Robust and accurate reconstruction of the time-dependent continuous volatility from option prices

초록

In this paper, we propose a robust and accurate reconstruction algorithm for the time-dependent continuous volatility function using observed option prices from the financial market and the Black-Scholes (BS) equation. The proposed algorithm consists of two steps: First, a time-dependent piecewise-constant volatility function is calculated. Second, a continuous volatility function is reconstructed by continuously connecting the jumps of the piecewise-constant volatility values at the expiration dates. We validate the accuracy and robustness of the proposed reconstruction of time-dependent continuous volatility by employing manufactured volatility and real financial market price data.

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