Option Pricing Model Report

An option is a right that gives its holder the option to trade a given risky asset (stock) at a certain price by a certain date. It is a typical tool in mathematical finance and modern financial market. Pricing an option before its expiration date is an interesting and often tricky mathematical

problem. In this project, we will develop a discrete-time model for the price movement of the underlying stock price, namely, the multi-period binomial model. It involves constructing a tree which represents different possible paths that the price of the underlying asset might follow. This tree is called the Binomial Tree. This model is based on an assumption about the evolution of the price of the underlying asset and the so called 'no-arbitrage principle'. After this, we shall price European call options based on binomial model we make. At last, we will try to calculate prices of call options by using C++, Python and Java, then to compare efficiencies of these three methods, in terms of program running time.

In this section, we will develop the framework into a complete valuation method. We begin by assuming that the stock price follows a multiplicative binomial process. The stock state price for each period can have two possible values: s_0^ u (u>1) with probability〖 q〗_u (0<〖 q〗_u<1), and s_0^ d (d=1/u) with probability (q_d=1 –q_u). To mention that, Q= (〖 q〗_u,q_d) is risk neutral measure which is a fundamental condition to make sure there is no arbitrage space. We can represent this movement with the following diagram: