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A futures contract is a standarized contract traded on a futures exchange. The futures contract obligates the holder to buy or sell a certain underlying instrument at a certain future date at a specified price. The futures date is called the delivery date or the final settlement date. The pre-set price is called the futures strike price.


The futures price of a traded financial security is its discounted expected value. In many cases, this is very easy to compute. In some cases, i.e., with stochastic dividend payments, a numerical solution can be useful.

ThetaML implementation

The following ThetaML model determines the futures price of a traded underlying 'S'. The underlying 'S' and the discount numeraire 'EUR' are processes simulated externally. For example, the process 'S' can be a stock price process that follows a Geometric Brownian Motion or a Heston Volatility process. The discount numeraire 'EUR' can be a constant discount curve as implemented in Discounting, or a stochastic process that has a dynamics as defined in the CIR model .

model future
  import S    "Underlying"
  import T    "Futures maturity"
  import EUR  "Discount numeraire"
  export P    "Futures price"
  %at current time, set 'P' to the expected discounted future values of 'V'
  P = E(V!)
  %the ThetaML command 'Theta' pass time by 'T' years
  Theta T
  %at the futures expiry time 'T', 'V' is equal to the underlying price at 'T'
  %note the future cash flows are discounted to time 0 by the discount numeraire 'EUR'
  V = S*EUR