SIMULATION OF CORPORATE BOND

1
SIMULATION OF CORPORATE BOND

• Paul Levallois
• Didier Li Kwan Pun
• Scott Rodger
• Ivan Todorovic

2
AIM

• Price 10-year zero-coupon bond subject to
• Interest rate movements
• Risk of default

3
INFORMATION SUPPLIED

• Stochastic processes for
• interest rate r(t)
• stock price S(t)
• volatility of stock price ss(t)
• Var-Cov matrix of Brownian Motion terms
• Default defined by stock price S reaching a
  certain low value K

4
SOLUTION PROCEDURE

• Diagonalize Var-Cov matrix
• Discretize the 3 processes using forward Euler
• Generate paths for S(t) and r(t)
• Default indicator
• X 0 if S(t) K for 0 lt t 10
• X 1 if S(t) gt K for 0 lt t 10
• Average over 1000 paths
• Price E X exp(- S r(t) ?t )

5
ANALYSIS

• Effect of default risk on price
• Effect of interest rate volatility on price
• Effect of time step size on bias
• For a continuous-time result, solution should
  converge as ?t 0

6
GRAPH OF RESULTS
7
LIMITATIONS

• Model for interest rates
• volatility too high
• original model allows rates to go negative
• modified to restrict movement in the range 0
  30
• should use a more realistic model (e.g. CIR)
• Some precision lost after Var-Cov matrix
  diagonalized

8
CONCLUSION

• Calculated risk-adjusted price of zero-coupon
  bond
• Solution converges in limit to continuous time
• Increasing time step reduces price
• Increasing i.r. volatility reduces price
• Increasing default risk reduces price