Pay-off formula
Insurance pay-off
Before buying an insurance product, we should know the cost. That cost can be calculated based on the pay-off formula.
N= 1/pe
N is the gross pay-off in percentage
pe is the probability of event. It takes value between 1 and 0, and never 0.
If the probability >15% draw-down of an asset class is 9% (calculated from historical data or Monte Carlo simulation), then pe = 0.09
now,
N=1/0.09, approximately 11 or 1100% of premium
n= N-100% of premium
n is the net pay-off
n here is 10 or 1000%
Assume that the market value M of the asset insured is 22500. We want to insure against >15% draw-down, i.e,
\[(0.85)X 22500=19125\]
So our target price, T is 19125
When to exercise the insurance
Once the pay-off reaches 1000% of yearly spent for insurance, we should exercise the option to use the insurance.For the given case, 306.8 X 10, 3068
should be the cut-off for exercising the option.