1. A New View of Mortgages (and life)

2. Scene 1 A farmer owns a horse farm outside Lexington on Richmond Road.
Demographic trends indicate that this part of Lexington is booming and is projected to continue to grow.
Problem: Current local government is hostile to development.

3. Scene 2
Local developer notices the horse farm and thinks that the site is an excellent candidate for a new shopping mall.
Developer knows that the local mayor is up for re-election next year. Outcome of election is uncertain, but has potential to install new mayor with pro-growth views.

4. Scene 3
What can the developer do to take advantage of this opportunity?
Approach farmer with an offer to buy an option to purchase the horse farm.

5. The Option
Developer pays the farmer $X for the right to purchase the horse farm after the election for $Y.
If pro-growth mayor wins, then horse farm will be worth $Z1 (where E[Z1] > Y).
developer exercises the right to purchase the land for $Y and either develops the shopping mall or sells to another for $Z1 (profit = Z1-Y).

6. The Option
If current mayor wins, horse farm will be worth $Z2 where $Z2 < $Y.
Can assume that Z2 is probably the value of the land as a farm.
Developer lets option expire without purchasing land
Farmer keeps the payment $X.

7. Next Example An insurance company has a large real estate portfolio.
The insurance company projects that it will need $1 million next year to fund possible claims.
What can it do to protect itself from changes in value to its real estate portfolio between now and when the claims will have to be paid.

8. Answer
Purchase an option to sell one of its properties for $1 million.
If prices go down then protected
If prices go up, will lose the appreciation but still locked in with enough funds to pay the claims.

9. Options In the first example, the developer purchased a CALL option.
the right to buy an asset
In the second example, the insurance company purchased a PUT option.
the right to sell an asset.

10. Call Option
Contract giving its owner the right to purchase a fixed number of shares of a specified common stock at a fixed price by a certain date
Stock = underlying security (ST = market price)
price = strike price (K)
date = expiration date
writer = person who issues the call (the seller)
buyer = person who purchases the call
call price = market price of the call, (CT)

11. Types of Call Options European Call = exercise only at maturity
American Call = exercise at any time up to maturity

13. Call Option Payoff at Maturity

14. Put Option
Contract giving its owner the right to sell a fixed number of shares of a specified stock at a fixed price at any time by a certain date.

16. Put Option Payoff at Maturity

17. Mortgages as Options
A mortgage is a promise to repay a debt secured by property.
property = collateral = underlying security = stock
However, a mortgage is much more complex than a simple stock option.
mortgage is a contract with several options

18. Mortgages as Options Default Option
right of borrower to stop making payments in exchange for the property
default = exercise of a PUT option

19. Mortgages as Options Prepayment Option
right of borrower to prepay the mortgage at any time
prepayment = exercise of a CALL option

20. Prepayment Paying off mortgage early (prior to maturity date)
Financial = when interest rates fall below contract rate
Non-financial = borrower moves, divorce, (not optimal with respect to interest rates)
prepayment is considered to be an American option
borrower may prepay at any time prior to maturity

21. Default Mortgage Default is defined as a failure to fulfill a contract
Technical default = breech of any provision of the mortgage contract
1 day late on payment
failure to pay property taxes
failure to pay insurance premiums

22. Default Industry Standards: Delinquency: missed payment
Default = 90 days delinquent
(3 missed payments)
Foreclosure: process of selling the property to pay off the debt
takes many months to foreclosure

23. Default Default is considered a European put option.
Borrowers will only default when a payment is due
Thus, the mortgage can be thought of as a string of default options. Every time you make a payment, you are purchasing a put option giving you the right to sell the house to the lender for the mortgage balance next month.

24. Default and Prepayment
Default and Prepayment are substitutes.
If borrower prepays the mortgage, then he can’t default
implies that default has no value
If borrower defaults on the mortgage, then she can’t prepay
implies that prepayment has no value

25. Mortgage Pricing
Ten years ago Enterprise S&L made a 30 year mortgage for $100,000 at an annual interest rate of 8%. The current market rate for an equivalent loan is 12%. What is the market value of this loan?

26. Mortgage Pricing Simplistic Answer: Price = $66,640
More Complex (realistic)
Price = PV of Payments - Value of Default Option - Value of Prepayment Option