State price deflators

[Shillington]

What are the advantages of using the state price deflator method over using the standard risk-neutral method?

As far as I can see it just appears to add in some notation without actually doing anything?

 

[Graham Aylott]

There are advantages to using state price deflators (SPDs). However, they're not mentioned in the CT8 course and so you don't need to know them.

In short, SPDs can be used to reflect the fact that the value of a unit of cashflow may well depend upon the circumstances in which it is received (as well as the time at which it is received.) This is due to diminishing marginal utility (DMU).

Recall from CT7 that DMU suggests that the value of an additional unit of cashflow will be lower the more income / wealth you have. Risk-neutral valuation uses the same discount factor, exp[-r(T-t)] say, to discount all cashflows payable at time T back to time t. However, using SPDs means that the discount factors used to discount cashflows from time T back to time t will be different depending on the state of the world (eg the node in a binomial tree) in which the cashflow is received. DMU implies that discount factors should have have lower numerical values (ie should discount cashflows more heavily) in "good" states and vice versa. On way of achieving this in practice is via the use of SPDs.

None of this is in the CT8 course, however, and so you don't need to worry about it.

Note also that it's possible to calculate numerical values for state price deflators without knowing the risk-neutral probabilities. However, the method of doing so again isn't in the CT8 course and so you don't need to know it.

Hope this helps.

Graham

 

[Akankwasa Denis]

Thank you Graham. I have been helped
I met this concept SPDs in financial mathematics.