Pricing and hedging exotic options using Monte Carlo method

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Julkaisun nimi: Pricing and hedging exotic options using Monte Carlo method
Tekijä: Timofeeva, Natalia
Muu tekijä: Helsingin yliopisto, Matemaattis-luonnontieteellinen tiedekunta
Julkaisija: Helsingin yliopisto
Päiväys: 2019
Kieli: eng
Opinnäytteen taso: pro gradu -tutkielmat
Oppiaine: Matematiikka
Tiivistelmä: This thesis attempts to show the advantages of Monte Carlo method in pricing and hedging exotic options. The popularity of exotic options increased recently, mostly due to their almost unlimited flexibility and adaptability to any circumstances. The negative side of exotic options is their complexity. Due to that many exotic options does not have analytic solutions. As a result numerical solutions are a necessity. The Monte Carlo method of simulations is very common method in computational finance. Monte Carlo method is based on the analogy between probability and volume. Starting point in pricing and hedging options with Monte Carlo method is stochastic differential equation based on Brownian motion in the Black-Scholes world. The fair option value in the Black-Scholes world is the present value of the expected payoff at expiry under a risk-neutral assumptions. The analysis start from the case of the simple European options and continue with introducing different kinds of exotic options. The dynamic hedging idea is used to derive the Black-Scholes Partial Differential Equation. The numerical approximation of the stochastic differential equation is derived through the lognormal asset price model. The Monte Carlo algorithms are constructed for pricing and delta hedging and then implemented to MATLAB. For generating Monte Carlo simulations is used N(0,1) pseudo-random generator. The analysis is limited to the cases of simple Barrier options, which are one of the most known and used type of the exotic options. Barrier options are path dependent options, which implies that the payoff depends on the path followed by the price of the underlying asset, meaning that barrier options prices are especially sensitive to volatility. That is why, we also introduce the variance reduction techniques by antithetic variates. For hedging barrier options were chosen the dynamic delta-hedging and static hedging strategies. All calculations and figures in the examples were made in MATLAB.


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