Question

Assume an economy where

• One period is one year

• The one year short term interest rate from time n to time n + 1 is rn.

• The rate evolves via a stochastic process: r0 = 0.02 rn+1 = Xrn
˜ P[X = 2k] = 1/3
for k ∈{−1,0,1}.
(1)
• Consider now a zero-coupon bond that matures in 3−years with common face and redemption value F = 100.

• Compute B0, the value of this zero-coupon bond.

• Also compute European Call Options on this bond that expire in

(a) 3 years with strike K = 97.

(b) 1 year with strike K = 97.

• Finally, compute American Put Options on this bond that expire in

(a) 3 years with strike K = 97.

(b) 1 year with strike K = 97.

I need detailed process please. Just picture I can't get it.

Answer 1

SOLUTION:-

By the given problem the rate involved via stochastic process,

  

   for  

Here we literate backwar form the values

  

Our general recusive formula is --

  

generating backward, we see that at t=

at time t = 2 we have that

our anocinted Bond and call option values at time 2

R2	B2	e2
0.08	92.59	0
0.04	96.15	0
0.02	98.04	1.04
0.01	99.01	2.01
0.005	99.50	2.50

Our anocinted Bond and call option values at time 1

r1	B1	C1
0.04	91.92	0.33
0.02	95.82	1.00
0.01	97.87	1.83

Our anocinted Bond and call option values at time 0

r0	B0	C0
0.02	93.39	1.03

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