A Volax Future is a financial date contract on the implicit of a DAX option at the money with three months remaining time. 1998 were introduced the Volax Future as the first Terminkontrakt on implicit to the DTB (today Eurex). After approximately 15.000 acted contracts the trade with the Volax Future was again stopped however at the end of of 1998 due to strongly sunk liquidity.

Since the publication of the Black Scholes model (1973) the enormous influence of the factor on the option price is well-known. Contrary to other option price factors, like the course of the Underlyings and the interest, the could be acted until 1998 not separately with only one financial instrument. In the following one shows, how the Volax Future was out-arranged on the implicit of the DAX option and there are which ranges of application for like the Volax Future.

1973 were in several respects a remarkable year for the international futures exchanges. On the one hand the collapse of the Bretton Woods of system of firm rates of exchange provided for significantly higher on the interest and foreign exchange markets and in the consequence for one to today unbroken upswing derivatives of the instruments within these ranges. On the other hand the CBOE introduced to Chicago as the first futures exchange of the world options on shares. This was only made possible by the results by Fischer Black and Myron Scholes, which published an option price model together for the evaluation of share options of European kind. Although the derivation of the option price formula in the original is very complex and the model applies only under ideal-typical premises, the model became generally accepted in practice fast. This very day it is the furthest common option price model. Because on the one hand the computational option price P of the Black Scholes model usually very close is because of the price, at which the respective option is actually acted. On the other hand the model needs only five input factors, i.e. the current share quotation S, the practice price E, the remaining time t of the option, the interest rate without risk r as well as the standard deviation \ sigma of the yield on shares. The latter factor is called also

The value of a Portfolios with options varies as a function of changes of the For security this gives it at present no pure Hedginginstrumente. The available essay points by the example of the Volax Futures to the implicit of DAX options, how a Future can look on implicit In addition first the implicit is defined and some its characteristics are represented. Subsequently, a Futureskurs for is deduced and the concrete arrangement of the is described. Whereupon constructing the ranges of application Hedging, speculation and arbitrage of such a derivative are explained.

Characteristics of implicit

Definition

If the price of an option as well as the price-affecting factors running time, course of the Underlyings, interest and base price are well-known, then the still which is missing size of can be determined by means of an option price model. The determined in this kind is called implicit The formula of the Black/Scholes model as well as the other option price popular prices cannot be changed over after the \ sigma. Therefore numeric approximation methods must be used for the determination of the implicit With European standard options, as they are subordinated in the Black Scholes model, for it the Newton Raphson procedure offers itself. It is very efficient and converged usually within three or four iterations to the looked for implicit

Black/Scholes subordinate constant in their model independently of the base price and the running time of the option. Therefore the implicit of an option would have with different base prices and differently is enough for running times to be always alike. This is not however the case. Diagram 1 shows the implicit of DAX call options with different base prices with same remaining time. The convex process of the implicit is remarkable. The further the base price is under the current DAX course, the implicit is the higher. Main cause for it is that the DAX net yields are not normaldistributed against the acceptance in the Black Scholes model. The table shows that the DAX net yields were leptokurtisch distributed between 2 January 1987 and 9 April 1997.

This meant, higher probabilities exist in relation to the normal distribution acceptance the fact that the DAX net yields do not change either or but exhibits extreme deviations from their average value. Crash situations are more probable in the DAX than extreme Kurssteigerungen. Further possible reasons for the result from the money/letter spans in the case of particularly far options lying from the money as well as the generally lower liquidity of options not on the money present. The existence of the has, as to be still shown is, a not insignificant influence on the organization of a

Time structure of the

Diagram 2 the implicit at the money of DAX calls present with different remainder running times. Against the acceptance of the Black/Scholes model different running times do not exhibit identical implicit This has essentially two causes. First of all economic basic conditions are subject to constant changes, which have again a changing influence on the course of the Underlying. Its are exposed constant fluctuations therefore to likewise. Expected for example an analyst for a future time a change of the economic fundamental data, about a change of interest by a Federal Bank resolution, then this influence on its estimate of the DAX development will have. This leads to the fact that the analyst uses in each case different for the option price regulation of options, which will run out before and/or after the Federal Bank resolution. A second reason is the Mean Reverting characteristic of the Volatilit¤ten do not remain at extreme values. Rather they return again and again to their average value of many years. Diagram 3 this characteristic on the basis the development of the VDAX, an index of the implicit of the DAX options. The VDAX shows the tendency to return again and again to its average of many years from 15,44 per cent. Its maximum value amounted to 26.56 per cent, its minimum value 9,36Prozent.

Computation of the forward

The time structure of the reminds strongly of an interest structure curve. Therefore the determination of the implicit forward takes place in analogy to a forward rate Agreement in the interest range. The existence of is first excluded that is called, for each running time existed only an implicit 4 the forward which can be computed as well as the sizes to it the available. Between the individual sizes the following relationship (stochastic independence from \ sigma_1 and \ sigma_F subordinates) applies:

\ left (T_1-T_0 \ right) \ sigma^2_1 + \ left (T_2-T_1 \ right) \ sigma^2_F = \ left (T_2-T_0 \ right) \ sigma^2_2

One dissolves this after equation the forward \ sigma_F, then arises as formula for the implicit forward

\ sigma_F = \ sqrt {\ frac {\ (T_2-T_0 \ right) \ sigma^2_2 left - \ (T_1-T_0 \ right) \ sigma^2_1 left} {T_2-T_1}}

Theoretically in such a way computed forward is also the fair course for an stock exchange-acted Future.

Articles in category "Volax Future"

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