Commodity Options Pricing- Key Factors To Calculate Premium

Published on Friday, August 24, 2018 by Chittorgarh.com Team | Modified on Thursday, February 29, 2024

Commodity Options Pricing Model (Commodity Options Pricing Formula)

Commodity options are priced using the Black 76 pricing model. The model was developed to extend the Black-Scholes model to evaluate commodity futures.

Black 76 Model explained

The Black-76 model, also known as Black's model or Black-Scholes-Merton (BSM) model, is a pricing model for derivatives used to value assets such as options on futures and floating rate notes with a cap.

The model was developed by Fischer Black by further developing the earlier and better-known Black-Scholes-Merton option pricing formula.

Black 76 Model meaning

The Black-76 model is a mathematical simulation of the dynamics of a financial market containing instruments such as futures, options, swaps, and forwards. This model is used to determine the fair price of financial instruments. It states that each option has a unique price, regardless of the risk associated with the underlying security and the expected return.

Black 76 Model assumptions

• There are no price jumps.
• There are no risk-free arbitrage opportunities.
• The risk-free interest rate is constant, the same for all maturities, and identical for bonds and loans.
• The volatility of the return on the underlying is known and constant.
• Unlimited short selling of the underlying is permitted.
• No taxes or transaction costs are incurred.
• The underlying share can be traded continuously and in very small quantities.
• Early exercise of the options is not permitted (this model can therefore only be used to value European options).

Black 76 Model formula

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 asset is directly proportional to the price of Call options on commodities. This means that an increase in the price of the underlying causes an increase in the price of the associated Call option and vice versa. The price of the underlying is inversely proportional to the price of the Put options on commodities. This means that an increase in the underlying price causes a fall in the price of the associated Put option and vice versa.

Time to expiration- The premium for call options is higher at the beginning of the month and decreases with each day that passes until expiration. The premium for put options is lower at the beginning of the month and increases with each day that passes until expiry.

Volatility- The higher the volatility, the higher the premium for call options. And vice versa. The premium for put options falls when volatility rises and rises when volatility falls.

Interest Rates- A rise in interest rates causes the premium for call options to rise, while the premium for put options falls.

Strike Price- An increase in the strike price of options reduces the premium of call options and increases the premium of put options.