maturity option in worthless and the value of the long-maturity option is close to zero". Again: "Consider next what happens is the stock price $St$ is very high when the short-maturity option expires. The short-maturity option costs the investore $St-K$ and the long maturity option is Worth a little more than $St-K$, where $K$ is the strike price of the options." Or: "If $St$ is close to $K$, the short-maturity option costs the investor either a small amount or nothing at all."
How can Hull say this? Maybe writing $Z=F(t_2)=S_{t1}e^{(r(t2-t1))]}$ so that payoff in $t_1$ can be interpreted $[c1-\max(S_{t1}-K,0)]+[-c_2+\max(S_{t1}e^{(r(T2-T1))}-K,0)]$ or in $t_0$ $(C_1-F(T_1)-K)+(-c_2+F(T_2)-K)$?
Excuse for the formules: $r(T_2-T_1)$ is the exponentation.
## Answer by dm63 (score 1)
https://quant.stackexchange.com/a/37402
Conceptually , the value of a calendar spread at T1 equals the "time value" of the remaining option. The time value equals the total value minus the intrinsic value. This time value is obviously a function of S(T1) and looks like a bell shaped curve centred on K. The expected value of the calendar spread at T1 could be found by taking the value at t < T1 (obtained from a model such as BS) and multiplying by exp (T1-t).
The calendar spread "looks cheap" if the volatility surface is inverted (long dated options cheaper than short dated). However you will only win if the stock price is near K at T1 .Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.