The output of the model is the mark to market value of such a contract, that is, the Equity Futures price less the strike (if long position).
Let t be the current date, and let 0 be the trade date, T be the maturity date, Let be the underlying (equity) price at time t, be the Equity Futures price for maturity T, and K be the strike price (delivery price).
The payoff at time T of an Equity Futures contract (long position) is then . The mark to market value of this contract at time t is: .
Let be the dates when corresponding discrete dollar dividends, , are paid (if a payment lag is applicable, then it should be added to the above dates). The present value of these dividends is then:
,
where is the (continuously compounded) zero in interest rate applicable from t to T as seen at t, is the distance between those dates in a given day count convention (usually, actual/365). Alternatively, let q be a (continuously compounded) dividend yield.
By no-arbitrage argument, the Equity Futures price is then:
.
Accordingly, the value of the Equity Futures contract (long position) at time t is:
Delta, sensitivity to underlying, is going to be computed as follows:
In the following listings the symbol ”//” marks commented out text fragments containing either explanatory information or possible alternatives for the values of the corresponding attributes.
Deal 1
VALUATION_AS_OF_DATE 20050509 VALUATION_AS_OF_TIME 00:00
GREEKS DELTA
RANDOM_OBJECT_TYPE EQUITY
UNDERLYING SPX
EXCHANGE Z
UND_CURRENCY USD=
DRIFT_RATE_FILE USD_RATE_CURVE (see https://finpricing.com/lib/IrCurveIntroduction.html)
DIVIDEND_FILE spx_div
ASP 1172.08
STRIKE 0
OPTION_TYPE EQUITY_FUTURES PAYOFF_CURRENCY USD= MODEL CLOSED_FORM CLASS EUROPEAN EXPDATE 20050617 EXPTIME 17:00 DISCOUNT_RATE_FILE USD_RATE_CURVE
BEGIN_FILE_INFO spx_div SPX Z 20050510 0.030443 SPX Z 20050511 0.641146 SPX Z 20050512 0.126079 SPX Z 20050513 0.131578 SPX Z 20050516 0.123795 SPX Z 20050517 0.124188 SPX Z 20050518 0.175363 SPX Z 20050519 0.010361 SPX Z 20050520 0.036185 SPX Z 20050523 0.009276 SPX Z 20050524 0.008820 SPX Z 20050525 0.113729 SPX Z 20050526 0.116603 SPX Z 20050527 0.122092 SPX Z 20050601 0.388127 SPX Z 20050602 0.006363 SPX Z 20050603 0.009627 SPX Z 20050606 0.067421 SPX Z 20050607 0.038778 SPX Z 20050608 0.232640 SPX Z 20050609 0.000359 SPX Z 20050610 0.031369 SPX Z 20050613 0.290447 SPX Z 20050614 0.056587 SPX Z 20050615 0.031406 SPX Z 20050616 0.009151 SPX Z 20050617 0.013423