Risk Analysis in Finance and Insurance, 2nd Edition

Problems 285

(a) A

0

=0.08; A

1

=0.02; A

2

= −0.003; A

3

=0.0001;

(b) A

0

=0.06; A

1

=0.01; A

2

= −0.001; A

3

=0.0001.

Find the price of a call option on the zero-coupon bond (with maturity T =4

years) with strike K = $80 and the expiration time T

1

=1year. Hint: use the

following pricing formula

C = B(0,T)Φ(d

1

) − KB(0,T

1

)Φ(d

2

),

where

d

1

=

ln



B(0,T)

B(0,T

1

)K



+

V

2

√

V

,d

2

= d

1

−

√

V

and V =0.25.

How the pricing formula will change for a face value that is different from

$1? Assuming that face value is $80, calculate the price of such option. Com-

pare it with the previous result.

Problem A.5.6 The market price of a two-year bond at time t =0is $100.

The bond has the following payment