scholarly journals Time-Discrete Hedging of Down-and-Out Puts with Overnight Trading Gaps

2022 ◽  
Vol 15 (1) ◽  
pp. 29
Author(s):  
Rainer Baule ◽  
Philip Rosenthal
Keyword(s):  
Numerical Study ◽  
Black Scholes ◽  
Hedge Ratios ◽  
Efficient Hedging ◽  
Complex Models ◽  
Analytical Formulas ◽  
Continuous Trading ◽  
Optimal Hedge ◽  
Discrete Hedging ◽  
Mean Variance

Hedging down-and-out puts (and up-and-out calls), where the maximum payoff is reached just before a barrier is hit that would render the claim worthless afterwards, is challenging. All hedging methods potentially lead to large errors when the underlying is already close to the barrier and the hedge portfolio can only be adjusted in discrete time intervals. In this paper, we analyze this hedging situation, especially the case of overnight trading gaps. We show how a position in a short-term vanilla call option can be used for efficient hedging. Using a mean-variance hedging approach, we calculate optimal hedge ratios for both the underlying and call options as hedge instruments. We derive semi-analytical formulas for optimal hedge ratios in a Black–Scholes setting for continuous trading (as a benchmark) and in the case of trading gaps. For more complex models, we show in a numerical study that the semi-analytical formulas can be used as a sufficient approximation, even when stochastic volatility and jumps are present.

Hedging and Optimal Hedge Ratios for International Index Futures Markets

2009 ◽  
Vol 12 (04) ◽  
pp. 593-610 ◽  
Author(s):  
Cheng-Few Lee ◽  
Kehluh Wang ◽  
Yan Long Chen
Keyword(s):  
Futures Markets ◽  
Minimum Variance ◽  
Stock Index ◽  
Stock Index Futures ◽  
Hedge Ratio ◽  
Index Futures ◽  
Static Hedging ◽  
Hedge Ratios ◽  
Optimal Hedge ◽  
Mean Variance

This empirical study utilizes four static hedging models (OLS Minimum Variance Hedge Ratio, Mean-Variance Hedge Ratio, Sharpe Hedge Ratio, and MEG Hedge Ratio) and one dynamic hedging model (bivariate GARCH Minimum Variance Hedge Ratio) to find the optimal hedge ratios for Taiwan Stock Index Futures, S&P 500 Stock Index Futures, Nikkei 225 Stock Index Futures, Hang Seng Index Futures, Singapore Straits Times Index Futures, and Korean KOSPI 200 Index Futures. The effectiveness of these ratios is also evaluated. The results indicate that the methods of conducting optimal hedging in different markets are not identical. However, the empirical results confirm that stock index futures are effective direct hedging instruments, regardless of hedging schemes or hedging horizons.

scholarly journals Accurate radial basis functions technique for competitive and efficient solutions of non-linear Black-Scholes equations

2020 ◽  
Vol 20 (4) ◽  
pp. 60-83
Author(s):  
Vinícius Magalhães Pinto Marques ◽  
Gisele Tessari Santos ◽  
Mauri Fortes
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Efficient Solutions ◽  
Basis Functions ◽  
Adaptive Scheme ◽  
Call Options ◽  
Black Scholes ◽  
Non Linear ◽  
Radial Basis ◽  
Complex Models

ABSTRACTObjective: This article aims to solve the non-linear Black Scholes (BS) equation for European call options using Radial Basis Function (RBF) Multi-Quadratic (MQ) Method.Methodology / Approach: This work uses the MQ RBF method applied to the solution of two complex models of nonlinear BS equation for prices of European call options with modified volatility. Linear BS models are also solved to visualize the effects of modified volatility.  Additionally, an adaptive scheme is implemented in time based on the Runge-Kutta-Fehlberg (RKF) method.

