# Commodity Options Pricing- Key Factors To Calculate Premium

Published on Friday, August 24, 2018 by Chittorgarh.com Team | Modified on Sunday, August 9, 2020

## How are Commodity Options priced (Commodity Options Pricing Formula)

Commodity Options are priced using the Black 76 Model. The model was developed to extend the Black Scholes model to price Commodity Futures.

A Call Option is priced as-

Call = e-rt[F*N (d1) - K*N (d2)]

d1 = ln(F/K)+(V2/2)T /V√T

d2=d1-V√T

Where,

F = Current underlying futures price

K = Strike price of the option

T = Time in years until the expiration of the option

R = Risk-free interest rate

V = Volatility of the underlying futures contract

N = Standard normal cumulative distribution function

A Put option is priced as-

Put = e-rt [K*N (-d2) - F*N (-d1)]

d1 = ln(F/K)+(V2/2)t /V√t

d2=d1-V√t

Where,

F = Current underlying futures price

K = Strike price of the option

t = Time in years until the expiration of the option

r = risk-free interest rate

V = volatility of the underlying futures contract

N = Standard normal cumulative distribution function

## Key Factors Influencing Commodity Options Premium

Underlying Price- The price of the underlying is directly proportional to the prices of Call Options in Commodities. This means an increase in the price of the underlying causes increase in the price of its Call Option and vice versa. The price of the underlying is inversely proportional to the prices of Put Options in Commodities. This means an increase in the price of the underlying causes fall in the price of its Put Option and vice versa.

Time Until Expiry- The premium on Call Options is higher at the beginning of the month and decreases with each passing day towards expiration. The premium on Put Options is lower at the beginning of the month and increases with each passing day towards expiration.

Volatility- As volatility increases, the premium on Call options increases. And vice versa. The premium of Put Options fall with the increase in volatility and increase with the decrease in volatility.

Interest Rates- An increase in the interest rates pushes up the premium of Call options while reducing the premium of Put Options.

Strike Price- An increase in the strike price of the Options reduces the premium of Call options while increasing the premium of Put options.

## Effect on Call and Put Option

 Factor Effect on Call Option Price Effect on Put Option Price Increase in the value of the underlying instrument Increase Decrease Increase in Time Value Increase Increase Increase in Volatility Increase Increase Increase in Interest rates Increase Decrease Increase in Strike Price Decrease Increase