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...
Info Ruz
Brandt and Kiniay 2005 show that both of these estimators are downward biased. This should not be a surprise as both are dependent on extreme prices and continuity was still assumed. At this point we have five estimators, each constructed to address a shortcoming of the last. So each iteration should be better. Is our choice of which estimator to use obvious Not really. When Brandt and Kinlay performed tests on more realistic simulated data discretely sampled, with drift and jumps , the...
More Formal Definition
A time series is mean-reverting if its returns have negative autocorrelation. Under this definition a below-average return in one period is compensated for by a higher-than-average return in subsequent periods. The VIX is mean-reverting under this definition. It has a daily autocorrelation of -0.04, weekly of -0.21, and monthly of -0.12. This model can be simply expressed as Rt p Rt-1 - f f aZt 3.1 Z is a draw from a standard normal distribution A realization of this process is given in Figure...
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...
Info Rqq
This allows a simple translation between daily returns and annualized volatility. Multiplying the daily return by 20 gives a useful quick-and-dirty estimate of annualized volatility. There are two basic ways of addressing the problem of the large sampling error. We can use the close-to-close estimator with higher-frequency data, or we can use another estimator that doesn't throw away all data points other than closing prices. Each has limitations. First we will try to develop better estimators,...