House Price Risk in Mortgage Contracts
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Research has shown that mortgage default is closely related to house prices. When house prices fall the borrower has an incentive to default. Since default incurs substantial cost to the lender, the borrower and many other market participants, as well as the society, house price is a risk in a mortgage contract. This was clearly demonstrated during the 2007-09 financial crisis. In this thesis I discuss some (potential) measures to manage mortgage default risk arising from low house prices. Chapter 1 is on mortgage insurance. Mortgage insurance is commonly used by lenders to transfer mortgage default risk to an insurer. After a brief introduction of the mortgage and mortgage insurance markets in US and Canada, I specify a simple mortgage insurance contract and a multiple state model for mortgage termination. The contract is then priced under the model. I explore the possibility of hedging house price risk in Chapter 2. If we assume a perfect market where house price risk can be traded exists, and a mortgage contract is a contingent claim on house prices, then the classic delta hedging is useful in hedging house price risk. In chapter 3 I discuss an innovative type of mortgage contract -- property index-linked mortgage. The purpose of this contract design is to reduce the borrower's propensity to default when house price declines. In particular, when house price declines, the mortgage balance and payment are reduced. I analyze this contract from the borrower's perspective and find that such contracts are effective in reducing default incentives and as a result, the lender may also be better off due to lower deadweight default cost. The last chapter focuses on house price basis risk. House price basis risk refers to the situation where the value of an individual property appreciates differently from the index. This may lead to problems such as suboptimal hedging, underpricing and lower efficiency for financial products involving house price index. In this chapter I develop a basis risk model that can be used to simulate reasonable individual house prices for a given index.