Na finančnih trgih se pri uporabi hedging tehnike pojavijo transakcijski stroški. V tem članku se obravnava problem uporabe delta hedging tehnike ter redukcije proporcionalnih transakcijskih ...stroškov. V literaturi navedene metode običajno temeljijo le na uporabi tako imenovanega faktorja gama, ki ponavadi predstavlja največji člen v aproksimacijski vrsti. Toda pri opcijah s kratkim časom dospetja, mesec ali nekaj tednov, lahko drugi členi vrste postanejo celo večji. Tedaj so potrebne natančnejše aproksimacije. V tem članku so analizirane aproksimacije višjega reda in njihova uporaba pri zmanjšanju povprečnih proporcionalnih transakcijskih stroškov. Na podlagi analize je podan ustrezno prilagojen faktor delta, s katerim se povprečni aproksimativni proporcionalni transakcijski stroški lahko zmanjšajo. Pripadajoča napaka hedging tehnike se pri tem ne poveča. Za ilustracijo metode je dodanih nekaj primerov.
Transaction costs of derivative hedging appear in financial markets. This paper considers the problem of delta hedging and the reduction of expected proportional transaction costs. In the literature ...the expected approximate proportional transaction costs are customarily estimated by the gamma term, usually the largest term of the associated series expansion. However, when options are to expire in a month or few weeks, other terms may become even larger so that more precise estimates are needed. In this paper, different higher-order estimates of proportional transaction costs are analyzed. The problem of the reduction of expected transaction costs is considered. As a result, a suitably adjusted delta is given, for which the expected approximate proportional transaction costs can be reduced. The order of the mean and the variance of the hedging error can be preserved. Several examples are provided.
Na finančnih trgih se pri uporabi hedging tehnike pojavijo transakcijski stroški. V tem članku se obravnava problem uporabe delta hedging tehnike ter redukcije proporcionalnih transakcijskih stroškov. V literaturi navedene metode običajno temeljijo le na uporabi tako imenovanega faktorja gama, ki ponavadi predstavlja največji člen v aproksimacijski vrsti. Toda pri opcijah s kratkim časom dospetja, mesec ali nekaj tednov, lahko drugi členi vrste postanejo celo večji. Tedaj so potrebne natančnejše aproksimacije. V tem članku so analizirane aproksimacije višjega reda in njihova uporaba pri zmanjšanju povprečnih proporcionalnih transakcijskih stroškov. Na podlagi analize je podan ustrezno prilagojen faktor delta, s katerim se povprečni aproksimativni proporcionalni transakcijski stroški lahko zmanjšajo. Pripadajoča napaka hedging tehnike se pri tem ne poveča. Za ilustracijo metode je dodanih nekaj primerov.
The paper deals with the problem of discrete-time delta hedging and discrete-time option valuation by the Black-Scholes model. Since in the Black-Scholes model the hedging is continuous, hedging ...errors appear when applied to discrete trading. The hedging error is considered and a discrete-time adjusted Black-Scholes-Merton equation is derived. By anticipating the time sensitivity of delta in many cases the discrete-time delta hedging can be improved and more accurate delta values dependent on the length of the rebalancing intervals can be obtained. As an application the discrete-time trading with transaction costs is considered. Explicit solution of the option valuation problem is given and a closed form delta value for a European call option with transaction costs is obtained. PUBLICATION ABSTRACT
A functional differential equation in Hilbert space with initial data on −h,0 is considered. An unbounded operator A and a square integrable weight function are acting in the distributed delay term. ...For a not necessarily continuous weight function the norm continuity of the associated solution semigroup is established at every t>h. In the case that the spectrum of A is real and negative, the asymptotic stability of the solution is obtained.
Transaction costs of derivative hedging appear in financial markets. This paper considers the problem of delta hedging and the reduction of expected proportional transaction costs. In the literature ...the expected approximate proportional transaction costs are customarily estimated by the gamma term, usually the largest term of the associated series expansion. However, when options are to expire in a month or few weeks, other terms may become even larger so that more precise estimates are needed. In this paper, different higher-order estimates of proportional transaction costs are analyzed. The problem of the reduction of expected transaction costs is considered. As a result, a suitably adjusted delta is given, for which the expected approximate proportional transaction costs can be reduced. The order of the mean and the variance of the hedging error can be preserved. Several examples are provided.
Hedging an option is easy in the basic Black-Scholes world. The only stochastic variable is the stock price, and by holding a short position in the stock equal to minus the partial derivative of the ...call price with respect to the stock, a momentarily riskless hedge of a call option is achieved. Delta-gamma hedges can manage both delta risk and the change in the delta, but volatility also changes over time, necessitating another Greek letter (or quasi-Greek in this case) -- and vega was invented. And as this article shows, in an option hedge, charm becomes as important a risk factor as gamma close to maturity. The delta of an in-the-money (out-of-the-money) call converges rapidly to +1.0 (0.0) right at maturity; so a delta-hedged position can quickly become quite unhedged in the last few days. When charm is large, a more accurate hedge can be achieved using a modified hedge ratio, different from the standard delta.
In financial derivatives markets different strategies for reduction of risk can be applied. This is especially important in times of financial crisis when more regulation of trading with risky ...instruments is needed. In this article the well known technique of delta hedging used in derivatives markets is considered. It is shown that for the appropriately adjusted delta the average hedging loss and the expected transaction costs can be reduced. PUBLICATION ABSTRACT
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