Parameter Estimation of Local Volatility in Currency Option Valuation

In quantitative finance and option pricing, one of the basic determinants of option prices is the volatility of the underlying asset. In this paper, we therefore, present a concise study of volatility in option pricing in the sense of Dupire’s approach. Thereafter, we outspread such study via the application of Ito formula to the modelling and valuation of currency option with local volatility. For the purpose of efficiency, we use the daily historical prices of stock-S&P 500 for a certain period to estimate the corresponding historical volatility. Graphical representation of the analysed daily historical data of stock prices with respect to a local volatility is presented