Optimal hedging of options with small but arbitrary transaction cost structure

1999 ◽  
Vol 10 (2) ◽  
pp. 117-139 ◽  
Author(s):  
A. E. WHALLEY ◽  
P. WILMOTT
Keyword(s):  
Asymptotic Analysis ◽  
Transaction Cost ◽  
Stochastic Control ◽  
Simple Expression ◽  
Cost Structure ◽  
Fixed Costs ◽  
Optimal Point ◽  
Underlying Asset ◽  
Black Scholes ◽  
Order Of Magnitude

In this paper we consider the problem of hedging options in the presence of cost in trading the underlying asset. This work is an asymptotic analysis of a stochastic control problem, as in Hodges & Neuberger and Davis, Panas & Zariphopoulou;. We derive a simple expression for the ‘hedging bandwidth’ around the Black–Scholes delta; this is the region in which it is optimal not to rehedge. The effect of the costs on the value of the option, and on the width of this hedging band is of a significantly greater order of magnitude than the costs themselves. When costs are proportional to volume traded, rehedging should be done to the edge of this band; when there are fixed costs present, trading should be done to an optimal point in the interior of the no-transaction region.

Value-at-Risk and Expected Shortfall approaches for option premiums and the probability of default estimation based on ARMA models

2021 ◽  
Vol 57 (3) ◽  
pp. 126
Author(s):  
Nikolai Berzon
Keyword(s):  
Time Series ◽  
Option Pricing ◽  
Discrete Time ◽  
Value At Risk ◽  
Probability Of Default ◽  
Pricing Models ◽  
Arma Process ◽  
Underlying Asset ◽  
Black Scholes

The need to address the issue of risk management has given rise to a number of models for estimation the probability of default, as well as a special tool that allows to sell credit risk – a credit default swap (CDS). From the moment it appeared in 1994 until the crisis of 2008, that the CDS market was actively growing, and then sharply contracted. Currently, there is practically no CDS market in emerging economies (including Russia). This article is to improve the existing CDS valuation models by using discrete-time models that allow for more accurate assessment and forecasting of the selected asset dynamics, as well as new option pricing models that take into account the degree of risk acceptance by the option seller. This article is devoted to parametric discrete-time option pricing models that provide more accurate results than the traditional Black-Scholes continuous-time model. Improvement in the quality of assessment is achieved due to three factors: a more detailed consideration of the properties of the time series of the underlying asset (in particular, autocorrelation and heavy tails), the choice of the optimal number of parameters and the use of Value-at-Risk approach. As a result of the study, expressions were obtained for the premiums of European put and call options for a given level of risk under the assumption that the return on the underlying asset follows a stationary ARMA process with normal or Student's errors, as well as an expression for the credit spread under similar assumptions. The simplicity of the ARMA process underlying the model is a compromise between the complexity of model calibration and the quality of describing the dynamics of assets in the stock market. This approach allows to take into account both discreteness in asset pricing and take into account the current structure and the presence of interconnections for the time series of the asset under consideration (as opposed to the Black–Scholes model), which potentially allows better portfolio management in the stock market.

scholarly journals A novel method of ESR oscillating magnetization value determination in strongly correlated metals

2018 ◽  
Vol 185 ◽  
pp. 02003 ◽  
Author(s):  
Marat Gilmanov ◽  
Alexey Semeno ◽  
Alexander Samarin ◽  
Sergey Demishev
Keyword(s):  
Resonance Field ◽  
Simple Expression ◽  
60 Ghz ◽  
Strongly Correlated ◽  
Static Magnetization ◽  
Spin Resonance ◽  
Order Of Magnitude ◽  
Novel Method ◽  
Value Determination ◽  
The One

We propose a powerful method of direct measurement of oscillating magnetization by the electron spin resonance, based on dependence of resonant conditions on geometry of the experiment. Theoretical consideration of the matter leads to a simple expression for oscillating magnetization. Approbation of this method is implemented by means of cavity ESR spectrometer (60 GHz) on two diverse metallic systems, where static magnetization at the resonance field varies by an order of magnitude. Quantitative values of oscillating magnetization (905 G for EuB6 at T = 4.2 K and 94 G for CeB6 at T = 1.8 K) are in appropriate agreement with the one obtained by the other methods.

scholarly journals How Firms Can Hedge Against Market Risk

2014 ◽  
Vol 37 (1) ◽  
pp. 39-49
Author(s):  
Krzysztof Echaust
Keyword(s):  
Absolute Risk ◽  
Future Price ◽  
Utility Model ◽  
Forward Contracts ◽  
Hedging Strategy ◽  
Underlying Asset ◽  
Absolute Risk Aversion ◽  
Black Scholes ◽  
Expected Utility Model ◽  
Constant Absolute Risk Aversion

Abstract The article presents a problem of proper hedging strategy in expected utility model when forward contracts and options strategies are available. We consider a case of hedging when an investor formulates his own expectation on future price of underlying asset. In this paper we propose the way to measure effectiveness of hedging strategy, based on optimal forward hedge ratio. All results are derived assuming a constant absolute risk aversion utility function and a Black-Scholes framework.

