MATH代写3075
FINANCIAL MATHEMATICS代写
Christian-Oliver Ewald and Marek Rutkowski School of Mathematics and Statistics
Related courses:

• MATH2070/2970: Optimisation and Financial Mathematics.
• STAT3011/3911: Stochastic Processes and Time Series.
• MSH2: Probability Theory.
• MSH7: Introduction to Stochastic Calculus with Applications.
• AMH4: Advanced Option Pricing.
• AMH7: Backward Stochastic Differential Equations with Applications.

 

Suggested readings:

• J. C. Hull: Options, Futures and Other Derivatives. 9th ed. Prentice Hall, 2014.
• S. R. Pliska: Introduction to Mathematical Finance: Discrete Time Models. Blackwell Publishing, 1997.
• S. E. Shreve: Stochastic Calculus for Finance. Volume 1: The Binomial Asset Pricing Model. Springer, 2004.
• J. van der Hoek and R. J. Elliott: Binomial Models in Finance. Springer, 2006.
• R. U. Seydel: Tools for Computational Finance. 3rd ed. Springer, 2006.

Chapter 1
Introduction
The goal of this chapter is to give a brief introduction to financial markets.
1.1 Overview of Financial Markets
A financial asset (or a financial security) is a negotiable financial instru-ment representing financial value. Securities are broadly categorised into: debt securities (such as: government bonds, corporate bonds (debentures), municipal bonds), equities (e.g., common stocks) and financial derivatives (such as: forwards, futures, options, swaps, swaptions, etc.). We present below a tentative classification of existing financial markets and typical securities traded on them:

1. Equity market - common stocks (ordinary shares) and preferred stocks (preference shares).
2. Equity derivatives market - equity options and forwards.
3. Fixed income market - coupon-bearing bonds, zero-coupon bonds, sovereign debt, corporate bonds, bond options.
4. Futures market - forwards and futures contracts, index futures, futures options.
5. Interest rate market - caps, floors, swaps and swaptions, forward rate agreements.
6. Foreign exchange market - foreign currencies, options and derivatives on foreign currencies, cross-currency and hybrid derivatives.
7. Exotic options market - barrier options, lookback options, compound op-tions and a large variety of tailor made exotic options.
8. Credit market - corporate bonds, credit default swaps (CDSs), collater-alised debt obligations (CDOs), bespoke tranches of CDOs.
9. Commodity market - metals, oil, corn futures, etc.Stocks (shares), options of European or American style, forwards and futures, annuities and bonds are all typical examples of modern financial securities that are actively traded on financial markets. There is also a growing interest in the so-called structured products, which are typically characterised by a complex design (and sometimes blamed for the market debacles).Organised exchanges versus OTC markets.There are two types of financial markets: exchanges and over-the-counter (OTC) markets. An exchange provides an organised forum for the buying and selling of securities. Contract terms are standardised and the exchange also acts as a clearing house for all transactions. As a consequence, buyers and sellers do not interact with each other directly, since all trades are done via the market maker. Prices of listed securities traded on exchanges are pub-licly quoted and they are nowadays easily available through electronic media. OTC markets are less strictly organised and may simply involve two institu-tions such as, for instance, a bank and an investment company. This feature of OTC transactions has important practical implications. In particular, pri-vately negotiated prices of OTC traded securities are either not disclosed to other investors or they are harder to obtain.Long and short positions.

If you hold a particular asset, you take the so-called long position in that asset. If, on the contrary, you owe that asset to someone, you take the so-called short position. As an example, we may consider the holder (long position) and the writer (short position) of an option. In some cases, e.g. for interest rate swaps, the long and short positions need to be specified by market convention.

Short-selling of a stock.

One notable feature of modern financial markets is that it is not necessary to actually own an asset in order to sell it. In a strategy called short-selling, an investor borrows a number of stocks and sells them. This enables him to use the proceeds to undertake other investments. At a predetermined time, he has to buy the stocks back at the market and return them to the original owner from whom the shares were temporarily borrowed. Short-selling prac-tice is particularly attractive to those speculators, who make a bet that the price of a certain stock will fall. Clearly, if a large number of traders do indeed sell short a particular stock then its market price is very likely to fall. This phenomenon has drawn some criticism in the last couple of years and restric-tions on short-selling have been implemented in some countries. Short-selling is also beneficial since it enhances the market liquidity and conveys additional information about the investors’ outlook for listed companies.