Digital skew adjustment
Definition · Level 12 · Exotics & structured
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A digital call is a call spread squeezed to a point, so its price depends on the slope of the smile. With the usual equity skew (higher volatility at lower strikes) it is worth more than flat-volatility Black–Scholes says.
Example
A digital call on a stock index is quoted a little above its flat-volatility value.
Where Tradecraft teaches it
Level 12 · Exotics & structured, in the lesson “Digital options: the yes/no bet”: A digital pays a fixed prize or nothing: price it with N(d2) and hedge it with a call spread.
Related terms
- Call-spread overhedgeHedging a short digital with 1/ε of the (K − ε)/K call spread, so the hedge never pays less than the digital does.
- Digital optionBinary payoff: a fixed prize if the underlying finishes beyond the strike, nothing otherwise.
- Asian optionAverage-price option: its payoff uses the average of the price on a set of dates, so it is less volatile and cheaper than the vanilla.
- Autocall barrierThe level, usually 100% of the starting level, at or above which the note is called on an observation date.
- AutocallableNote that repays early, at par plus a coupon, if the underlying is at or above the autocall barrier on an observation date.
- Barrier optionAn option that switches on (knock-in) or off (knock-out) if the underlying touches a set level before expiry.