Suppose you buy a new home and finance (90 %) of the price with a mortgage from

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Suppose you buy a new home and finance $90 \%$ of the price with a mortgage from a bank. Suppose that a few years later the value of your home falls below your mortgage balance and you decide to default on your loan. Califomia has antideficiency judgment legislation that states that the bank can only recover the value of the house itself, not the entire mortgage balance.?

Suppose you take out a 15 -year mortgage for $90 \%$ of the home price, and suppose that the risk-free rate is constant at $10 \%$. Assume also that the house has a net value to you (perhaps in saved rent) of $5 \%$ of its market value each year. Housing prices have a volatility of $18 \%$ per year. What is the value of this put option for a loan of $\$ 90$ ? What is the fair value for the interest rate on your mortgage? (Use the small $\Delta t$ approximation.)

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