Question

Practice Question (5)

A vacant lot has been zoned to construct today either 100 offices or 100 . Assume that:
a) Construction must occur immediately and cannot be delayed.
b) Construction costs are $150 per office or $155 per apartment. .
c) The current price of offices is $500 and the current price of the apartments is $450.
d) The rental rate is S30 per office and $20 per apartment (net of expenses, to be received at the end of the year).
e) The real estate market can evolve as follows: In one year:

1) if the real estate market booms, offices will sell for $600 and apartments for $525.
2) if the real estate market does poorly, offices will sell for $385 and apartments for $420.

The construction technology allows you to convert offices into apartments at an additional cost of $10 per unit.

Find the value of the conversion option described in the last bullet point (just the conversion option alone, not the whole construction project) using the replicating portfolio method.

Answer 1

The computation of the initial asset–liability value is not the subject of this paper. It could be estimated by the same methods. The value of insurance liabilities in practice includes a risk margin that is determined as cost of future solvency capital for the asset–liability portfolio.

Formally, we assume that primary and sample random variables A(ω)=A(ω1)A(ω)=A(ω1) and A(j)(ω)=A(j)(ω2)A(j)(ω)=A(j)(ω2), etc., with ω=(ω1,ω2)ω=(ω1,ω2), are modeled on a product space Ω=Ω′×Ω′Ω=Ω′×Ω′, F=F′⊗F′F=F′⊗F′ equipped with product probability measures M=M′⊗M′M=M′⊗M′.

While the rebalancing frequency of a real insurance asset–liability portfolio is adaptive, quarterly rebalancing for the long-term projection is a reasonable assumption.