Advances in Risk Management

116 IDIOSYNCRATIC RISK, SYSTEMATIC RISK AND STOCHASTIC VOLATILITY or, equivalently, under the minimal martingale measure: dR(t,I ...

HAYETTE GATFAOUI 117 Gt=Ft∪{Is,t≤s≤T} and compute the two first moments of probability dis- tribution of ln ( VT Vt ) conditiona ...

118 IDIOSYNCRATIC RISK, SYSTEMATIC RISK AND STOCHASTIC VOLATILITY 6.4 SIMULATION STUDY We use Monte Carlo accelerators to examin ...

HAYETTE GATFAOUI 119 and correlation coefficientρ(t,It). On the other hand, the greater beta is, the higher firm value’s volatil ...

120 IDIOSYNCRATIC RISK, SYSTEMATIC RISK AND STOCHASTIC VOLATILITY Table 6.1 Average values of daily simulated variables on [t,T] ...

HAYETTE GATFAOUI 121 Table 6.2Average monthly simulated values of firm’s debt


λ β −1.5 − 1 −0.5 0 0.5 1 1.5 0.2 2.25 4.93 ...

122 IDIOSYNCRATIC RISK, SYSTEMATIC RISK AND STOCHASTIC VOLATILITY Table 6.3 Average monthly simulated values of firm’s equity
...

HAYETTE GATFAOUI 123 Table 6.5 Average monthly simulated values of credit spreads in basis points


λ β −1.5 − 1 −0.5 0 0.5 ...

124 IDIOSYNCRATIC RISK, SYSTEMATIC RISK AND STOCHASTIC VOLATILITY 9000 8000 7000 6000 5000 4000 3000 2000 1000 0 0.51.5
0.5
...

HAYETTE GATFAOUI 125 Table 6.6Average bounds of simulated aggregate volatility in percent


λ β 0 0.5 1 1.5 0.2 17.84 41.13 ...

126 IDIOSYNCRATIC RISK, SYSTEMATIC RISK AND STOCHASTIC VOLATILITY Table 6.7 Average bounds of simulated credit spreads in basis ...

HAYETTE GATFAOUI 127 we obtain an asymptotically mean reverting stochastic volatility process relative to time. Moreover, an int ...

128 IDIOSYNCRATIC RISK, SYSTEMATIC RISK AND STOCHASTIC VOLATILITY and ratios. In the same way, Phoa (2003) underlines the cohere ...

HAYETTE GATFAOUI 129 WhenμI(It)=λε− ( 2 −λ ) ln(It),σI(It)= √ ln (It), andIt>1;R(t,It)=β^2 γ^2 t^2 α+ ln(It). Then,R(t, ...

130 IDIOSYNCRATIC RISK, SYSTEMATIC RISK AND STOCHASTIC VOLATILITY Delbaen, F. and Schachermayer, W. (1996) “The Variance-Optimal ...

HAYETTE GATFAOUI 131 Jarrow, R.A., Lando, D. and Yu, F. (2005) “Default Risk and Diversification: Theory and Applications”,Mathe ...

CHAPTER 7 A Comparative Analysis of Dependence Levels in Intensity-Based and Merton-Style Credit Risk Models Jean-David Fermania ...

JEAN-DAVID FERMANIAN AND MOHAMMED SBAI 133 of the time, the increments of the asset process are assumed Gaussian. Thus, a correl ...

134 A COMPARATIVE ANALYSIS OF DEPENDENCE LEVELS In this model, the correlation between default events is related to the correlat ...

JEAN-DAVID FERMANIAN AND MOHAMMED SBAI 135 Table 7.1Average default rates over 1981–2002 Rating CCC B BB BBB A AA AAA PD (%) (1 ...