# How would you hedge this structure?

I have a contingent claim and I want to find out what is the best structure to meet the continent claim, how to price it and how to hedge it. I am looking more for a qualitative answer.

Suppose I want to best replicate this claim $H$:

Given a stock $S_t$, $\text{exp} = 1$ (yrs), I need a payoff $H$ in which,

Conditional on $S_\text{exp} / S_0 \leq 0.8$, i.e the stock price decreased $20\%$ one year from now relative to the current price, then $H = \max{(0, V_\text{exp} - 0.17)}$, where $V_\text{exp}$ is the realized volatility one year from now. If the stock price did not meet the first criteria, the payout is just zero.

I decided to to use a stochastic vol process. I found the parameters of the stochastic vol process by running Monte Carlo simulations and simulating stock paths, and trying to find the parameters such that I am able to best fit the market prices.

An important assumption is that I can only trade the stock and options on the stock. I cannot trade volatility. Clearly, the market is incomplete because I have two uncertainties (Brownian motion in the stock and in the stochastic volatility). I am having difficulty deciding what is the best structure to best fulfill this contingent claim and yet be able to sufficiently hedge it using stocks and options.