Table 1

Parameters for the simulation

Panel A. Parameters for price process SM,t
κMθMσM,vμM,vμM,S (%)σM,S (%)ρMλM (%)
P-measure0.0260.540.081.48−2.632.89−0.480.6
Q-measure0.0570.2460.088.78−5.395.78−0.480.6
Panel B. Parameters for the idiosyncratic risks of Si
P-measureQ-measure
κiθiμi,vμi,S (%)σi,S (%)λi (%)κiθiμi,vμi,S (%)σi,S (%)λi (%)σi,vρiβi,Dβi,J
AXP0.0230.0401.5870.11.70.0340.0120.0793.175−1110.0350.119−0.5501.120.55
BA0.0280.3171.1900.01.20.0680.0120.7944.762−490.0980.119−0.6000.891.45

Note(s): Panel A provides parameters for Eqs. (24) and (26) to simulate the daily returns of the market index, which are taken from Table 1 of Neuberger (2012). Here, μM,v denotes the mean of JM,v,t, which follows an exponential distribution; μM,S and σM,S denote the mean and standard deviation of JM,t, which follows a normal distribution; ρM is the correlation between WM,t and BM,t; and λM is the jump intensity of the Poisson process NM,t. In addition, we set gM=λM(eμM,S+12σM,S21) to ensure that SM is a martingale under both P and Q measures. Panel B provides parameters for Eqs. (25) and (27) to simulate the daily returns of two individual stocks among 29 stocks listed in Tables 6 and 7 of Gourier (2016). Some parameters in Panel B are modified from the original source. For example, κi = 0.023 in the first row is obtained from κ = 5.9 in Gourier (2016) by dividing it by 252 to simulate daily return processes. In addition, while Gourier (2016) assumes that jump intensity is an affine function of the instantaneous variance process, our model assumes a constant jump intensity. Accordingly, we set λi=100252(λ0G+λ1GθG) (%), where λ0G and λ1G are the intercept and slope parameters, respectively, in Gourier (2016). Finally, we set gi=λM(eβi,JμM,S+12βi,J2σM,S21)λi(eμi,S+12σi,S21) to ensure Si is a martingale under both P- and Q-measures

or Create an Account

Close subscription notice
Close access options