Adapting Stock Option Pricing and Greeks to Futures Options

Summary

The note explains how a stock option pricing routine can be adapted to price an option on a futures contract. Its approach converts the observed futures price into a discounted pseudo spot price using the relationship between futures, interest rates, and any dividend yield, then passes that value to an existing stock option formula. Applying this transformation to Black–Scholes leads to the Black 1976 framework for futures options.

The same chain rule idea applies to Greeks: the sensitivity to the futures price can be obtained by multiplying the stock-price delta by the sensitivity of the pseudo spot price to the futures price. This offers a way to reuse existing pricing tools when a separate futures-option function is unavailable. The explanation is brief and illustrates delta rather than deriving every Greek. It also does not discuss American exercise features, model assumptions, or the exact MATLAB function interface, so users must check that their pricing model matches the contract and option style.

Key ideas

• A futures price can be converted to a discounted pseudo spot price for use in a stock option formula.
• Applying the transformation to Black–Scholes gives the Black 1976 futures option formula.
• Greeks with respect to the futures price can be derived by the chain rule.
• The described method does not specify how to handle American exercise or verify a particular software interface.

Tags

# How do I compute volatility and greeks of the american option on futures using matlab toolbox?


# How do I compute volatility and greeks of the american option on futures using matlab toolbox?












I have learned some knowledge on option pricing by myself at a very beginne level. I'm using Matlab R2009b finacial derivative toolbox. I found option pricing functions for american options on stock, but not on futures. I have read documentations of the toolbox, and still have no idea how to compute volatility and greeks of american option on futures.

What functions can I use to compute the volatility and greeks of american option on futures?

## Answer by Alex C (score 1)

https://quant.stackexchange.com/a/27661

If you have a formula for options on stock, you can turn it into a formula for options on futures by using the relation $S=F e^{-(r-d)T}$. In other words you observe the price of the future F, you turn it into S by this relation and then you pass this pseudo stock price to the options on stock function or program that you have.

When you do this to the Black-Scholes formula you get the "Black 1976" formula which is the simplest options on future formula available.

For the Greeks, a similar approach works. For example $\Delta_F=\frac{\partial C}{\partial F}$ (the Delta in terms of the futures price) can be found as $\frac{\partial C}{\partial S}\frac{\partial S}{\partial F}$ where $\frac{\partial C}{\partial S} =\Delta_S$ is the standard delta that your existing program knows how to compute.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.