Abstract:
The theory of option pricing made a dramatic step forward when Black and Scholes
published a centennial paper with a solution for the prices of European call and put
options. However, their solution only deals with the perfect markets. In the realworld, the markets are not perfect and the predictions from their formula deviate
significantly from the market prices. This is because of the assumptions on which the
model is based.
Heston model is one of the newer models which extends the classical Black-Scholes
model and can produce better estimates of option prices with non-constant variable
volatility. However, this variable volatility needs to be accurately predicted itself,
but the price which is often taken as input for finding implied volatility is not always
given. In this thesis, two neural network models for learning historical volatility were
constructed and compared in order to predict the implied volatility for the option
without knowing its price. The results of prediction were tested and evaluated.
The better performing model was used to approximate implied volatility and the
result was incorporated into the solution grid and finite difference scheme for the
Heston model was applied to produce the option price. The generated prices were
compared to the prices generated by the classical Black-Scholes model in several
different scenarios.