We introduce a general framework for stochastic volatility models, with the risky asset dynamics given by: dXt(ω, η) = μt η)Xt(ω, η)dt +σt(η)(ω,η)dWt(ω) where (ω, η) ∈ (Ω × H,fΩ⊗fH, PΩ⊗PH). In particular, we allow for random discontinuities in the volatility σ and the drift μ. First we characterize the set of equivalent martingale measures, then compute the mean- variance optimal measure P̃, using some results of Schweizer on the existence of an adjustment process β. We show examples where the risk premium λ=(μ- r)/σ follows a discontinuous process, and make explicit calculations for P̃.
Biagini F, Guasoni P (2002). Mean-variance hedging with random volatility jumps. STOCHASTIC ANALYSIS AND APPLICATIONS, 20(3), 471-494 [10.1081/SAP-120004112].
Mean-variance hedging with random volatility jumps
Guasoni P
Co-primo
2002
Abstract
We introduce a general framework for stochastic volatility models, with the risky asset dynamics given by: dXt(ω, η) = μt η)Xt(ω, η)dt +σt(η)(ω,η)dWt(ω) where (ω, η) ∈ (Ω × H,fΩ⊗fH, PΩ⊗PH). In particular, we allow for random discontinuities in the volatility σ and the drift μ. First we characterize the set of equivalent martingale measures, then compute the mean- variance optimal measure P̃, using some results of Schweizer on the existence of an adjustment process β. We show examples where the risk premium λ=(μ- r)/σ follows a discontinuous process, and make explicit calculations for P̃.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
