It added it has pledged assets to GM as security for the final payment.
Continuity condition: When the borrower defaults, the value of the pledged assets is equal to the value of the loan.
Therefore, when the borrower defaults, the value of the pledged assets must be equal to the value of the loan.
Theorem 3: If the probability distribution of the pledged assets yield does not depend on the value of the pledged assets V, then x does not depend on V, and the loanable amount is a linear function of the value of the pledged assets.
Proof of theorem 3: According to Merton (1973), theorem 9, if the probability distribution of the pledged assets yield does not depend on the value of the pledged assets V, the value of the put option is a homogeneous function of the strike price and the current value of the pledged assets.
Theorem 1: In general, the value of the pledged assets V, the risk-free rate r, the maturity date of the fixed-rate zero-coupon loans T, the current time t, the loan rate R, and the volatility of the pledged assets determine the pledged loan-to-value ratio.
At maturity, if the value of the loan is more than the value of the pledged assets, the loan will default.
At maturity, if the value of the loan is more than the value of the pledged assets, the borrower will default and the investor will lose the difference.
That could mean pledging assets like real estate, or specific revenue streams like tax receipts.
Insurance people have traditionally thought in terms of physical assets: inventory, machinery, buildings, cash.
Insurance people have thought in terms of physical assets: inventory, machinery, buildings, cash.
