Stochastic vs Deterministic Approach

[Yash A]

In chapter 14, Models(1), it is mentioned that positive liability will be calculated if stochastic method is used whereas deterministic method would produce zero liability (eg costing guarantees and options).

Why is this the case?

 

[Mark Willder]

In chapter 14, Models(1), it is mentioned that positive liability will be calculated if stochastic method is used whereas deterministic method would produce zero liability (eg costing guarantees and options).

Why is this the case?

Hi Yash

The following example might help.

Let's say that interest rates are 5% pa today. An insurer decides to sell a unit-linked contract with a guaranteed return of 1% pa.

If a deterministic model is used then the insurer might value the option at a prudent rate, let's say 2% (as this is much lower than the current 5% interest rate). This would give the option a value of zero as the contract is assumed to earn more than the guarantee.

If a stochastic model is used then many simulations will be performed. Most of these simulations will use an interest rate bigger than 1% and so again place a value of zero on the guarantee. But at least some of the simulations will use an interest rate lower than 1% to give the guarantee a positive value.

Best wishes

Mark