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60202
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Is the typical BSM model priced off the "forward" price of the underlying?

March 22nd, 2018, 2:10 pm

Pretty much every article I read on options and option pricing, they lead you to believe that the option price is based on the current spot price.  For example, option prices are based off what Apple is trading right now.  Is this true?

My understanding is that the option price is actually based on the forward price of Apple with the same expiration as the option itself.  So an option is actually priced off the current apple stock price adjusted by e^(rt).   Same with options on futures.  The option on a future is based on the forward price of that future, not the future itself.  Now, the forward price of a future tends to be similar if not the same as the future as carry costs for a future are minimal so r is close to 0.

Is my understanding correct? If that's true, doesn't that mean that every option expiration is based on distinct underlyings (respective forward prices),  not just one underlying (whatever the prevalent spot price is).
 
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bearish
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Re: Is the typical BSM model priced off the "forward" price of the underlying?

March 22nd, 2018, 4:33 pm

Pretty much every article I read on options and option pricing, they lead you to believe that the option price is based on the current spot price.  For example, option prices are based off what Apple is trading right now.  Is this true?

My understanding is that the option price is actually based on the forward price of Apple with the same expiration as the option itself.  So an option is actually priced off the current apple stock price adjusted by e^(rt).   Same with options on futures.  The option on a future is based on the forward price of that future, not the future itself.  Now, the forward price of a future tends to be similar if not the same as the future as carry costs for a future are minimal so r is close to 0.

Is my understanding correct? If that's true, doesn't that mean that every option expiration is based on distinct underlyings (respective forward prices),  not just one underlying (whatever the prevalent spot price is).
If you are looking to value a European option it is helpful to separate your analysis into two steps: first find the forward price to the option maturity date, and then value the option relative to that price. The forward price embeds the financing cost, as you allude to, but also the effects of dividends, storage cost, convenience yield, short sale constraints/borrowing cost, and probably something I have overlooked. In the cases where you can actually trade the forwards (e.g. FX) or futures (not the same thing, but pretty close for the current purpose) it is definite useful to think of the option as referring to them. In other markets, e.g single stock, this would merely be a way of thinking about the problem, and the option and related hedging is ultimately based on the spot stock price process. And for American and more exotic options, you definitely need to focus on the spot price process.
 
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Alan
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Re: Is the typical BSM model priced off the "forward" price of the underlying?

March 22nd, 2018, 7:17 pm

All good points. An interesting setup which really forces the "forward price" point of view for Euro-style options is where the underlying spot is not a tradable security, but there is a futures market. For example, this is true with VIX options. 

A cleaner hypothetical example would be options on, let's say, the noon temperature on expiration in Chicago. Today it is July 1, the temperature is 87 degrees F. Your option expires on Dec. 25. We'll say there is a futures market  -- you can imagine what it will say. 

The point is: my pathetic retail broker (who shall remain nameless) still runs all options through the BSM model, using the *spot*, and reporting the implied vols. Well, you can see how hopelessly mis-priced this option is going to look by their system.  Ditto for more realistic options that actually exist, say on VIX, or even on tradables like a stock that is simply hard-to-borrow, etc. as bearish alluded to.    
 
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Re: Is the typical BSM model priced off the "forward" price of the underlying?

May 2nd, 2018, 1:38 pm

Pretty much every article I read on options and option pricing, they lead you to believe that the option price is based on the current spot price.  For example, option prices are based off what Apple is trading right now.  Is this true?

My understanding is that the option price is actually based on the forward price of Apple with the same expiration as the option itself.  So an option is actually priced off the current apple stock price adjusted by e^(rt).   Same with options on futures.  The option on a future is based on the forward price of that future, not the future itself.  Now, the forward price of a future tends to be similar if not the same as the future as carry costs for a future are minimal so r is close to 0.

Is my understanding correct? If that's true, doesn't that mean that every option expiration is based on distinct underlyings (respective forward prices),  not just one underlying (whatever the prevalent spot price is).
If you are looking to value a European option it is helpful to separate your analysis into two steps: first find the forward price to the option maturity date, and then value the option relative to that price. The forward price embeds the financing cost, as you allude to, but also the effects of dividends, storage cost, convenience yield, short sale constraints/borrowing cost, and probably something I have overlooked. In the cases where you can actually trade the forwards (e.g. FX) or futures (not the same thing, but pretty close for the current purpose) it is definite useful to think of the option as referring to them. In other markets, e.g single stock, this would merely be a way of thinking about the problem, and the option and related hedging is ultimately based on the spot stock price process. And for American and more exotic options, you definitely need to focus on the spot price process.
So we are supposed to use the implied forward price to price options then?  Or is it only for European options - sorry, I'm a bit confused by your answer.