# Valuation of Derivative Assets

## Official Course Description

- LTH Course Description (SV)
- NF Course Description (SV)
- LTH Course Description (EN)
- NF Course Description (EN)

## Description

The course consists of two related parts. In the first part we will look at option theory in discrete time. The purpose is to quickly introduce fundamental concepts of financial markets such as free of arbitrage and completeness as well as martingales and martingale measures. We will use tree structures to model time dynamics of stock prices and information flows.

In the second part we will study alternative models formulated in continuous time. The models we focus on are formulated as stochastic differential equations (SDE:s). Most of the second part is devoted to the probability theory required to understand the SDE models. We go through the underlying theory of Brownian motion, stochastic integrals, Ito's formula, measure changes and numeraires. We here also apply the theory on valuation of derivatives both for the stock and interest rate market. We derive e.g. the Black-Scholes formula and how replicating portfolios for options are created.