Subdiffusive fractional Black–Scholes model for pricing currency options under transaction costs
| Autor: | Foad Shokrollahi |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Transaction cost
lcsh:Mathematics ta111 currency option General Medicine Black–Scholes model lcsh:QA1-939 01 natural sciences inverse subordinator process 010305 fluids & plasmas transaction costs 010104 statistics & probability Exchange rate subdiffusion process Discrete time and continuous time Argument Valuation of options Currency 0103 physical sciences Econometrics Economics Call option 0101 mathematics |
| Zdroj: | Cogent Mathematics & Statistics, Vol 5, Iss 1 (2018) |
| ISSN: | 2331-1835 |
| Popis: | A new framework for pricing European currency option is developed in the case where the spot exchange rate follows a subdiffusive fractional Black–Scholes. An analytic formula for pricing European currency call 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 $$\Delta t = {\left({{{{t^{\alpha - 1}}} \over {\Gamma (\alpha )}}} \right)^{ - 1}}{\left({{2 \over \pi }} \right)^{{1 \over {2H}}}}{\left({{k \over \sigma }} \right)^{{1 \over H}}}$$, 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. |
| Databáze: | OpenAIRE |
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