Odd-lot mini-option hedges versus implied volatility

A mini-option for an odd-lot holding

Scaled equity options introduced in March 2014 were specified as one-tenth the value of a standard contract and referenced 10 shares. That size let an odd-lot holding take an overlay without buying more stock to reach a 100-share lot.

After about a year of listing, most volume in those scaled contracts was concentrated in Apple, Amazon, Google, a gold exchange-traded fund, and a broad-market exchange-traded fund, rather than across every odd-lot name.

Three overlays on ten Google shares

A covered-call case on 10 Google shares bought at 500 sold a one-month 500-strike scaled call for 30 of premium. That credit remained if the shares expired at 500, but a jump to 600 still required delivery at 500.

A married-put case bought a one-month 500-strike scaled put for a little less than 10 points to cover about 5,000 of stock for 30 days. A rise to 600 left about 90 points after the premium, and a 100-point decline still allowed sale at 500, while a sideways path consumed the protection cost.

A collar on the same 10-share lot combined the long put and the short call so that protection and leftover upside were both limited.

Full-lot diagrams as a scale model

Full-contract payoff diagrams were treated as a ten-times scale model. Costs and risks for 10 shares plus one scaled contract were read by removing about 90 percent from the full-size prices.

A single overlay in a market-regime block

The same issue placed single-position overlays inside a recurring market-regime block that included index-option volatility skew, sentiment extremes, and put-call ratios.

Expected return and the Black-Scholes calculator

An expected-return worksheet treated average profit or loss as meaningful only across many trades. It required historical volatility on the underlying line and implied volatility on the option line, including multi-leg spread quantities.

Implied volatility was to be compared with prior composite implied-volatility readings rather than used as an isolated level.

A pricing calculator recovered implied volatility from strike, underlying price, and historical volatility with a Black-Scholes engine. It reported greeks across many stock-and-strike pairs and plotted profit-and-loss under a lognormal price assumption at expiration and at earlier dates.