Macroeconomic Environment and the Optimal Mortgage Contrac

Transcription

1 Macroeconomic Environment and the Optimal Mortgage Contract Design - A Simulation Approach Melanie Sturm University Regensburg June 24, 2009

2 Motivation Risks connected to a mortgage depend on volatile interest rates borrower income house value Wrong expectation / over-optimism about the progress of stochastic variables can lead to sufficient losses and financial instability. Optimal mortgage contract design mitigating negative outcomes of over-optimism?

3 Focus: interest rate risk Mortgage Rate Mortgage Payment r t + d ARM cr t,md = r 0 + d FRM min(r 0,.., r t ) + d DRM for md = ARM for md = FRM for md = DRM (1) with M 0,md = LTV 0,md H 0,md MP t,md = M t,md AF cr t,md 240 t+1 (2)

4 The Margin d is charged to cover expected expenses and losses Profit / Loss in Period t { PL t := M t (cr t,md r t ) for d t = 0 min(m t (cr t,md r t), (1 ξ)h t (1 + r t) M t) for d t = 1 (3)

5 Mean Reverting Process Stochastic Variables move in the direction of their means µ i at speed α i. dr t = α r (µ r r t )dt + σ r dw r,t (4) Correlations dy t = α y (µ y y t )dt + σ y dw y,t (5) dh t = α h (µ h h t )dt + σ h dw h,t (6) dw y,t dw h,t = ρ y,h dt dw y,t dw r,t = ρ y,r dt, dw h,t dw r,t = ρ h,r dt (7) with ρ y,h dt, ρ y,r dt, ρ h,r dt [ 1; 1]

6 Over-Optimism / Unexpected Movements house value: jump extended Vasicek process: with dh t = α h (µ h h t )dt + σ h dw h,t + dj h,t (8) N t J t = Z j ; dj t = Z Nt dn t (9) j=1 The jump models an extreme movement in the short run. borrower income: the borrower is more likely to loose her job if the economy goes down

7 borrower with a more doubtful income should be more constrained in taking mortgages with a high LTV no matter of the mortgage contract design. If the borrower takes the interest rate risk, a mortgage comes along with a great downside risk regarding wrong expectations about the house appreciation and the borrower income The borrower should be constrained in the LTV and PTI ratio she borrows at. If the lender takes the interest rate risk the risk arising out of risky borrower income and thus volatile house values is minimized. The downside risk faced by the lender is still manageable at higher LTV and PTI ratios. but the borrower is constraint the most in her housing decision (lower initial mortgage balance)

8 Further Research Affordability of housing the lender s exposition to interest rate risk combinations: fixing the mortgage rate in the early stage of a mortgage; adjusting the mortgage rate in the later stage of a mortgage when the mortgage is partly payed off and the interest payment makes up a smaller part of the mortgage payment shorter interest fixing periods