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skafetaur
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Posts: 41
Joined: June 11th, 2023, 3:31 pm

Black-Scholes and Forward Price

February 26th, 2024, 2:55 pm

My understanding is that Black-Scholes options pricing uses the spot price of the underlying. Please see this screenshot from a chapter in the book "Options Volatility and Pricing" by Sheldon Natenberg. It reads that the Black-Scholes model values options from the forward price. Can anyone comment on that, please?
B-S Forward.png
 
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DavidJN
Posts: 244
Joined: July 14th, 2002, 3:00 am

Re: Black-Scholes and Forward Price

February 26th, 2024, 3:26 pm

What is the difference between a spot price and a forward price? Understand that and the option question should be easy. 
 
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bearish
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Joined: February 3rd, 2011, 2:19 pm

Re: Black-Scholes and Forward Price

February 27th, 2024, 1:53 pm

There are at least a couple of ways to think about this. At a relatively high level of abstraction you may notice that, with everything else held constant, the forward price is an invertible function of the stock price. Thus, if you have an expression for the value of the option as a function of the forward price, you can easily substitute in the forward price expressed in terms of the stock price, and the end result is the option price in terms of the stock price. And vice versa. At a modeling level, there’s often some economy of thought arising from separating factors that affect the spot/forward relation (e.g. discounting, dividend payments, borrowing cost, time) and those that affect the option/forward relation (mostly volatility and time).
 
skafetaur
Topic Author
Posts: 41
Joined: June 11th, 2023, 3:31 pm

Re: Black-Scholes and Forward Price

March 10th, 2024, 4:11 pm

Thank you, Bearish!