Abstract
This research aims to investigate a model for pricing of currency options in which value governed by the fractional Brownian motion model (FBM). The fractional partial differential equation and some Greeks are also obtained. In addition, some properties of our pricing formula and simulation studies are presented, which demonstrate that the FBM model is easy to use.
Highlights
A currency options refers to an agreement that gives right to the holder in order to buy or sell a defined amount of foreign currency at a constant exercise price on option exercise
Black and Scholes (1973) put forward option pricing in 1973, which leads to be studied by different scholars (Dravid et al 1993; Toft and Reiner 1997; Kwok 2000; Duan and Wei 1999) claim that two issues in stock markets are not able to be presented clearly in this option pricing introduced by BS in accordance with Brownian motion (BM)
We show empirical studies and simulation in “Numerical studies” section in order to indicate the efficiency of the fractional Brownian motion model (FBM) model and final section of the paper is “Conclusion”
Summary
A currency options refers to an agreement that gives right to the holder in order to buy or sell a defined amount of foreign currency at a constant exercise price on option exercise. Black and Scholes (1973) put forward option pricing in 1973, which leads to be studied by different scholars (Dravid et al 1993; Toft and Reiner 1997; Kwok 2000; Duan and Wei 1999) claim that two issues in stock markets are not able to be presented clearly in this option pricing introduced by BS in accordance with Brownian motion (BM). These concepts refer to asymmetric leptokurtic features and the volatility smile. These characteristics could be functions of utility, measures of risk aversion, or yield expecting
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