
Stochastic Volatility and Realized Stochastic Volatility Models 445
Σ
†−1
∼ W(ν
1
, Σ
1
) and accept it with probability
min
σ
†−1
η
σ
†−1
ǫ
exp
(
−
α
2
1
(1 − φ
2
)
2σ
†2
η
−
R
2
n
2σ
†2
ǫ
exp(α
n
)
)
σ
−1
η
σ
−1
ǫ
exp
−
α
2
1
(1 − φ
2
)
2σ
2
η
−
R
2
n
2σ
2
ǫ
exp(α
n
)
1
.
After sampling α, we set h
t
= α
t
+ µ for t = 1, . . . , n and µ = log(σ
2
ǫ
).
21.3 Realized SV Model
21.3.1 Realized volatil ity
Suppo se that the log-price p(s) follows the simple diffusion process:
dp(s) = µ(s)dt + σ(s)dW (s), (21.16)
where W(s) is a standard Brownian proce ss and µ(s) and σ(s) are the mean
and the standard deviation of dp(s) respectively, which may be time-varying
but a re assumed to b e independent of dW ...