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Black Scholes model

P

Procrastinator

Member
Hi,

Could someone help me with this query please?

If I'm using the Black Scholes model to price an option on a Total Return Index, should S(t) refer to the Total Return Index value or the Price Index? My real question is if there is no Total Return Index, do I need to adjust the Price Index for dividend yield to use as my S(t) or should the Price Index be used? :confused:

I've tried doing a quick research on this on the web, but no satisfying responses so far. Any takers please?

Thanks
 
Options on a Total Return index

For an option on a Total Return Index (or on a portfolio with dividends reinvested in the portfolio), S(t) will represent the Total Return Index (or portfolio value) and since this already allows for dividends, no separate allowance will be needed (q or D).

If there is no Total Return Index, I'm not sure how you'd have an option on it, but let's go with it anyway. If you had S(t) as the Price Index, you'd need to define S*(t), say, as the Total Return Index from this, where S*(t)=S(t)exp(qt) for some specified time 0. Then S*(t) would be used in the Black-Scholes formula.
 
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