Feature: A premium's vol, or why there is none

Description: The vol a premium implies is found by inverting the price. Trust it only when it is computed: a premium with no time value is clamped, and one deep in the money near expiry is faint -- any vol prices it, so the number means nothing -- while the delta at that vol still holds.

File name: implied-vol.feature

Relative path: features/implied-vol.feature

Scenarios

Chart

Status Progress

Passed	100.00 %
Failed	0.00 %

Scenario Outline: The vol that priced a premium is the vol it implies

Given an SPX at 7500

And a rate of 0.045

Given a call struck at 7480

And 4 days to expiry

And a vol of 0.18

Then the implied vol recovers the vol that priced it within 0.00000001

Scenario Outline: The vol that priced a premium is the vol it implies

Given an SPX at 7500

And a rate of 0.045

Given a put struck at 7480

And 4 days to expiry

And a vol of 0.18

Then the implied vol recovers the vol that priced it within 0.00000001

Scenario: A premium with time value implies its vol

Given an SPX at 7500

And a rate of 0.045

Given a call struck at 7500

And 4 days to expiry

And a premium of 58.2131620126

When the vol it implies is sought

Then the implied vol is computed

And the implied vol is 0.18 within 0.0001

Scenario: A premium at intrinsic is clamped, and its delta still holds

Given an SPX at 7500

And a rate of 0.045

Given a call struck at 7300

And 0.27 days to expiry

And a premium of 200

When the vol it implies is sought

Then the implied vol is clamped

And the delta is 1 within 0.005

Scenario: A worthless premium is clamped, and its delta is nothing

Given an SPX at 7500

And a rate of 0.045

Given a call struck at 7550

And 0.27 days to expiry

And a premium of 0

When the vol it implies is sought

Then the implied vol is clamped

And the delta is 0 within 0.005

Scenario: Deep in the money near expiry the vol is faint, and the delta holds

Given an SPX at 7500

And a rate of 0.045

Given a call struck at 7300

And 0.27 days to expiry

And a premium of 200.2428296367

When the vol it implies is sought

Then the implied vol is faint

And the delta is 1 within 0.005