Option Hedging with Smooth Market Impact

2016 ◽  
Vol 02 (01) ◽  
pp. 1650002 ◽  
Author(s):  
Robert Almgren ◽  
Tianhui Michael Li
Keyword(s):  
Discrete Time ◽  
Market Impact ◽  
Large Collection ◽  
Public Markets ◽  
The Public ◽  
Option Hedging ◽  
A Value ◽  
First Case ◽  
Black Scholes ◽  
Optimal Hedge

We consider intraday hedging of an option position, for a large trader who experiences temporary and permanent market impact. We formulate the general model including overnight risk, and solve explicitly in two cases which we believe are representative. The first case is an option with approximately constant gamma: the optimal hedge trades smoothly towards the classical Black–Scholes delta, with trading intensity proportional to instantaneous mishedge and inversely proportional to illiquidity. The second case is an arbitrary non-linear option structure but with no permanent impact: the optimal hedge trades toward a value offset from the Black–Scholes delta. We estimate the effects produced on the public markets if a large collection of traders all hedge similar positions. We construct a stable hedge strategy with discrete time steps.

scholarly journals What They Did Not Tell You about Algebraic (Non-) Existence, Mathematical (IR-)Regularity and (Non-) Asymptotic Properties of the Full BEKK Dynamic Conditional Covariance Model

2019 ◽  
Vol 12 (2) ◽  
pp. 66 ◽  
Author(s):  
Michael McAleer
Keyword(s):  
Dynamic Models ◽  
Asymptotic Properties ◽  
Regularity Conditions ◽  
Covariance Model ◽  
Conditional Covariance ◽  
Risky Assets ◽  
Volatility Models ◽  
Hedge Ratios ◽  
Covariance Models ◽  
Optimal Hedge

Persistently high negative covariances between risky assets and hedging instruments are intended to mitigate against risk and subsequent financial losses. In the event of having more than one hedging instrument, multivariate covariances need to be calculated. Optimal hedge ratios are unlikely to remain constant using high frequency data, so it is essential to specify dynamic covariance models. These values can either be determined analytically or numerically on the basis of highly advanced computer simulations. Analytical developments are occasionally promulgated for multivariate conditional volatility models. The primary purpose of the paper is to analyze purported analytical developments for the most widely-used multivariate dynamic conditional covariance model to have been developed to date, namely the Full BEKK model, named for Baba, Engle, Kraft and Kroner. Dynamic models are not straightforward (or even possible) to translate in terms of the algebraic existence, underlying stochastic processes, specification, mathematical regularity conditions, and asymptotic properties of consistency and asymptotic normality, or the lack thereof. The paper presents a critical analysis, discussion, evaluation and presentation of caveats relating to the Full BEKK model, and an emphasis on the numerous dos and don’ts in implementing the Full BEKK and related non-Diagonal BEKK models, such as Triangular BEKK and Hadamard BEKK, in practice.

Wechselkursrisiko und Risikopolitik in internationalen Unternehmen

2008 ◽  
Vol 59 (1) ◽  
Author(s):  
Udo Broll ◽  
Jack E. Wahl
Keyword(s):  
Exchange Rate ◽  
Risk Aversion ◽  
Income Effect ◽  
Exchange Rate Risk ◽  
Hedge Ratio ◽  
International Firm ◽  
Rate Risk ◽  
Risk Effect ◽  
Optimal Hedge ◽  
Mean Variance

SummaryThe aim of this study is to analyze the importance of the elasticity of risk aversion with regard to an increase in exchange rate risk for exports and hedging in an international firm. Mean-variance preferences allow for an immediate study of the entailed substitution and income effect. These effects may cancel out, that is to say, the optimal hedge ratio remains unchanged although the exchange rate risk increases. The elasticity of risk aversion provides an unambiguous answer to the question how to measure such risk effect.

Existence of Unbiased Estimators of the Black/Scholes Option Price, Other Derivatives, and Hedge Ratios

1997 ◽  
Vol 13 (6) ◽  
pp. 791-807 ◽  
Author(s):  
John L Knight ◽  
Stephen E. Satchell
Keyword(s):  
Option Price ◽  
Statistical Bias ◽  
Unbiased Estimators ◽  
Black Scholes ◽  
Hedge Ratios

In this paper, we reexamine the question of statistical bias in the classic Black/Scholes option price where randomness is due to the use of the historical variance. We show that the only unbiased estimated option is an at the money option.

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