Evaluating long-put moneyness when implied volatility shifts

Strike choice as an evaluation

Editorial framing: treat strike selection as a testable evaluation of a long-put plan. A long-put here is a purchased European put on a broad stock-index underlying, evaluated as a directional holding through an expected decline.

The archive workflow compares theoretical percentage outcomes across percent-moneyness under an assumed move, an implied-volatility path, and a stated holding window. Editorial reading: use the finished percent-moneyness-percent-profit-curve only as a regime-aware guide for when out-of-the-money puts beat deeper strikes.

Percent-moneyness

Percent-moneyness is how far in-the-money an option is as a percentage of spot. The signed reading is positive when the option is in-the-money, zero when it is at-the-money, and negative when it is out-of-the-money.

The same definition is applied to every strike so that in-the-money, at-the-money, and out-of-the-money puts sit on one scale.

How the curve is built

A percent-moneyness-percent-profit-curve is built by valuing the same European index option at the start and end of an assumed trend with a pricing model, converting the two prices into a percentage change, and repeating the calculation across strikes while keeping time-to-maturity fixed.

European index put and call fair values can be computed from spot, strike, the continuous risk-free rate, time-to-maturity as a year fraction, and annualized volatility. The continuous rate is linked to the nominal annualized rate by a natural-log transform.

Implied-volatility is the annualized volatility input used to value the option at the start and end of the assumed trend. Time-to-maturity is the remaining life at the start of that trend and is held constant while strikes are compared.

Critical points on a typical put curve

On the typical curve for puts in a downtrend with rising implied-volatility, two critical points appear. Optimal-moneyness is the percent-moneyness that produces the highest theoretical percentage profit under the assumed path. Breakeven-moneyness is the least percent-moneyness that still avoids a theoretical loss even when the market moves in the option's favor.

Those two critical moneyness levels depend mainly on the percentage market move, the change in implied-volatility over the trend, the starting implied-volatility level, and the option's time-to-maturity.

A spreadsheet implementation

The evaluation can be implemented as a multi-sheet spreadsheet. User parameters include starting implied-volatility, days to maturity, expected spot change, starting spot, and expected implied-volatility change.

How to read the curve

Theoretical curves should be read dynamically as raw guidance for choosing out-of-the-money versus in-the-money options, not as precise profit or exact optimal-moneyness readings.

When cheaper puts look better

When theoretical curves favor out-of-the-money puts, a conservative allocation can still split risk between those cheaper puts and at-the-money puts rather than treating strike choice as all-or-nothing.