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2008issue C111

Ratio write delta adjustment when the tape rises

A two-to-one ratio write owns 100 shares and sells two near-the-money calls. The archive walk-through prices those calls from historical volatility, interest rates, and time, then resets the book from model delta when an early rise turns net share-equivalent short.

  • A two-to-one ratio write owns 100 shares, sells one near-the-money call against those shares, and sells a second near-the-money call.
  • Historical volatility, interest rates, and days until expiration help choose the calls and assign each option a delta, scaled so 100 shares equal 100 delta.
  • A book that starts near delta-neutral can become short 50 or more delta if the stock rises, with listed responses of buying another 100 shares, closing the extra short call, or rolling it.
  • Forward projections a few days to a week ahead estimate net delta at different strikes, and conversion pricing is the next step after Black-Scholes-style valuation of the same inputs.
Entries in this reading3 entries
Current trackBlack-Scholes Model20 readingsDelta hedging31 readingsCovered call writing53 readings

A two-to-one ratio write is described as owning 100 shares, selling one near-the-money call against those shares, and selling a second near-the-money call.

The share-backed short call is covered-call writing. The extra short call leaves more short calls than those shares can cover, which is the ratio-write structure.

Pricing inputs, implied volatility, and delta

The pricing inputs named for choosing which calls to sell are historical volatility, interest rates, and days until expiration.

Implied volatility taken from observed call and put prices can be compared with historical volatility to look for a large gap.

Each option is assigned a delta from those pricing factors, on a scale where 100 shares equal 100 delta. The Black-Scholes model is the baseline that turns volatility, interest rates, and time to expiration into theoretical value and delta.

An early rise can turn the book short

An example that can start near delta-neutral is long 100 shares at 32 and short two near-term 35-strike calls.

If the stock rises to 34, that book can become short 50 or more delta.

Listed ways to reset the extra short call

Delta-hedging changes stock or option holdings to keep net delta near a chosen target as the underlying and time change.

Listed responses to an early rise include buying another 100 shares to create two covered calls, closing the extra short call, or rolling that call, using the contract that looks misvalued on the same criteria.

Forward net delta, time decay, and conversion

Forward projections a few days to a week ahead are used to estimate net delta at different strikes. Time decay is treated as helpful for the short-call side of the example.

Premium is distinguished from value. Conversion pricing, long stock, short call, and long put, is presented as a next step after Black-Scholes-style valuation of the same inputs.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
13 of 18 in the Black-Scholes Model track
201046-55 pp.Next on Black-Scholes ModelExpiration-dated volatility cones as portfolio contextImplied volatility was the market-implied width used both to price the option and to draw a probability cone.
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
By fieldOptions and volatility435 readingsBy year2008150 readings
All 20 readings tagged Black-Scholes Model
Also on Black-Scholes Model5 readings
2019Black-Scholes construction from a covered-call balance sheet1988Constructing option premiums against a Black-Scholes baseline1988Critiquing Black-Scholes early exercise on futures options1989Limit fills around option fair value1990When volatility skews are regimes, not mispricings