Numerical and Analytical Computation of the Implied Volatility from Option Price Measurements under Regime–Switching.

The paper aims to develop an algorithm to solve the inverse problem of identifying the volatility with given point measurements in a regime-switching economy. This value is of a particular importance since it is one of the main ingredients forming the option premia. After a review on the existing results for the classical Black–Scholes framework (equivalent to one regime), the direct and the inverse problems considering two regimes are defined. The forward problem is solved by applying the Simpson’s rule to an existing exact formula, while the inverse problem is tackled using a root-finding algorithm, namely Levenberg–Marquardt. What is more, a closed-form approximation formula for computing the implied volatility is proposed when at-the-money case is assumed. The numerical performance of the algorithms is studied and they are compared with a FDS approach. The paper is closed with a discussion and final remarks outlining the usefulness and applicability of the results. [ABSTRACT FROM AUTHOR]