Administrative fees and costs of mandatory private pensions in transition economies

2005 ◽  
Vol 4 (1) ◽  
pp. 31-55 ◽  
Author(s):  
ANTON DOBRONOGOV ◽  
MAMTA MURTHI
Keyword(s):  
Transition Economies ◽  
Economies Of Scale ◽  
Sunk Costs ◽  
Operating Costs ◽  
Fixed Costs ◽  
Limited Information ◽  
Private Pensions ◽  
Individual Account ◽  
Order Of Magnitude ◽  
History Of

This paper discusses fees and costs of pension companies in transition economies drawing on examples from four countries – Croatia, Hungary, Kazakhstan and Poland – where second pillar pensions have the longest history of implementation. It finds that at current levels, charges are likely to reduce returns on individual account balances by around 1% per annum on average. Exact rates vary by country and company. Fee structures are complex and, generally speaking, poorly understood by consumers. The limited information on costs that is available suggests that, by and large, companies are able to meet their operating costs within a few years after starting operations. There are large sunk costs in setting up business. As a result the industry displays strong economies of scale. Based on the available evidence, the paper estimates fixed costs to be of the order of $35 per account per year (the 95% confidence interval is $21–$49 per account per year). Given costs of this order of magnitude, individual accounts need to be of the order of 4–6% of average wages for the second pillar to be viable i.e. to deliver a return greater than what can be expected from an unchanged first pillar.

scholarly journals The Extended Black-Scholes Model with-LAGS-and “Hedging Errors”

2003 ◽  
Author(s):  
Mondher Bellalah
Keyword(s):  
Stock Price ◽  
Standard Form ◽  
Small Time ◽  
Market Model ◽  
Short Term ◽  
Hedging Strategy ◽  
Underlying Asset ◽  
Elapsed Time ◽  
Black Scholes Model ◽  
Black Scholes

The Black-Scholes model is derived under the assumption that heding is done instantaneously. In practice, there is a “small” time that elapses between buying or selling the option and hedging using the underlying asset. Under the following assumptions used in the standard Black-Scholes analysis, the value of the option will depend only on the price of the underlying asset S, time t and on other Variables assumed constants. These assumptions or “ideal conditions” as expressed by Black-Scholes are the following. The option us European, The short term interest rate is known, The underlying asset follows a random walk with a variance rate proportional to the stock price. It pays no dividends or other distributions. There is no transaction costs and short selling is allowed, i.e. an investment can sell a security that he does not own. Trading takes place continuously and the standard form of the capital market model holds at each instant. The last assumption can be modified because in practice, trading does not take place in-stantaneouly and simultaneously in the option and the underlying asset when implementing the hedging strategy. We will modify this assumption to account for the “lag”. The lag corresponds to the elapsed time between buying or selling the option and buying or selling - delta units of the underlying assets. The main attractions of the Black-Scholes model are that their formula is a function of “observable” variables and that the model can be extended to the pricing of any type of option. All the assumptions are conserved except the last one.

scholarly journals BIAYA TRANSAKSI DAN ANALISIS KEUNTUNGAN PETANI PADA SISTEM RESI GUDANG KOPI ARABIKA GAYO DI KABUPATEN ACEH TENGAH

2018 ◽  
Vol 6 (1) ◽  
pp. 49-60
Author(s):  
Keumala Fadhiela ◽  
Dwi Rachmina ◽  
Ratna Winandi
Keyword(s):  
Transaction Costs ◽  
Transaction Cost ◽  
Cost Structure ◽  
Arabica Coffee ◽  
Average Percentage ◽  
Costs Analysis ◽  
The Cost ◽  
Percentage Ratio

The purpose of this study was to analyze the structure of transaction cost and analyze farmers profit on Arabica Gayo Coffee Warehouse Receipt System (WRS) in Central Aceh District. Transaction Costs Analysis (TCA) was used to analize transaction cost structure at selling delay activity and financing activity on WRS. While the ratio of transaction costs to farmers' profit was used to determine the level of effectiveness of WRS. The research was conducted at PT. Ketiara Warehouse, West Aceh district, Aceh. The selected samples were all 4o farmers of Arabica Gayo WRS in Central Aceh Regency. The highest transction cost was on delay selling activity (64,07%) than transaction cost on warehouse receipt financing activity (35,93%). Implementation of the warehouse receipt system in PT. Ketiara provided more benefits to the participants because average percentage ratio between the cost of the transaction with the benefit of <10 percent.  Transaction costs and effectiveness of WRS need more attention and focus on the improvement of these two things to maximize the implementation and sustainability of Gayo Arabica Coffee WRS in Central Aceh District.

