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Register a new userThe valuation of European option with transaction costs by mixed fractional Merton model
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Authors
Foad Shokrollahi
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This paper deals with the problem of discrete-time option pricing by the mixed fractional version of Merton model with transaction costs. By a mean-self-financing delta hedging argument in a discrete-time setting, a European call option pricing formula is obtained. We also investigate the effect of the time-step $delta t$ and the Hurst parameter $H$ on our pricing option model, which reveals that these parameters have high impact on option pricing. The properties of this model are also explained.
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An investor with constant absolute risk aversion trades a risky asset with general It^o-dynamics, in the presence of small proportional transaction costs. In this setting, we formally derive a leading-order optimal trading policy and the associated welfare, expressed in terms of the local dynamics of the frictionless optimizer. By applying these results in the presence of a random endowment, we obtain asymptotic formulas for utility indifference prices and hedging strategies in the presence of small 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.
The purpose of this paper is to analyze the problem of option pricing when the short rate follows subdiffusive fractional Merton model. We incorporate the stochastic nature of the short rate in our option valuation model and derive explicit formula for call and put option and discuss the corresponding fractional Black-Scholes equation. We present some properties of this pricing model for the cases of $alpha$ and $H$. Moreover, the numerical simulations illustrate that our model is flexible and easy to implement.
A stochastic model for pure-jump diffusion (the compound renewal process) can be used as a zero-order approximation and as a phenomenological description of tick-by-tick price fluctuations. This leads to an exact and explicit general formula for the martingale price of a European call option. A complete derivation of this result is presented by means of elementary probabilistic tools.
A new framework for pricing the European currency option is developed in the case where the spot exchange rate fellows a time-changed fractional Brownian motion. An analytic formula for pricing European foreign currency option is proposed by a mean self-financing delta-hedging argument in a discrete time setting. The minimal price of a currency option under transaction costs is obtained as time-step $Delta t=left(frac{t^{beta-1}}{Gamma(beta)}right)^{-1}left(frac{2}{pi}right)^{frac{1}{2H}}left(frac{alpha}{sigma}right)^{frac{1}{H}}$ , which can be used as the actual price of an option. In addition, we also show that time-step and long-range dependence have a significant impact on option pricing.
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