## Spreadsheet Instructions

In all spreadsheets, user input is required in white cells. Yellow cells are the result of calculations. This spreadsheet uses MLE and the solver add-in to estimate a GARCH(1,1) model. It also shows the volatility term structure consistent with this model. This sheet makes use of the Solver add-in so it is not protected. Enter the ticker symbol in the Get Quotes box. Go to the Historical Prices link, which is third from the top in the box More on (ABC) on the left of the page. Set the start...

## Maximum Likelihood Estimation

Generally, when traders or risk managers use EWMA, they arbitrarily choose the smoothing parameter, X. We could also do this for GARCH and arbitrarily set values for the parameters. However, those who believe the variance process is described by a GARCH model generally do not do this, relying instead on maximum likelihood estimation to find the parameters for each underlying. (This is one of the often-stated objections to GARCH that it is subject to retrospective curve fitting of the...

## References

Which Free Lunch Would You Like Today, Sir Wilmott, November, 64-79. Ahoniemi, K. 2006. Modeling and Forecasting Implied Volatility An Econometric Analysis of the VIX Index. Discussion Paper 129, Helsinki Center of Economic Research. Ait-Sahalia, Y., P. Mykland, and L. Zhang. 2005. How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise. Review of Financial Studies 18 351-416. Alexander, C. 2001a. Market Models A Guide to...

## Implied Volatility Dynamics

In the previous chapter we looked at ways to measure and forecast realized volatility. In a sports gambling context this would be akin to us forecasting which team would be most likely to win the game. In this chapter we look at the ways implied volatility can move. This would be the equivalent of predicting how the bookmakers' line might move before the game. Remember that we are not trading either realized or implied volatility directly. We are trading the spread between the two, so edge can...

## Traders Definition

A time series is mean-reverting if it can be profitably traded by methods that assume that moves tend to reverse instead of continue. This definition allows for a lot of different processes. It is far broader than assuming negative autocorrelation. A number of the classical technical indicators can form the basis for such a system. Please note that we are asserting nothing about the general efficacy of technical analysis it is just being used as a test in this specific case. FIGURE 3.6 A...

## The Asymptotic Solution of Whalley and Wilmott

If we assume that the transaction costs are small relative to the value of the option in the BSM world , it is possible to derive some approximate solutions to the full problem. This was first done by Whalley and Wilmott 1997 . They show that the boundaries of the no-transaction regions are given by A pexp -r T - t XSr2V 49 where X is the proportional transaction cost that is, transaction costs are of the form where N is the total number of shares traded Although the authors considered the case...

## The Double Asymptotic Method of Zakamouline

The two relatively simple transaction cost models are those of Leland and Whalley and Wilmott. They can both be viewed as special cases of the Hodges and Neuberger model Leland describes how to replicate an option in the presence of transaction costs when we are risk-neutral Whalley and Wilmott incorporate risk aversion but insist on the costs being small. While these models are simple to apply and use, and will almost certainly be an improvement over more ad hoc methods, they lose some of the...