Abstract
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 , 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.
Highlights
The standard European currency option valuation model has been presented by Garman and Kohlhagen ðG À KÞ (Garman & Kohlhagen, 1983)
According to the features of the subdiffusion process and the fractional Brownian motion, we propose the new model for pricing European currency options by using the fractional Brownian motion, subdiffusive strategy, and scaling time in discrete time setting, to get behavior from financial markets
We illustrate how to price a currency options in discrete time setting for both cases: with and without transaction costs by applying subdiffusive fractional Brownian motion model
Summary
The standard European currency option valuation model has been presented by Garman and Kohlhagen ðG À KÞ (Garman & Kohlhagen, 1983). According to the features of the subdiffusion process and the fractional Brownian motion, we propose the new model for pricing European currency options by using the fractional Brownian motion, subdiffusive strategy, and scaling time in discrete time setting, to get behavior from financial markets. The main contribution of this paper is to derive an analytical formula for European call currency option without using the arbitrage argument in discrete time setting when the exchange rate follows a subdiffusive FBS n o. The rest of the paper proceeds as follows: In Section 2, we provide an analytic pricing formula for the European currency option in the subdiffusive FBS environment and some Greeks of our pricing model are obtained. By using α-self-similar and non-decreasing sample paths of TαðtÞ, we can obtain that α-self-similar and non-decreasing sample paths of TαðtÞ, EðΔTαðtÞÞ 1⁄4 EðTαðt þ ΔtÞ À TαðtÞÞ
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