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Abstract
In the Black-Scholes options pricing formulas one parameter that cannot be directly observed is the volatility of the stock price. If actual market data of the price V are known, then the volatility can be viewed as unknown and can be calculated via the implicit equation (),,,,,0VvSTtKrσ−=.
The volatility σplays the role of the unknown parameter. The volatility σdetermined in this way is called implied volatility and is the root of the equation()(),,,,,0fVvSTtKrσ σ =− = . Iterative methods such as Newton’s method, can then be used to find the root. In this work we propose an approach that uses a genetic algorithm to find the implied volatility.
Keywords: option pricing, implied volatility, genetic algorithm
The volatility σplays the role of the unknown parameter. The volatility σdetermined in this way is called implied volatility and is the root of the equation()(),,,,,0fVvSTtKrσ σ =− = . Iterative methods such as Newton’s method, can then be used to find the root. In this work we propose an approach that uses a genetic algorithm to find the implied volatility.
Keywords: option pricing, implied volatility, genetic algorithm