Pricing Options Using Monte Carlo Simulation
|Author:||Bc. Ryan Dutton|
|Year:||2019 - summer|
|Leaders:|| prof. Ing. Oldřich Dědek CSc.
|Work type:|| Bachelors
|Awards and prizes:|
|Abstract:||Monte Carlo simulation is a valuable tool in computational finance. It is widely used to
evaluate portfolio management rules, to price derivatives, to simulate hedging strategies, and
to estimate Value at Risk. The purpose of this thesis is to develop the mathematical foundation
and an algorithmic structure to carry out Monte Carlo simulation to price a European call
option, investigate Black-Scholes model to look into the parallel between Monte Carlo
simulation and Black-Scholes model, provide a solution for Black-Scholes model using
Lognormal distribution of a stock price rather than solving Black-Scholes original partial
differential equation, and finally compare the results of Monte Carlo simulation with BlackScholes closed-form formula.
Author’s contribution can be best described as developing the mathematical foundation and the
algorithm for Monte Carlo simulation, comparing the simulation results with the Black-Scholes
model, and investigating how path-dependent options can be implemented using simulation
when closed-form formulas may not be available.