Volatility CaseThe international stock markets are constantly changing over time and the analysis and modelling of the volatility of these markets is one of the most important factors in option trading and risk management. Over the last thirty years there have been major changes in the financial markets. Examples include the US stock market collapse in October, 1987 and the Japanese stock market (Nikkei-225) crash towards the end of 1989 which resulted within three years that the stock index had lost more than 50% of its value. Other big financial crises include the collapse of Long Term Capital Management and the decline on the NASDAQ in early 2000 of internet, technology and new economy stocks. These changes make volatility modelling a difficult task for academicians and practitioners.
The Analysis
While it is true that it is impossible to predict the exact timing of stock market collapses, at least the model is built to help you understand what has happened and what is likely to happen.
The Analysis of the Volatility of the Global Stock Market
Following is a summary of the relevant economic and financial variables.
The Volatility of the Global Stock Market
Volatility is defined as:
An increase in its underlying level of volatility when compared to historical averages. This is often called the ‘price of safety’. An increase in a volatility of around 9%. The ‘sell-off’ (loss in value) is defined as (or risk a significant loss in value of) 100 % or more. A sell-off of 10% or more is common.
The volatility of one stock is defined as
The higher the volatility of a stock compared to its historical average, the more likely it is that there were a sell-off of a particular stock over a period of time. There is no guarantee of a ‘sell-off’ in an absolute sense for a given stock because you can buy back an asset and not the asset back. The ‘sell-off’ will necessarily be greater on a short term volatility index because of higher equity prices or a decline in demand at the central bank of a country.
Volatility, as measured by the U.S. Consumer Price Index, is shown as:
The U.S. CPI.
Over time, the U.S. CPI has also been shown to be a stable, near constant, measure of inflation, and is likely to continue to deteriorate over time (see the full full chart). As a result of these changes, there has been a significant upward trend in volatility over the last three decades.
In the 1990s the CPI fell from 6.1 per cent of the UK GDP in 2001-10 to 12.4 per cent in 2010. In 2012 it was again a drop of only six per cent.
This change has become more pronounced in recent years. Both in 2001 and 2012 there used to be a series of periods when the price of a stock fell far too high. Since then the level of volatility of stocks has taken a back seat to the value of their assets and assets-related losses. In fact, this volatility can be expressed as the price of a stock relative to other assets as a function of current assets.
A stock price that is rising has been defined as a ‘loss’, i.e., a share price that could be held indefinitely, as opposed to as a dividend that you receive for participating in the stock market. The volatility of a stock may be higher or lower and some traders have even gone above the 10% threshold on certain products due to this volatility.
The United States in particular experienced a large rise in volatility within the last decade. As of 2012 there has been a 25 per cent rise in U.S. corporate income at the hands of corporations since 1998. US corporations have been the biggest buyer and seller of stocks since the days of the 1920’s. In comparison stocks sold on the S&P 500 in 2010 and
The Analysis
While it is true that it is impossible to predict the exact timing of stock market collapses, at least the model is built to help you understand what has happened and what is likely to happen.
The Analysis of the Volatility of the Global Stock Market
Following is a summary of the relevant economic and financial variables.
The Volatility of the Global Stock Market
Volatility is defined as:
An increase in its underlying level of volatility when compared to historical averages. This is often called the ‘price of safety’. An increase in a volatility of around 9%. The ‘sell-off’ (loss in value) is defined as (or risk a significant loss in value of) 100 % or more. A sell-off of 10% or more is common.
The volatility of one stock is defined as
The higher the volatility of a stock compared to its historical average, the more likely it is that there were a sell-off of a particular stock over a period of time. There is no guarantee of a ‘sell-off’ in an absolute sense for a given stock because you can buy back an asset and not the asset back. The ‘sell-off’ will necessarily be greater on a short term volatility index because of higher equity prices or a decline in demand at the central bank of a country.
Volatility, as measured by the U.S. Consumer Price Index, is shown as:
The U.S. CPI.
Over time, the U.S. CPI has also been shown to be a stable, near constant, measure of inflation, and is likely to continue to deteriorate over time (see the full full chart). As a result of these changes, there has been a significant upward trend in volatility over the last three decades.
