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Option pricing in the moderate deviations regime.
Peter Friz1, Stefan Gerhold2, Arpad Pinter2
1TU and WIAS Berlin Germany.
This study provides new estimates for call option prices near expiration in diffusion models. The findings offer accurate calculations for moderately out-of-the-money options, improving financial modeling.
Area of Science:
- Quantitative Finance
- Mathematical Finance
- Financial Derivatives
Background:
- Call option pricing is crucial in financial markets, especially near expiration.
- Existing models often focus on at-the-money or deep out-of-the-money options.
- A need exists for accurate pricing in the moderately out-of-the-money regime.
Purpose of the Study:
- To develop and analyze asymptotic estimates for call option prices close to expiry.
- To bridge the gap between at-the-money and out-of-the-money pricing regimes.
- To provide accurate approximations for implied volatilities in diffusion models.
Main Methods:
- Utilizing small-time moderate deviation theory for asymptotic analysis.
- Deriving first and higher-order expansions for option prices and implied volatilities.
- Applying methods to generic local and stochastic volatility models.
Main Results:
- Obtained novel asymptotic expansions for call option prices and implied volatilities.
- Demonstrated that these expansions involve simple expressions of model parameters.
- Showcased the applicability to a wide range of volatility models.
Conclusions:
- The derived estimates accurately price moderately out-of-the-money call options near expiry.
- The methodology is general and applicable to complex financial models like the Heston model.
- Numerical results confirm the high accuracy of the proposed asymptotic expansions.

