Subdiffusive fractional Brownian motion regime for pricing currency\n options under transaction costs

2016/12/20 by Foad Shokrollahi, Shokrollahi, Foad
Economics, Econometrics and Finance · Physics and Astronomy · #Stochastic processes and financial applications #Complex Systems and Time Series Analysis #Advanced Thermodynamics and Statistical Mechanics

paper · pdf · doi:10.48550/arxiv.1612.06665

Abstract

A new framework for pricing the European currency option is developed in the\ncase where the spot exchange rate fellows a time-changed fractional Brownian\nmotion. An analytic formula for pricing European foreign currency option is\nproposed by a mean self-financing delta-hedging argument in a discrete time\nsetting. The minimal price of a currency option under transaction costs is\nobtained as time-step \Δ\nt=\( fract^\β-1\Γ(\β)\)^-1\(\(2)/(\π)\)^\(1)/(2H)\(\(\α)/(\σ)\)^\(1)/(H)\n, which can be used as the actual price of an option. In addition, we also show\nthat time-step and long-range dependence have a significant impact on option\npricing.\n

Citations

• The Pricing of Options and Corporate Liabilities

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