The Curve

by s7ven

The Right · Options

Pricing and risk

Volatility, the sensitivities derived from a pricing model, and the obligations that arrive at expiry.

6 terms

Implied volatility across strikes A curve plotting implied volatility against strike price. It is highest at low strikes, falls to a minimum slightly above the money, and rises modestly at high strikes, producing an asymmetric smile. HIGH LOW IMPLIED VOLATILITY AT THE MONEY PUTS BID UP CALLS STRIKE →
A single-volatility model predicts a flat line here. Equity index markets have not produced one since 1987. The usual explanation is steady demand for downside protection, which bids up the price of low strikes, and price expressed in volatility units is what implied volatility is.
Implied volatilityIV

The volatility figure that, put into a pricing model, returns the option's current market price.

It is a statement about price expressed in the units of volatility, not a forecast issued by anyone. Saying IV is high is another way of saying options are expensive.

See also skew
The Greeks

Sensitivities of an option's price to its inputs. Delta to the underlying's price, gamma to delta itself, theta to time, vega to implied volatility, rho to interest rates.

They are model outputs and inherit that model's assumptions. They are also instantaneous, describing the present moment rather than the whole range of moves an underlying might make.

Theta

The rate at which an option's extrinsic value declines as time passes, all else held equal.

Decay is not linear. It accelerates as expiry approaches, and it is concentrated in options near the money.

Skew and the smile

The pattern of implied volatility varying across strikes at the same expiry, rather than being flat as a simple model would predict.

The shape became pronounced in equity index options after the 1987 crash, and is generally attributed to persistent demand for downside protection.

Exercise and assignment

Exercise is the holder invoking their right. Assignment is the resulting obligation being delivered to a short holder, selected by the clearing house.

American-style options can be exercised any time before expiry, so a short position can be assigned without warning. European-style options can only be exercised at expiry.

Pin risk

The uncertainty a short option holder faces when the underlying settles very close to the strike, leaving assignment unpredictable.

The position is neither cleanly expired nor cleanly assigned until after the market has closed, which is precisely when the resulting exposure cannot be hedged.