Advances in Risk Management

96 AN ESSAY ON STOCHA ST IC VOLATILITY AND T HE YIELD CURVE 5.5.2 Algorithm A standard setup of the Kalman filter is applicable ...

RAYMOND THÉORET, PIERRE ROSTAN AND ABDELJALIL EL-MOUSSADEK 97 After integrating by parts, we obtain the discrete time specificat ...

98 AN ESSAY ON STOCHA ST IC VOLATILITY AND T HE YIELD CURVE Table 5.2 Example of ML parameter estimates obtained for the 10 Dec. ...

RAYMOND THÉORET, PIERRE ROSTAN AND ABDELJALIL EL-MOUSSADEK 99 5.7.2 Improvement of the Monte Carlo simulation To improve the per ...

100 AN ESSAY ON STOCHA ST IC VOLATILITY AND T HE YIELD CURVE Maturity 1 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 23456789 Vari ...

RAYMOND THÉORET, PIERRE ROSTAN AND ABDELJALIL EL-MOUSSADEK 101 Maturity Yield 0510 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0 ...

102 AN ESSAY ON STOCHA ST IC VOLATILITY AND T HE YIELD CURVE 0 1 1.5 2 2.5 3 3.5  10
^3 51015 Maturity RMSE 20 25 30 EKF 1 Sig ...

RAYMOND THÉORET, PIERRE ROSTAN AND ABDELJALIL EL-MOUSSADEK 103 Table 5.3F&V+EKF are the RMSE computed with the plain F&V ...

104 AN ESSAY ON STOCHA ST IC VOLATILITY AND T HE YIELD CURVE This technique of variance reduction was first introduced by Théor ...

RAYMOND THÉORET, PIERRE ROSTAN AND ABDELJALIL EL-MOUSSADEK 105 Campbell, J.Y., Lo, A.W. and MacKinlay, A.C. (1997)The Econometri ...

106 AN ESSAY ON STOCHA ST IC VOLATILITY AND T HE YIELD CURVE Longstaff, F. and Schwartz, E. (1992) “Interest Rate Volatility and ...

CHAPTER 6 Idiosyncratic Risk, Systematic Risk and Stochastic Volatility: An Implementation of Merton’s Credit Risk Valuation Hay ...

108 IDIOSYNCRATIC RISK, SYSTEMATIC RISK AND STOCHASTIC VOLATILITY authors have investigated this assumption to test whether cred ...

HAYETTE GATFAOUI 109 risk is mainly driven by idiosyncratic risk (Campbell and Taksler, 2003). Though market variance has no pre ...

110 IDIOSYNCRATIC RISK, SYSTEMATIC RISK AND STOCHASTIC VOLATILITY In the light of such results, we extend the work of Gatfaoui ( ...

HAYETTE GATFAOUI 111 dIt It =μI(t,It)dt+σI(t,It)dWIt (6.2) where functionalsμX(t,Xt),σX(t,Xt),μI(t,It) andσI(t,It) are continuou ...

112 IDIOSYNCRATIC RISK, SYSTEMATIC RISK AND STOCHASTIC VOLATILITY financial and corporate events), which are known to impact ass ...

HAYETTE GATFAOUI 113 x,y∈{t,Vt,It}. Applying multivariate Ito’s lemma to the global variance of firm value’s instantaneous retur ...

114 IDIOSYNCRATIC RISK, SYSTEMATIC RISK AND STOCHASTIC VOLATILITY where α 1 (t,Vt,It)=α(t,Vt,It)ςβ √ 1 −ρ^2 (t,Vt,It); α 2 (t,Vt ...

HAYETTE GATFAOUI 115 6.3.1 Model specification Targetingaconvenientdegreeofsimplification, wemaketwomajorassump- tions. First, w ...