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?

  • $\begingroup$ Model?????????? $\endgroup$ – user16651 Jun 10 '16 at 10:01

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.


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