OPTION_SERIES — European Option Price Series

Track one fixed-strike, fixed-expiry European option through historical underlying observations. Each observation uses the remaining calendar time to the fixed end date, not a rolling constant tenor.

Syntax

OPTION_SERIES(Series,start,end,strike,vol,rate,yield,type)

Series: Positive underlying spot-price series.
start, end: Integer YYYYMMDD dates, inclusive. End is the fixed expiry and may be later than the last underlying observation.
strike: Fixed positive exercise price in underlying quote units.
vol: Nonnegative annualized volatility, as a number or series.
rate: Annual continuously compounded quote-currency interest rate, as a number or series.
yield: Annual continuous income yield, or base-currency interest rate for FX, as a number or series. Use 0 for no yield.
type: Quoted string CALL or PUT, case-insensitive.

Numeric inputs use decimals: 0.20 volatility means 20%, and 0.05 rate means 5%. Each percent-marked input series is independently divided by 100; unmarked series must already use decimals. Negative rates and yields are allowed.

Calculation

Uses the existing BlackScholes pricing and delta functions with continuous yield. Time is calendar days remaining divided by 365.25. Rates, yield and volatility observed at each date are treated as constant over its remaining tenor.

Returns theoretical European option premiums in the same quote units as the underlying, per unit of underlying. Contract sizes and initial premiums are not applied. This is position value, not profit/loss.

At expiry, price equals intrinsic payoff. Delta is 1/0 for an in/out-of-money call and 0/-1 for an in/out-of-money put. At the strike, the expiry derivative is undefined; this command uses 0.5 for calls and -0.5 for puts as a charting convention. Before expiry with zero volatility, price is the positive part of the discounted spot-minus-strike difference (reversed for puts); delta uses the corresponding yield discount factor and a half-delta convention at the deterministic payoff boundary.

Example

OPTION_SERIES(DEXJPUS,20050101,20050315,105,0.10,IR3TIB01JPM156N,IR3TIB01USM156N,"CALL")

Illustrative USD/JPY option with strike 105 yen per dollar and assumed 10% annualized volatility. DEXJPUS is yen per dollar, so the JPY rate is rate and the USD rate is yield. This CALL is a call on USD against JPY. The three-month interbank series are monthly historical proxies, not exact expiry-matched continuous discount curves.

Strategies and changes

Both commands return normal SeriesOperator results; there are no command-specific extracts. Subtract calls at different strikes for a call-spread value; add call and put premiums at the same strike for a straddle value. Combine delta series with the same signed quantities for strategy delta. Multiply by position size separately and account for the initial premium when calculating P/L.

First differences of option prices measure total value changes, not pure theta. First differences of delta measure changes in exposure. To isolate time decay, hold spot, volatility and rates constant and reduce time to expiry. Daily spot data produces daily results; other frequencies retain their observation dates. No missing dates or expiry observation are synthesized.

Validation and assumptions

Requires eight arguments, valid ordered dates, positive strike and selected spot values, finite inputs and nonnegative volatility. All series must have nonnull, strictly increasing dates. Supplied parameter series must contain finite values and cover every pre-expiry valuation date. Uses each series' existing interpolation method within its calendar-date bounds; extrapolation is rejected. Interpolation across gaps can use later observations, so this is not automatically a point-in-time backtest. Rates and volatility are not evaluated at expiry, although input structure is still validated.

Invalid inputs, empty selected intervals and nonfinite results return a descriptive command error rather than a partial series. Inputs are not modified. This model assumes European exercise, lognormal positive spot and continuous yield; it does not model early exercise, discrete dividends, a volatility smile, transaction costs or separate discount curves.

Related commands: OPTION_SERIES, OPTION_DELTA_SERIES, FORWARD_SERIES.