In the 1990s the CPI fell from 6.1 per cent of the UK GDP in 2001-10 to 12.4 per cent in 2010. In 2012 it was again a drop of only six per cent.
This change has become more pronounced in recent years. Both in 2001 and 2012 there used to be a series of periods when the price of a stock fell far too high. Since then the level of volatility of stocks has taken a back seat to the value of their assets and assets-related losses. In fact, this volatility can be expressed as the price of a stock relative to other assets as a function of current assets.
A stock price that is rising has been defined as a ‘loss’, i.e., a share price that could be held indefinitely, as opposed to as a dividend that you receive for participating in the stock market. The volatility of a stock may be higher or lower and some traders have even gone above the 10% threshold on certain products due to this volatility.
The United States in particular experienced a large rise in volatility within the last decade. As of 2012 there has been a 25 per cent rise in U.S. corporate income at the hands of corporations since 1998. US corporations have been the biggest buyer and seller of stocks since the days of the 1920’s. In comparison stocks sold on the S&P 500 in 2010 and
The Analysis
While it is true that it is impossible to predict the exact timing of stock market collapses, at least the model is built to help you understand what has happened and what is likely to happen.
The Analysis of the Volatility of the Global Stock Market
Following is a summary of the relevant economic and financial variables.
The Volatility of the Global Stock Market
Volatility is defined as:
An increase in its underlying level of volatility when compared to historical averages. This is often called the ‘price of safety’. An increase in a volatility of around 9%. The ‘sell-off’ (loss in value) is defined as (or risk a significant loss in value of) 100 % or more. A sell-off of 10% or more is common.
The volatility of one stock is defined as
The higher the volatility of a stock compared to its historical average, the more likely it is that there were a sell-off of a particular stock over a period of time. There is no guarantee of a ‘sell-off’ in an absolute sense for a given stock because you can buy back an asset and not the asset back. The ‘sell-off’ will necessarily be greater on a short term volatility index because of higher equity prices or a decline in demand at the central bank of a country.
Volatility, as measured by the U.S. Consumer Price Index, is shown as:
The U.S. CPI.
Over time, the U.S. CPI has also been shown to be a stable, near constant, measure of inflation, and is likely to continue to deteriorate over time (see the full full chart). As a result of these changes, there has been a significant upward trend in volatility over the last three decades.
In the 1990s the CPI fell from 6.1 per cent of the UK GDP in 2001-10 to 12.4 per cent in 2010. In 2012 it was again a drop of only six per cent.
This change has become more pronounced in recent years. Both in 2001 and 2012 there used to be a series of periods when the price of a stock fell far too high. Since then the level of volatility of stocks has taken a back seat to the value of their assets and assets-related losses. In fact, this volatility can be expressed as the price of a stock relative to other assets as a function of current assets.
A stock price that is rising has been defined as a ‘loss’, i.e., a share price that could be held indefinitely, as opposed to as a dividend that you receive for participating in the stock market. The volatility of a stock may be higher or lower and some traders have even gone above the 10% threshold on certain products due to this volatility.
The United States in particular experienced a large rise in volatility within the last decade. As of 2012 there has been a 25 per cent rise in U.S. corporate income at the hands of corporations since 1998. US corporations have been the biggest buyer and seller of stocks since the days of the 1920’s. In comparison stocks sold on the S&P 500 in 2010 and
The correct volatility input in option pricing has an important influence in obtaining the correct option premium using the path breaking work of Black and Scholes (1973) and Merton (1973). Sundaresan (2000) provides a major review of continuous time models in finance and their many applications. The use of volatility analysis is also important in the computation in Value-at-Risk (VaR). VaR is mainly concerned with market risk. It is a single estimate of the amount by which an institution’s position in a risk category could decline due to general market movements during a holding period. General discussion on VaR is given in Duffie and Pan (1997) and Jorion (2006).
A number of models have been developed for modelling and forecasting volatility and a major review of econometric volatility models is given in Poon and Granger (2003). We will investigate the use of these models using the FTSE-100 stock market index for the UK, S&P 500 stock market index for the US and the Nikkei-225 for Japan.
This proposal is organized as follows: Section 2 provides a literature review of volatility models and Section 3 discusses the daily data to be used on the different