Compute the Option Price on a Future

Consider a call European option on the Crude Oil Brent futures. The option expires on December 1, 2014 with an exercise price of $120. Assume that on April 1, 2014 futures price is at $105, the annualized continuously compounded risk-free rate is 3.5% per annum and volatility is 22% per annum. Using this data, compute the price of the option.

Define the RateSpec.

ValuationDate = datetime(2014,1,1);
EndDates = datetime(2015,1,1);
Rates = 0.035;
Compounding = -1;
Basis = 1;
RateSpec  = intenvset('ValuationDate', ValuationDate, 'StartDates', ValuationDate,...
'EndDates', EndDates, 'Rates', Rates, 'Compounding', Compounding, 'Basis', Basis')

RateSpec = struct with fields:
           FinObj: 'RateSpec'
      Compounding: -1
             Disc: 0.9656
            Rates: 0.0350
         EndTimes: 1
       StartTimes: 0
         EndDates: 735965
       StartDates: 735600
    ValuationDate: 735600
            Basis: 1
     EndMonthRule: 1

Define the StockSpec.

AssetPrice = 105;
Sigma = 0.22;
StockSpec  = stockspec(Sigma, AssetPrice)

StockSpec = struct with fields:
             FinObj: 'StockSpec'
              Sigma: 0.2200
         AssetPrice: 105
       DividendType: []
    DividendAmounts: 0
    ExDividendDates: []

Define the option.

Settle = datetime(2014,4,1);
Maturity = datetime(2014,12,1); 
Strike = 120;
OptSpec = {'call'};

Price the futures call option.

Price = optstockbyblk(RateSpec, StockSpec, Settle, Maturity, OptSpec, Strike)

Price = 
2.5847