Abstract:
Derivative securities, when used correctly, can help investors to increase theirs
expected returns and minimize theirs exposure to risk. Options o er in
uence
and insurance for risk-averse investors. The pricing problems of the exotic options
in nance do not have analytic solutions under stochastic volatility model
and so it is di cult to calculate option prices or at least it requires a lot of time
to compute them. Also the e ect of stochastic volatility model resolving shortcoming
of the Black-Scholes model its ability to generate volatility satisfying the
market observations and also providing a closed-form solution for the European
options. This study provides the required theoretical framework to practitioners
for the option price estimation. This thesis focuses on pricing for
oating strike
lookback put option and testing option pricing formulas for the Heston stochastic
volatility model, which de nes the asset volatility as the stochastic process.
Euler Maruyama method is the numerical simulation of a stochastic di erential
equation and generate the stochastic process way approximation. To simulate
stock price and volatility stochastic processes in Heston's model the Euler discretization
can be used to approximate the paths of the stock price and variance
processes on a discretize grid. The pricing method depends on the partial differential
equation approach on Heston stochastic volatility model and homotopy
analysis method. Heston model has received the most attention then it can give
a acceptable explanation of the underlying asset dynamics. The resulting formula
is well connected to a Black-Scholes price that is the rst term of the series
expansion, which makes computing the option prices fairly e cient.
