Pricing currency options by generalizations of the mixed fractional brownian motion
Option pricing is an active area in financial industry. The value of option pricing is usually obtained by means of a mathematical option pricing model. Since fractional Brownian motion and mixed fractional Brownian motion processes have some important features in order to get typical tail behavi...
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| Format: | Thesis |
| Language: | English |
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2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/69127/1/FS%202016%2049%20IR.pdf |
| _version_ | 1796978873411305472 |
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| author | Shokrollahi, Foad |
| author_facet | Shokrollahi, Foad |
| author_sort | Shokrollahi, Foad |
| collection | UPM |
| description | Option pricing is an active area in financial industry. The value of option pricing is
usually obtained by means of a mathematical option pricing model. Since fractional
Brownian motion and mixed fractional Brownian motion processes have some important
features in order to get typical tail behavior from financial markets, such as:
self-similarity and long-range dependence, they can play a significant role in pricing
European option and European currency options. In this thesis, some extensions of
the mixed fractional Brownian motion model are proposed to wider classes of pricing
options systems.
In Chapter 3, a new framework for pricing the European currency option is developed
in the case where the spot exchange rate follows a mixed fractional Brownian motion
with jumps. An analytic formula for pricing European foreign currency options is
proposed using the equivalent martingale measure. For the purpose of understanding
the pricing model, some properties of this pricing model are discussed in Chapter
3 as well. Furthermore, the actuarial approach to pricing currency options which
transform option pricing into a problem of equivalent of fair insurance premium is
introduced.
In addition, in Chapter 4, the problem of discrete time option pricing by the mixed
fractional Brownian model with transaction costs using a mean self-financing delta
hedging argument is considered in a discrete time setting. A European call currency
option pricing formula is then obtained. In particular, the minimal pricing of an
option under transaction costs is obtained, which shows that time step dt and Hurst
exponent H play an important role in option pricing with transaction costs.
Finally, Chapter 5 considers the problem of discrete time option pricing by a mixed fractional subdiffusive Black-Scholes model. Under the assumption that the price of
the underlying stock follows a time-changed mixed fractional Brownian motion, a
pricing formula for the European call option and European call currency option is
derived in a discrete time setting with transaction costs. |
| first_indexed | 2024-03-06T10:00:47Z |
| format | Thesis |
| id | upm.eprints-69127 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T10:00:47Z |
| publishDate | 2016 |
| record_format | dspace |
| spelling | upm.eprints-691272019-06-26T01:01:41Z http://psasir.upm.edu.my/id/eprint/69127/ Pricing currency options by generalizations of the mixed fractional brownian motion Shokrollahi, Foad Option pricing is an active area in financial industry. The value of option pricing is usually obtained by means of a mathematical option pricing model. Since fractional Brownian motion and mixed fractional Brownian motion processes have some important features in order to get typical tail behavior from financial markets, such as: self-similarity and long-range dependence, they can play a significant role in pricing European option and European currency options. In this thesis, some extensions of the mixed fractional Brownian motion model are proposed to wider classes of pricing options systems. In Chapter 3, a new framework for pricing the European currency option is developed in the case where the spot exchange rate follows a mixed fractional Brownian motion with jumps. An analytic formula for pricing European foreign currency options is proposed using the equivalent martingale measure. For the purpose of understanding the pricing model, some properties of this pricing model are discussed in Chapter 3 as well. Furthermore, the actuarial approach to pricing currency options which transform option pricing into a problem of equivalent of fair insurance premium is introduced. In addition, in Chapter 4, the problem of discrete time option pricing by the mixed fractional Brownian model with transaction costs using a mean self-financing delta hedging argument is considered in a discrete time setting. A European call currency option pricing formula is then obtained. In particular, the minimal pricing of an option under transaction costs is obtained, which shows that time step dt and Hurst exponent H play an important role in option pricing with transaction costs. Finally, Chapter 5 considers the problem of discrete time option pricing by a mixed fractional subdiffusive Black-Scholes model. Under the assumption that the price of the underlying stock follows a time-changed mixed fractional Brownian motion, a pricing formula for the European call option and European call currency option is derived in a discrete time setting with transaction costs. 2016-03 Thesis NonPeerReviewed text en http://psasir.upm.edu.my/id/eprint/69127/1/FS%202016%2049%20IR.pdf Shokrollahi, Foad (2016) Pricing currency options by generalizations of the mixed fractional brownian motion. Doctoral thesis, Universiti Putra Malaysia. Brownian motion processes Options (Finance) - Prices - Mathematical models Mathematical analysis |
| spellingShingle | Brownian motion processes Options (Finance) - Prices - Mathematical models Mathematical analysis Shokrollahi, Foad Pricing currency options by generalizations of the mixed fractional brownian motion |
| title | Pricing currency options by generalizations of the mixed fractional brownian motion |
| title_full | Pricing currency options by generalizations of the mixed fractional brownian motion |
| title_fullStr | Pricing currency options by generalizations of the mixed fractional brownian motion |
| title_full_unstemmed | Pricing currency options by generalizations of the mixed fractional brownian motion |
| title_short | Pricing currency options by generalizations of the mixed fractional brownian motion |
| title_sort | pricing currency options by generalizations of the mixed fractional brownian motion |
| topic | Brownian motion processes Options (Finance) - Prices - Mathematical models Mathematical analysis |
| url | http://psasir.upm.edu.my/id/eprint/69127/1/FS%202016%2049%20IR.pdf |
| work_keys_str_mv | AT shokrollahifoad pricingcurrencyoptionsbygeneralizationsofthemixedfractionalbrownianmotion |