HW1-3: A continuous annuity pays $1 dt at every time 0 t T, for a total...

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HW1-3: A continuous annuity pays $1 dt at every time 0 t T, for a total undiscounted payoff dt = T if no default. The continuous risk-free rate r is constant over time, and the default time is exponentially distributed at constant hazard rate . (a) Find the price a(0,7) of a risk-free annuity. (b) Find the price A(0,T) of a defaultable annuity. (c) Show that the credit spread on the unit zero-coupon bond with fixed recovery 0 R 1 at default may be expressed as: S (0, T) [RA(0,T) b(0,T) +1 F(T)] where b(0, T) = e-T is the price of the risk-free zero-coupon bond and F(-) is the default cdf. In HW1-3: A continuous annuity pays $1 dt at every time 0 t T, for a total undiscounted payoff dt = T if no default. The continuous risk-free rate r is constant over time, and the default time is exponentially distributed at constant hazard rate . (a) Find the price a(0,7) of a risk-free annuity. (b) Find the price A(0,T) of a defaultable annuity. (c) Show that the credit spread on the unit zero-coupon bond with fixed recovery 0 R 1 at default may be expressed as: S (0, T) [RA(0,T) b(0,T) +1 F(T)] where b(0, T) = e-T is the price of the risk-free zero-coupon bond and F(-) is the default cdf. In

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a To find the price a0 T of a riskfree annuity we can integrate the payments over time t from 0 to T ... View the full answer