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• W2295218119 abstract "The volatility of financial assets is animportant parameter in risk managemant, portfolio trading andoption pricing. Implied volatility (IV) is obtained from the wellknown Black-Scholes (BS) formula for option pricing, when theoption price is known. Albeit its defectiveness the BS model haskept popularity and resulting IV has become a state variable thatis interesting by itself, reflecting current market situations. IVsform a highly correlated multivariate system and cannot evolveindependently for different strike and maturity values. Thereforethe IV surface should be analysed as a whole by simultaneousexamination of several slices that form the surface. It is commonto display IVs as a function of option maturity $tau$ andmoneyness $kappa$, which is the strike price devided by the thefuture asset price. To examine variation of IVs across moneynessand maturity dimension and in time, the IV log returns are used,i.e. the log differences$IV_{t}(kappa,tau)-IV_{t-1}(kappa,tau)$ for time points $t$ and$t-1$. Time dependent variation of the data is usually analysedusing principal components. It turns out that main modes ofvariation is due to up-and-down shifts of the whole surface in thefirst place, and further, in the second place, it is due to achanging slope of the surface in moneyness and in maturitydimension and, in the third place, due to curvature changes. Inthis work we analyse a further aspect of variation of IV logreturns, namely the variation that appears within the log returnsurface. We are interested in how the daily changes of IV smilesvary for different option maturities. To this end we apply a newmethod that extends the heteroscedastic variance model to a modelwith a functional variance process (FVP), introduced by Muller,Stadtmuller and Yao (2006). By including random components forvariation we can model locally changing variances of datastructures of increasing complexity. The method combines methodsfrom nonparametrical estimation (local polynomial smoothing) andprincipal component analysis. Our empirical findings are based on adata set of daily IV surfaces on stock, index and swap options.Swap IVs are an exception being observed in direction of swapmaturity and option maturity instead of moneyness and optionmaturity in case of stock and index IVs. Due to structuraldifferences between data for options with short and long maturitywe decided to perform the analysis independently for correspondingdata sets. The resulting FVPs, determined at fixed points in time,are maximal in regions where options are in-the-money, i.e. wheremoneyness is less or equal to one, and decrease for increasingmoneyness. In case of swap IV the variance process is maximal forswap maturities in between three and five years. For daily changesof IVs this means that changes vary most from one option maturityto another where moneyness / swap maturity is in the mentionedregions. Moreover, we determine FVPs at different points in time toget an impression of the time dependent development of theseprocesses and thus of time dependent changes of daily variation ofthe IV surface. The shape of a FVP remains in time, meaning thatour findings at fixed days are valid in general." @default.
• W2295218119 created "2016-06-24" @default.
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• W2295218119 date "2007-05-30" @default.
• W2295218119 modified "2023-09-27" @default.
• W2295218119 title "Analysis of Implied Volatility Surfaces" @default.
• W2295218119 hasPublicationYear "2007" @default.
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