ABSTRACT
The main topic of this Chapter is the pricing of financial derivatives. A financial derivative is a contract which is derived from an underlying asset. Its fair value is defined as the price for which a neutral market participant would be willing to buy or sell the contract. The contract is valuated to market prices on regular basis in order to obtain a marked-to-market valuation. This valuation guarantees that the market is arbitrage free, that is it is not possible to make a profit without taking any risk. First, we focus on the options, which have the spot price as underlying. They are priced through the continuous time model of Black and Scholes and the discrete time Binomial model. The main mathematical passages are described and the main financial relationships are enlightened. In addition, the volatility smile is explained. Secondly, if the underlying is the forward/futures price, we propose the Black model. Finally, the Monte Carlo approach to price also other financial derivatives is introduced. We conclude by pricing Asian options.
