Pricing European Barrier Options With Rebates

Abstract

In Vietnam, derivatives market has just started officially very recently, in August, 2017, with futures contracts on VN30 index. It is a very new investment area for Vietnamese investors. This market is however expected to strongly develop soon and then enhance greatly Vietnamese economy. In fact, trading volume on futures contracts on VN30 index is increasing significantly over last few months, and is expected to increase with an even faster rate. One important type of financial derivatives products is options. In Vietnam, covered call (a type of call options) will be traded soon. Options will bring greater leverage to speculators and bring more risk management tools for hedgers. Options thus have great potential chance in Vietnamese financial markets. Understanding clearly the pricing formulas for these products is very urgent, then the object of the thesis formulate the pricing models of European barrier options with rebates using the probabilistic approach. It includes deriving the Black - Scholes - Merton model by the Martingale approach which is model of European options. Then European down and out call options with rebates is formulated by using theory of Wiener process like Reflection Principle, First Passage Time, Markov Property and Stochastic Differential Equations as It¯ o Calculus and One-Dimensional Diffusion Process. Further, testing real data for normal distribution using R – Studio software. Lastly, using the final formula to calculate the option price of the underlying asset price of stocks in Vietnam. The stock is applied that must be satisfied given conditions by previous testing.