1,299 research outputs found
Fractional delta hedging strategy for pricing currency options with transaction costs
This study deals with the problem of pricing European currency options in discrete time setting, whose prices follow the fractional Black Scholes model with transaction costs. Both the pricing formula and the fractional partial differential equation for European call currency options are obtained by applying the delta-hedging strategy. Some Greeks and the estimator of volatility are
also provided. The empirical studies and the simulation findings show that the fractional Black Scholes with transaction costs is a satisfactory model.fi=vertaisarvioitu|en=peerReviewed
Option pricing in fractional models
This thesis deals with application of the fractional Black-Scholes and mixed fractional Black-Scholes models to evaluate different type of options. These assessments are considered in four individual papers. In the first articles, the problem of geometric Asian and power options pricing is investigated when the stock price follows a time changed mixed fractional model. In this model, an inverse subordinator process in the mixed fractional Black-Scholes model replaces the physical time. The aim of the third paper is to evaluate the European currency option in a fractional Brownian motion environment by the time-changed strategy. Also, the impact of time step and long range dependence are obtained under transaction costs.
Conditional mean hedging under fractional Black-Scholes model is the propose of the second article. The conditional mean hedge of the European vanilla type option with convex or concave positive payoff under transaction costs is obtained. In the fourth article, the mixed fractional Brownian motion with jump process are incorporated to analyze European options in discrete time case. By a mean delta hedging strategy, the pricing model is proposed for European option under transaction costs.Väitöskirja tarkastelee fraktionaalisen Black–Scholes -mallin ja sekoitetun fraktionallisen Black–Scholes -mallin käyttöä erityyppisten optioiden arvottamisessa. Tätä tutkitaan neljässä artikkelissa. Ensimmäisessä artikkelissa tarkastellaan geometrisia aasialaisia optioita ja potenssioptioita, kun osakehinta noudattaa aikamuunnettua sekoitettua fraktionaalista mallia. Tässä mallissa sekoitun fraktionaalisen Black–Scholes -mallin käänteinen subordinaattoriprosessi korvaa fysikaalisen ajan. Kolmannen artikkelin tarkoitus on hinnoitella eurooppalainen valuuttaoptio fraktionaalisen Brownin liikkeen mallissa aikamuunnetulla strategialla. Lisäksi aika-askeleen ja pitkän aikavälin riippuvuuden vaikutusta tutkitaan transaktiokulujen alaisuudessa.
Ehdollinen keskiarvosuojaaminen fraktionaalisessa Black–Sholes -mallissa on toisen artikkelin aihe. Ehdollinen keskiarvosuojaus eurooppalaiselle vaniljaoptiolle, jolla on konveksi tai konkaavi positiivinen tuottofunktio transaktiokulujen vallitessa, on artikkelin päätulos. Neljännessä artikkelissa tutkitaan eurooppalaisia optioita diskreetissä ajassa mallissa, joka on hypyllinen sekoitettu fraktionaalinen Brownin liike. Käyttäen keskiarvoista deltasuojausstrategiaa artikkelissa johdetaan hinnoittelumalli eurooppalaisille optioille transaktiokulujen vallitessa.fi=vertaisarvioitu|en=peerReviewed
Measuring the error of dynamic hedging: a Laplace transform approach
We compute the expected value and the variance of the discretization error of delta hedging and of other strategies in the presence of proportional transaction costs. The method, based on Laplace transform, applies to a fairly general class of models, including Black-Scholes, Merton's jump-diffusion and Normal Inverse Gaussian. The results obtained are not asymptotical approximations but exact and efficient formulas, valid for any number of trading dates. They can also be employed under model mispecification, to measure the influence of model risk on a hedging strategy.hedging, Laplace transform
Hedging in fractional Black-Scholes model with transaction costs
We consider conditional-mean hedging in a fractional Black-Scholes pricing
model in the presence of proportional transaction costs. We develop an explicit
formula for the conditional-mean hedging portfolio in terms of the recently
discovered explicit conditional law of the fractional Brownian motion
Conditional-Mean Hedging Under Transaction Costs in Gaussian Models
We consider so-called regular invertible Gaussian Volterra processes and
derive a formula for their prediction laws. Examples of such processes include
the fractional Brownian motions and the mixed fractional Brownian motions. As
an application, we consider conditional-mean hedging under transaction costs in
Black-Scholes type pricing models where the Brownian motion is replaced with a
more general regular invertible Gaussian Volterra process.Comment: arXiv admin note: text overlap with arXiv:1706.0153
A non-arbitrage liquidity model with observable parameters for derivatives
