Answer to Question #204972 in Financial Math for Stefano Balters

Question

1. Consider an arbitrage-free market, where the yield to maturity is described by (time is measured in years)
2. h(0, t) = 0.02 + 0.005t
   

• Compute v(0, 1), v(0, 2), v(0, 3), m(0, 1), δ(0, 3).
• In such market, compute the no-arbitrage price of a ZCB with maturity 3 years and notional 200.

Answer 1

• V(0,1)

h(0,t)=0.02+0.005(1)

=0.02+0.005

Therefore, V(0,1) = 0.025.

• V(0,2)

h(0,t)=0.02+0.005(2)

= 0.02+0.01

Therefore, v(0,2) =0.3

• V(0,3)

h(0,t)=0.02+0.005(3)

=0.02+0.015

Therefore, v(0,3)=0.035.

• M(0,1)

h(0,t)=0.02+0.005(1)

=0.02+0.005

Therefore, m(0,1) = 0.025.

• M(0,3)

h(0,t)=0.02+0.005(3)

0.02+0.015

Therefore, m(0,3)=0.035.

B) the no arbitrage price for a 3year period and notional of 200.

A(0,3)*200

h(0,t)={0.02+0.005(3)}*200

(0.02+0.015)*200

0.035*200

=7