scholarly journals BIAYA TRANSAKSI DAN ANALISIS KEUNTUNGAN PETANI PADA SISTEM RESI GUDANG KOPI ARABIKA GAYO DI KABUPATEN ACEH TENGAH

2018 ◽  
Vol 6 (1) ◽  
pp. 49
Author(s):  
Keumala Fadhiela ◽  
Dwi Rachmina ◽  
Ratna Winandi
Keyword(s):  
Transaction Costs ◽  
Transaction Cost ◽  
Cost Structure ◽  
Arabica Coffee ◽  
Average Percentage ◽  
Costs Analysis ◽  
The Cost ◽  
Percentage Ratio

<em>The purpose of this study was to analyze the structure of transaction cost and analyze farmers profit on Arabica Gayo Coffee Warehouse Receipt System (WRS) in Central Aceh District. Transaction Costs Analysis (TCA) was used to analize transaction cost structure at selling delay activity and financing activity on WRS. While the ratio of transaction costs to farmers' profit was used to determine the level of effectiveness of WRS. The research was conducted at PT. Ketiara Warehouse, West Aceh district, Aceh. The selected samples were all 4o farmers of Arabica Gayo WRS in Central Aceh Regency. The highest transction cost was on delay selling activity (64,07%) than transaction cost on warehouse receipt financing activity (35,93%). Implementation of the warehouse receipt system in PT. Ketiara provided more benefits to the participants because average percentage ratio between the cost of the transaction with the benefit of &lt;10 percent.  Transaction costs and effectiveness of WRS need more attention and focus on the improvement of these two things to maximize the implementation and sustainability of Gayo Arabica Coffee WRS in Central Aceh District.</em>

On the Incompleteness of Korean Stock Index Options Market

2004 ◽  
Vol 12 (2) ◽  
pp. 25-43
Author(s):  
Jung Soon Hyun ◽  
Byung Kun Rhee
Keyword(s):  
Risk Factor ◽  
Estimation Method ◽  
Stock Index ◽  
Additional Risk Factor ◽  
Options Market ◽  
Pricing Kernel ◽  
Index Options ◽  
Additional Risk ◽  
Underlying Asset ◽  
Black Scholes

When the Black-Scholes assumptions hold market is instantaneously complete and options are redundant securities. This paper tests whether options are needed for spanning of the pricing kernel in addition to the risk-free bond and underlying asset in Korean stock index options market. Using Hansen's GMM estimation method, we find that pricing kernel cannot be spanned with the risk-free bond and underlying asset. Options are needed for spanning to incorporate the additional risk factor. This result is consistent with previous results using American options market data.

scholarly journals A Black–Scholes inequality: applications and generalisations

2019 ◽  
Vol 24 (1) ◽  
pp. 1-38 ◽  
Author(s):  
Michael R. Tehranchi
Keyword(s):  
Probability Density ◽  
Implied Volatility ◽  
Binary Operation ◽  
Free Market ◽  
Market Model ◽  
Convex Order ◽  
Underlying Asset ◽  
Black Scholes

Abstract The space of call price curves has a natural noncommutative semigroup structure with an involution. A basic example is the Black–Scholes call price surface, from which an interesting inequality for Black–Scholes implied volatility is derived. The binary operation is compatible with the convex order, and therefore a one-parameter sub-semigroup gives rise to an arbitrage-free market model. It is shown that each such one-parameter semigroup corresponds to a unique log-concave probability density, providing a family of tractable call price surface parametrisations in the spirit of the Gatheral–Jacquier SVI surface. An explicit example is given to illustrate the idea. The key observation is an isomorphism linking an initial call price curve to the lift zonoid of the terminal price of the underlying asset.

Bifractional Black-Scholes Model for Pricing European Options and Compound Options

2020 ◽  
Vol 8 (4) ◽  
pp. 346-355
Author(s):  
Feng Xu
Keyword(s):  
Empirical Studies ◽  
Asset Price ◽  
European Options ◽  
Hedging Strategy ◽  
Underlying Asset ◽  
Bifractional Brownian Motion ◽  
Compound Options ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Delta Hedging

AbstractRecent empirical studies show that an underlying asset price process may have the property of long memory. In this paper, it is introduced the bifractional Brownian motion to capture the underlying asset of European options. Moreover, a bifractional Black-Scholes partial differential equation formulation for valuing European options based on Delta hedging strategy is proposed. Using the final condition and the method of variable substitution, the pricing formulas for the European options are derived. Furthermore, applying to risk-neutral principle, we obtain the pricing formulas for the compound options. Finally, the numerical experiments show that the parameter HK has a significant impact on the option value.

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