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2002issue C101

Calendar income from volatility skew and time stops

The archive case builds a same-underlying calendar that sells a nearer month richer in implied volatility than the purchased month, prices each leg with the model that matches the underlying, and, once a credit or debit spread is on, exits on a time stop that leaves residual life in the long option.

  • Calendar-spread results in the described case depend more on the volatility of the options used than on sideways movement in the underlying.
  • The calendar sells a nearer month whose implied volatility is higher than that of the purchased month and treats that gap as mean-reverting.
  • After a credit or debit spread is on, the money-management rule uses a time stop rather than a price stop and plans the exit with residual life in the long option.
  • Stock-option legs use a Black-Scholes model with a dividend adjustment. Futures-option legs use a Black model that omits dividends.
Entries in this reading3 entries

How the case organizes the trade

The archive describes a calendar that sells one expiry and buys another on the same underlying. Remaining value in the long option and the volatility gap between months drive the outcome. Options appear as a defined-risk overlay relative to an existing stock system, with the entry, the exit, and the choice not to enter handled as one sequence.

Enter from the sold-versus-bought volatility gap

The described calendar sells a nearer month whose implied volatility is higher than that of the purchased month. That listing state is the volatility skew used for entry. The case treats the gap as mean-reverting.

Volatility can matter more than a quiet underlying

Calendar-spread results in the described case depend more on the volatility of the options used than on sideways movement in the underlying. Rising implied volatility can support the calendar because remaining value sits in the purchased longer-dated option. An upward or downward break in the underlying can leave the calendar intact when the long option still embeds a view of future conditions.

Match the pricing model to the underlying

For stock options, the Black-Scholes model includes a dividend-adjustment input because the dividend affects the stock price and, through delta, the option price. For futures options, the commonly cited pricing form is a Black model that does not include dividends.

Use a time stop after the spread is on

After a credit or debit spread is in place, the described money-management rule uses a time stop rather than a price stop. The exit is planned with residual life, illustrated as at least 30 days to expiration, so remaining premium is left in the long option.

Compare the overlay before replacing the stock system

The case treats options as a complement to an existing stock system only after comparing reward-to-risk with the original stock procedure. It notes that day-horizon replacement is limited by liquidity, the bid-ask spread, and commissions. Expiration-month cycles are described as a device to limit simultaneous option symbols. Listing every month for every optionable stock would expand that symbol set by at least a factor of four.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
7 of 18 in the Black-Scholes Model track
20031-3 pp.Next on Black-Scholes ModelConstructing option value from historical and implied volatilityA listed call is the right to buy, and a listed put the right to sell, at a stated strike price on or before a stated expiration. One standard equity contract covers 100 shares, so the cash amount is the quoted premium multiplied by 100.
All readings on this track · 18 readings
  1. 1988Critiquing Black-Scholes early exercise on futures options
  2. 1988Constructing option premiums against a Black-Scholes baseline
  3. 1989Limit fills around option fair value
  4. 1990When volatility skews are regimes, not mispricings
  5. 1994Estimating closeout value on a Treasury bond options strangle
  6. 1996Constructing option theta from premium, volatility, and moneyness
  7. 2002Calendar income from volatility skew and time stops
  8. 2003Constructing option value from historical and implied volatility
  9. 2004Calendar construction from exercise style, time budget, and carry
  10. 2005A mid-life payoff chart is a volatility-regime assumption
  11. 2005Exotic option payoffs beyond the vanilla premium
  12. 2006Auditing index volatility inputs in call income studies
  13. 2008Ratio write delta adjustment when the tape rises
  14. 2010Expiration-dated volatility cones as portfolio context
  15. 2015Auditing buy-write recovery overlays against pricing and scenario breaks
  16. 2015Odd-lot mini-option hedges versus implied volatility
  17. 2018Implied volatility as an option-premium construction gauge
  18. 2019Black-Scholes construction from a covered-call balance sheet
All 20 readings tagged Black-Scholes Model
Also on Black-Scholes Model5 readings