Options Pricing and Risk Sensitivity

Options contracts can be traded before they expire. The valuation and settlement calculations of an options contract includes an estimation of the contract's current pricing, and several other values representing risk sensitivity.

Estimation Models

Two models are available in MineMarket to estimate options pricing:

  1. Black-Scholes
  2. Monte Carlo
Black-Scholes

In the Black-Scholes model, call and put option prices are estimated using a combination of the strike price, market price, volatility, interest rate, dividend rate and time to options contract expiry. The dividend rate is assumed to be zero for commodities.

For more information, see: http://www.macroption.com/black-scholes-formula/.

Monte Carlo

Like the Black-Scholes model, the Monte Carlo model estimates option prices using a combination of the strike price, market price, volatility, interest rate, dividend rate and time to options contract expiry. The dividend rate is assumed to be zero for commodities.

However, the Monte Carlo model also includes a random number that is sampled from a normal distribution; and hence, the calculation is run many times.

For more information, see: https://www.investopedia.com/terms/m/montecarlosimulation.asp.

Results

The valuations and settlement of an options contract includes the estimated option price.

A number of other values representing risk sensitivity are also displayed. These values are known as "the Greeks" because most are named after letters in the Greek alphabet:

  • Delta—Represents the rate of change between the option contract's premium and the underlying asset's price
  • Gamma—Represents the rate of change between the option contract's delta and the underlying asset's price
  • Theta—Measures sensitivity of the value based on time to expiry
  • Vega—Measures sensitivity to volatility
  • Rho—Measures sensitivity to the interest rate

For more information, see: https://www.investopedia.com/terms/g/greeks.asp.

Required Configuration

The following configuration and information is required to estimate options pricing for the Black-Scholes and Monte Carlo models:

  • A multi-maturity interest rate series (see Interest Rates)
  • A volatility curve
  • Specification of the price estimation model in the settlement method
  • Specification of the interest rate series and volatility curve in the market commodity

If a standard interest rate series is used instead of a multi-maturity interest rate series, all required values must be available. Missing values can be interpolated in multi-maturity interest rate series.

The following additional configuration is required to estimate options pricing for the Monte Carlo model:

  • Specification of the number of simulations in the settlement method