hard · Quantitative Finance derivatives
In a stochastic-volatility model (e.g. Heston), a long-dated cliquet pays the sum of capped monthly returns. A risk manager observes that, holding the market vanilla surface fixed, switching from a local-volatility model to a pure stochastic-volatility model materially changes the cliquet price even though both are calibrated to the same vanillas.
What is the primary financial reason for this model dependence?
- Local and stochastic volatility imply different forward-smile dynamics, and the cliquet's value depends on the forward smile, which vanillas do not pin down
- Local volatility produces arbitrage in the vanilla surface that stochastic volatility removes, so the price gap reflects an arbitrage adjustment to the cliquet
- The two models assign different prices to the underlying forwards, so the discrepancy is a difference in the calibrated drift rather than in volatility dynamics
- Stochastic volatility violates put–call parity for the monthly options embedded in the cliquet, inflating the capped-return legs relative to local volatility
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