Optimal Security Design

[CLK]

A general question with respect to the design of an investment strategy for a retirement fund.

I have read reference material which mentions that one approach to developing such a strategy is to identify the desired payoff function at retirement of the relevant individual or group and to use option pricing techniques to derive the investment strategy that provides this outcome.
I struggle to make a direct connection between option pricing and the derivation of the investment strategy.
It seems sensible that the optimal investment strategy would be that which replicates the desired payoff. Determining the current price of the desired payoff follows directly from this.
The material I am referencing lists the following steps:

1. Derive the optimal payoff function of the investor's pension plan as a function of the asset prices at that time;
2. Price the investor's desired payoff function using standard option pricing techniques; and
3. Determine the replicating portfolio of the investor's desired payoff function using the delta method or an alternative.

I do not see how step (2) precedes (3), and with reference to step (1) I do not realise the importance of deriving the payoff function "as a function of the asset prices." I have had exposure only to basic option pricing at the level of the earlier technical subjects of the Faculty's education syllabus.
For the purpose of determining an optimal investment strategy, I would have described the process as:

1. Identify the desired payoff function; and
2. Determine the replicating portfolio and hence price.

Could someone possibly help connect the general gaps in my understanding or provide instruction on how I can address them efficiently?

 

[Stuart Underwood]

Did you mean to post this in the SP4 forum? (It feels quite removed from SP4, so I'm not sure I can help.)

 

[CLK]

Hi Stuart,
Thanks.
Yes, it is essentially liability driven investment I would think.
I seem to have difficulty in following the approach that I mentioned in my original post.
I thought that a high level overview might remedy my understanding.
Any information that you consider useful would of course be appreciated too.

 

[Stuart Underwood]

Hi - it's been 15 years since I studied what's now CM2 - so your knowledge of the detail of things like 'payoff function' 'option pricing techniques' and 'delta hedging' is likely to be better than mine!

On the plus side, this means in terms of SP4 that should be a steer not to worry about this, as this sort of technical knowledge has not been tested.