Delta, Vanna and Charm Exposure: Option Greeks in Dollars

Delta exposure is the dollar amount of stock that all open options on a security behave like. Vanna exposure is how much that amount changes when implied volatility moves by one point, and charm exposure is how much it changes as one day passes. Vyreon reports each for calls and puts, plus a conventional net figure that depends on an assumption about who holds the options.

What Is Delta Exposure?

An option's delta is how much its price moves for a $1 move in the stock. A call with a delta of 0.5 behaves like half a share. Delta exposure adds this up across every open contract and expresses it in dollars of the underlying:

Delta exposure = Σ open interest × delta × 100 × S

where S is the share price and 100 is the standard number of shares per contract.

Illustrative example: 1,000 open calls with a delta of 0.5 on a $100 stock behave like 50,000 shares, or $5,000,000 of stock.

What Is Vanna Exposure?

Vanna is how an option's delta changes when implied volatility changes. Vanna exposure is the change in dollar delta exposure for a one-point rise in implied volatility (for example, from 20% to 21%), in US dollars of delta per volatility point. It answers: if options were priced as more volatile, how much more or less stock would these positions represent?

What Is Charm Exposure?

Charm, sometimes called delta decay, is how an option's delta changes as time passes with the price and volatility unchanged. Charm exposure is the change in dollar delta exposure over one calendar day, in US dollars of delta per day. In the Black–Scholes–Merton model it grows as expiry approaches, for contracts near the money whose deltas shift quickly as time runs out.

Per Side And Conventional Net

For each Greek, Vyreon publishes:

Calls: the total across open call contracts.
Puts: the total across open put contracts.
Net, conventional: a single figure that assumes dealers (market makers) are long the calls and short the puts.

The call and put totals need no assumption. The net figure does: open-interest data does not show who holds which side, so dealer positions are not observed. Vyreon states the assumption next to every net number. The same convention underlies net gamma exposure and the gamma flip.

How Vyreon Measures It

Contracts: every listed contract with open interest that expires after the session and whose implied volatility can be solved from its closing quote.
Open interest: as of the previous session's close.
Implied volatility: solved for each contract from its closing quote at the session's unadjusted closing share price, with the federal funds rate and a carry inferred from the same option chain.
Greeks: Black–Scholes–Merton with those inputs.
Units: delta in US dollars of the underlying; vanna in US dollars of delta per volatility point; charm in US dollars of delta per calendar day.
Multiplier: 100 shares per contract.

What It Does Not Tell You

Who holds the options. Net figures are conventions built on an unobserved assumption, and can have the wrong sign if that assumption fails.
Whether anyone hedges these exposures, or when.
Where the price is going. These are descriptions of open positions at one close, not forecasts.
Changes during the day. Open interest updates once a day, and the Greeks are computed at the close.

Sources

Fischer Black and Myron Scholes, "The Pricing of Options and Corporate Liabilities", Journal of Political Economy (1973), and Robert C. Merton, "Theory of Rational Option Pricing", Bell Journal of Economics and Management Science (1973): the pricing model behind the Greeks used here.
John C. Hull, Options, Futures, and Other Derivatives (Pearson, many editions): delta and the other Greeks.
Espen Gaarder Haug, The Complete Guide to Option Pricing Formulas (2nd ed., 2007): formulas for second-order Greeks, including vanna and charm.

Net delta, vanna and charm exposure, and the dealer-positioning assumption behind them, are market conventions; we know of no peer-reviewed source establishing the assumption.