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Prepayment option and the interest rate differential between a fixed- and floating-rate mortgage loan

Prepayment option and the interest rate differential between a fixed- and floating-rate mortgage loan. Jyh -Bang Jou Graduate Institute of National Development, National Taiwan University, Taiwan Tan (Charlene) Lee Department of Accounting and Finance ,

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Prepayment option and the interest rate differential between a fixed- and floating-rate mortgage loan

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  1. Prepayment option and the interest rate differential between a fixed- and floating-rate mortgage loan Jyh-Bang Jou Graduate Institute of National Development, National Taiwan University, Taiwan Tan (Charlene) Lee Department of Accounting and Finance, University of Auckland, New Zealand

  2. Observation • FRM (fixed-rate mortgage loan) • ARM (adjustable rate mortgage loan) • The former rate contains a premium, why? • From the bank’s view Market interest rate = 6%, FRM = 6.5% 6% 7% (Bank’s downside) (Bank’s upside) 5%

  3. Why important? • Brueckner and Follain (1985), Campbell and Cocco (2003) • Mortgage choice = f (Interest rate differential, household characteristics) • Main factor: Interest rate differential • Other: Higher/more stable income, lower risk aversion, more likely to move out  ARM

  4. Research interest • Possible to use the concept of financial options to explain the differential? • From a borrower’s view • Schwartz and Torous (1992), Hilliard et. al. (1998) • Penalties: Flat admin fees, proportional to the loan balance, or extra interest payment (e.g. 6months ) (No action) 7% (Option to refinance) 5%

  5. Option to refinance • From a borrower’s view • Max (Payoff - Exercise price, 0) • Payoff = Savings on the interest payment • Exercise price = Penalties • Value of the option = Interest rate differential (No action) 7% (Option to refinance) 5%

  6. Optional to refinance • For simplification, we assume there’s no option to default, focusing on the cost side. We further assume it’s an interest only loan, with loan balance = $ 1 • FRM • Max • Our goal is to derive the option premium, (as the interest rate differential) (No action) 8% (May refinance) 4%

  7. Research design • FRM (6.5%) ARM ARM • ARM (6%) ARM ARM • Our model can be generalized to the case • ARM FRM ARM FRM t1 t2 t3 t4 T • The difference after t1, will be cancelled out

  8. Methodology • Interest rate, , is mean-reverting • Hull and White (1990): finite difference method • Trinomial model • is the value of the fixed-rate loan, denotes for the adjustable rate loan

  9. Comparative Statics results

  10. Results

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