This example shows how to compute option prices on futures using the Black option pricing model. Consider two European call options on a futures contract with exercise prices of $20 and $25 that expire on September 1, 2008. Assume that on May 1, 2008 the contract is trading at $20, and has a volatility of 35% per annum. The risk-free rate is 4% per annum. Using this data, calculate the price of the call futures options using the Black model.

This example shows how to compute option prices on forwards using the Black pricing model. Consider two European options, a call and put on the Brent Blend forward contract that expires on January 1, 2015. The options expire on October 1, 2014 with an exercise price of $200 and $98 respectively. Assume that on January 1, 2014 the forward price is at $107, the annualized continuously compounded risk-free rate is 3% per annum and volatility is 28% per annum. Using this data, compute the price of the options.

Define the `RateSpec`

.

RateSpec =
FinObj: 'RateSpec'
Compounding: -1
Disc: 0.9704
Rates: 0.0300
EndTimes: 1
StartTimes: 0
EndDates: 735965
StartDates: 735600
ValuationDate: 735600
Basis: 1
EndMonthRule: 1

Define the `StockSpec`

.

Define the options.

Price the forward call and put options.

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`

.

RateSpec =
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`

.

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

Define the option.

Price the futures call option.