Calibration of the Financial Model Based on Market Data (S&P 500)

The goal of this project was to calibrate financial models applying numerical methods. Using the set of market data (S&P 500; dataset contains 280 strike values for different maturities), the implied volatility (volatility smile) was calibrated in the Black-Scholes model for call and out Europian Options. The algorithm of Newton was used to calibrate implied volatility. The existence and unicity of the solution was investigated mathematically. Besides that Vega of un option was investigated.

As an additional practical problem an implied volatility for call options traded on the London Internetional Financial Futures and Option Exchange (LIFFE, as reported in the Financial Times on Wednesday, 22 Audust 2001) was calibrated. The data is for the FTSE 100 index, which is an average of 100 shares quoted on the London Stock Exchange.

The project was implemented in Matlab.