As some of you observe, I have been posting a handful of undergraduate and postgraduate materials or courses here. Some close students also asked me to share more on financial engineering. So here, I want to start on a simple series on Financial Engineering, and will finish up the analytics materials before I finish this definitely. I am quite excited to share this to be honest!
Firstly, I will break this up into two parts for simplicity. Part one shall focus on using straight forward stochastic models to price derivative securities in various asset classes. We will look at equities, fixed income, credit and mortgage-backed securities. At the same time, we try to evaluate their roles during a financial crisis too.
I want to state clearly that this is really post graduate materials and we need strong knowledge in statistics, linear algebra and calculus. Instead of using my favourite Matlab here, I’ll use Excel to keep it reader friendly. Let’s begin with an overview of what we will be studying on.
Financial markets enable efficient allocation of resources, across time and states of nature. What does this mean? If I’m young and have a high salary, the existence of a financial market enable me to invest in stocks & bonds to finance retirement, home ownership, etc. Without the existence of a financial market, we can only consume. In this series, I’ll discuss a fair amount of hedging too, so what is hedging? A hedge is like a barrier of bush, its to prevent entry. In finance, hedging is akin to a financial position one takes to offset any potential (incoming) losses, etc. For example, Starbucks buy stocks on coffee bean producers as a form of hedging so when the coffee bean prices soar (cost of production soar) but their stocks will appreciate.
What are the roles of markets?
1. Gather information
2. Liquidity (Supply & Demand)
3. Promote efficiency and fairness
Why create so many products to sell? (Needs)
1. Hedge risk
2. Allow speculation
3. Raise funds
4. Fund liabilities
There are two kinds of market models: Discrete time models and Continuous Time models. For simplicity, we will do Discrete time models in Part 1 first. Discrete time models have two types: Single period and multi-period models. We look at Discrete time model first because from it, we can appreciate all important concepts but with simplicity. Although one can argue that we can’t really obtain a closed form solution here and need use numerical calculations.
Next, I’ll address the difference between Financial Economics and Financial Engineering. The former uses equilibrium arguments to price equities, bonds, etc and set interest rates. The latter assume price of equities and interest rates are given, and price derivatives on equities, bonds, interest rates, etc using the no-arbitrage condition (we will get to it on session 2).
So what are we interesting in solving for Financial Engineering?
1. Security pricing
2. Portfolio selection: choosing a trading strategy to maximise the utility.
3. Risk Management: understanding the risks inherent in a portfolio. Tail risk, value at risk and conditional value at risk.