Valuation of power options under Heston's stochastic volatility model

The continuity and estimates of a solution to mixed fractional constant elasticity of variance system with stochastic volatility and the pricing of vulnerable options

“…are positively correlated if 0.5 < H < 1, uncorrelated if H = 0.5, and negatively correlated if 0 < H < 0.5. At the end of this section, we give some notations, function spaces, and conclusions to prove our main results (for details, see [13][14][15]).…”

“…where λ is a real constant, P is a physical probability measure, and {F t , t ≥ 0} denotes the P-completion of the filtration generated by (B(t), B H (t)). An mfBm {M H (t), t ≥ 0} has the following properties [12,13] 1. M H (0) = 0 and E[M H (t)] = 0 for any t ≥ 0.…”

“…In this section, we prove moment estimates and continuity of the solution of the mixed fractional CEV system (1.2)-(1.3) by extending the idea of [13] for a mixed stochastic differential equation.…”

“…The paper [12] also studies the existence and uniqueness of a strong solution to (1.1). Certain L p estimates of (1.1) are proved in [13]. However, all the existing SV models mentioned are based on the Brownian motion with increments following the independent norm distribution.…”

“…|V 1 (s)| dB H (s)| p . Applying the B-D-G inequality[13,15] to E[A 3 ] and using the inequality x ≤ 1 + x 2 , we have…”