Abstract
We obtain a Hull and White type option price decomposition for a general local volatility model. We apply the obtained formula to CEV model. As an application we give an approximated closed formula for the call option price under a CEV model and an approximated short term implied volatility surface. These approximated formulas are used to estimate model parameters. Numerical comparison is performed for our new method with exact and approximated formulas existing in the literature.
Highlights
In [1], a decomposition of the price of a plain vanilla call under the Heston model is obtained using Itocalculus
These models are sometimes called local volatility models in the industry and GARCH-type volatility models in financial econometrics. Recall that these models are different from the so-called stochastic volatility models, like Heston model, where the volatility process is driven by an additional source of randomness, not perfectly correlated with the stock price innovations
We notice that ideas developed in [1] for Heston model can be used for spot-dependent volatility models
Summary
In [1], a decomposition of the price of a plain vanilla call under the Heston model is obtained using Itocalculus. The model presented here assumes the volatility is a deterministic function of the underlying stock price, and there is only one source of randomness in the model These models are sometimes called local volatility models in the industry and GARCH-type volatility models in financial econometrics. For the particular case of CEV model, we obtain an approximation of the at-the-money (ATM) implied volatility curve as a function of time and an approximation of the implied volatility smile as a function of the log-moneyness, close to the expiry date. We use these approximations to calibrate the CEV model parameters
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