Table 2.

Simulation results under the $\mathrm{\Gamma }$-OU Hawkes volatility model for a European call option. Parameters are as in Table 1, top panel refers to set A (true option price: 5.6645), central panel refers to set B (true option price: 12.4740), bottom panel refers to set C (true option price: 11.7605). Other parameters: $S_0=100$, $K=100$ and $T=1$. $\mathcal{M}\times {10}^4$ is the total number of simulations, $\mathcal{N}\times {10}^2$ is the number of time steps in the Euler scheme. Further notes: CPU is in seconds

	Euler				Exact
$\mathcal{M}\times {10}^4$	$\mathcal{N}\times {10}^2$	bias	RMSE	CPU	RMSE	CPU
Set A
1	1	0.0669	0.1000	0.16	0.0758	0.17
4	2	0.0333	0.0498	0.80	0.0375	0.38
16	4	0.0170	0.0252	6.18	0.0186	1.22
64	8	0.0092	0.0177	47.19	0.0093	4.71
256	16	0.0049	0.0068	425.33	0.0047	19.67
Set B
1	1	0.1988	0.2685	0.16	0.1800	0.22
4	2	0.0996	0.1341	0.80	0.0912	0.59
16	4	0.0473	0.0652	6.14	0.0454	2.24
64	8	0.0240	0.0329	46.05	0.0226	9.16
256	16	0.0136	0.0177	421.49	0.0113	35.59
Set C
1	1	0.1547	0.2672	0.16	0.2206	0.25
4	2	0.0796	0.1379	0.80	0.1124	0.72
16	4	0.0328	0.0641	6.10	0.0562	2.61
64	8	0.0179	0.0332	46.81	0.0278	10.30
256	16	0.0115	0.0181	420.54	0.0139	40.51