We develop a parameterised model for liquidity effects arising from the trading in an asset. Liquidity is defined via a combination of a trader's individual transaction cost and a price slippage impact, which is felt by all market participants. The chosen definition allows liquidity to be observable in a centralised order-book of an asset as is usually provided in most non-specialist exchanges. The discrete-time version of the model is based on the CRR binomial tree and in the appropriate continuous-time limits we derive various nonlinear partial differential equations. Both versions can be directly applied to the pricing and hedging of options; the nonlinear nature of liquidity leads to natural bid-ask spreads that are based on the liquidity of the market for the underlying and the existence of (super-)replication strategies. We test and calibrate our model set-up empirically with high-frequency data of German blue chips and discuss further extensions to the model, including stochastic liquidity
Robust hedging of digital double touch barrier options
In this dissertation, we present basic idea and key results for model-free pricing and hedging of digital double barrier options. Besides we extend this model to the market with non-zero interest rate by allowing some model-based trading. Moreover we apply this hedging strategies to Heston stochastic volatility model and compare its performances with that of delta hedging strategies in such setting. Finally we further interpret these numerical results to show the advantages and disadvantages of these two types of hedging strategies
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A fast numerical algorithm is developed to price European options with
proportional transaction costs using the utility maximization framework
of Davis (1997). This approach allows option prices to be computed by
solving the investor's basic portfolio selection problem, without the inser-
tion of the option payo into the terminal value function. The properties
of the value function can then be used to drastically reduce the number of
operations needed to locate the boundaries of the no transaction region,
which leads to very e cient option valuation. The optimization problem
is solved numerically for the case of exponential utility, and comparisons
with approximately replicating strategies reveal tight bounds for option
prices even as transaction costs become large. The computational tech-
nique involves a discrete time Markov chain approximation to a continuous
time singular stochastic optimal control problem. A general de nition of
an option hedging strategy in this framework is developed. This involves
calculating the perturbation to the optimal portfolio strategy when an
option trade is execute
Efficient option pricing with transaction costs
A fast numerical algorithm is developed to price European options with proportional transaction costs using the utility-maximization framework of Davis (1997). This approach allows option prices to be computed by solving the investor’s basic portfolio selection problem without insertion of the option payoff into the terminal value function. The properties of the value function can then be used to drastically reduce the number of operations needed to locate the boundaries of the no-transaction region, which leads to very efficient option valuation. The optimization problem is solved numerically for the case of exponential utility, and comparisons with approximately replicating strategies reveal tight bounds for option prices even as transaction costs become large. The computational technique involves a discrete-time Markov chain approximation to a continuous-time singular stochastic optimal control problem. A general definition of an option hedging strategy in this framework is developed. This involves calculating the perturbation to the optimal portfolio strategy when an option trade is executed
Option Pricing with Transaction Costs Using a Markov Chain Approximation
An e cient algorithm is developed to price European options in the pres-
ence of proportional transaction costs, using the optimal portfolio frame-
work of Davis (1997). A fair option price is determined by requiring that
an in nitesimal diversion of funds into the purchase or sale of options
has a neutral e ect on achievable utility. This results in a general option
pricing formula, in which option prices are computed from the solution of
the investor's basic portfolio selection problem, without the need to solve
a more complex optimisation problem involving the insertion of the op-
tion payo into the terminal value function. Option prices are computed
numerically using a Markov chain approximation to the continuous time
singular stochastic optimal control problem, for the case of exponential
utility. Comparisons with approximately replicating strategies are made.
The method results in a uniquely speci ed option price for every initial
holding of stock, and the price lies within bounds which are tight even as
transaction costs become large. A general de nition of an option hedg-
ing strategy for a utility maximising investor is developed. This involves
calculating the perturbation to the optimal portfolio strategy when an
option trade is executed
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