I'm trying to compute a forward variance like this paper https://arxiv.org/pdf/2105.04073.pdf.
The paper shows that under rough stochastic volatility model assumption, options can be hedged with the underlying and variance swap.
I'm particularly interested in etablished a baseline for my work by replicating the experiment hedging VIX option which is modeled by
$$VIX_t = C e^{X_t}, \quad X_t = \sigma W^H_t,$$ where $W^H$ is a fractional Brownian motion.
I can follow the paper to the part of getting delta hedge which is
- $dP_t = N(d_t^1) dVIX_t$.
- $dP_t = \frac{N(d^1_t)e^{-\frac{1}{2}}(c^T(T) - c^T(t))}{2\sqrt{F^T_t}}dF_t^T$.
Here, $F^t$ is the forward variance ($F^T_t = \mathbb{E}_Q[VIX^2_T|\mathcal{F}_t]$).
To perform back test, the paper mentioned that the back test uses synthetic forward variance curve data, computed from S&P index options.
I wonder how the forward variance is computed here? Can I compute it using realized variance swap.
Additional questions after editting:
The initial value of the hedging portfolio is initialized with the ATM VIX option price with maturity 1.5 months computed within the model
Does this mean that the strike $K$ is set to $S_0$?
the quantity of the hedging asset in the portfolio is initialized with the corresponding model-based hedge ratio.
Does "model-based hedge ration" mean the delta hedge in the above formula?
(I'm from ML background, so I may not know many basic concepts in finance)
