scholarly journals Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Jiao-Jiao Sun ◽  
Shengwu Zhou ◽  
Yan Zhang ◽  
Miao Han ◽  
Fei Wang
Keyword(s):  
Brownian Motion ◽  
Transaction Costs ◽  
Fractional Brownian Motion ◽  
Asset Price ◽  
Brownian Motion Process ◽  
Proportional Transaction Costs ◽  
Cost Rate ◽  
Lookback Option ◽  
Fixed Proportion ◽  
The Impact

The pricing problem of lookback option with a fixed proportion of transaction costs is investigated when the underlying asset price follows a fractional Brownian motion process. Firstly, using Leland’s hedging method a partial differential equation satisfied by the value of the lookback option is derived. Then we obtain its numerical solution by constructing a Crank-Nicolson format. Finally, the effectiveness of the proposed form is verified through a numerical example. Meanwhile, the impact of transaction cost rate and volatility on lookback option value is discussed.

Pricing European options and currency options by time changed mixed fractional Brownian motion with transaction costs

2016 ◽  
Vol 03 (01) ◽  
pp. 1650003 ◽  
Author(s):  
Foad Shokrollahi ◽  
Adem Kılıçman ◽  
Marcin Magdziarz
Keyword(s):  
Brownian Motion ◽  
Transaction Costs ◽  
Fractional Brownian Motion ◽  
Discrete Time ◽  
Empirical Studies ◽  
Time Step ◽  
Currency Option ◽  
Mixed Fractional Brownian Motion ◽  
Text Model ◽  
The Impact

This study investigates a new formula for option pricing with transaction costs in a discrete time setting. The value of the financial assets is based on time-changed mixed fractional Brownian motion [Formula: see text] model. The pricing method is obtained for European call option using the time-changed [Formula: see text] model in a discrete time setting. Particularly, the minimal value [Formula: see text] of an option respect to transaction costs is obtained. Furthermore, the new model for pricing currency option is presented by utilizing the time-changed [Formula: see text] model. In addition, the impact of time step [Formula: see text], Hurst parameter H and transaction costs [Formula: see text] are also investigated, which substantiate that these parameters play a significant role in our pricing formula. Finally, the empirical studies and the simulation findings corroborate the theoretical bases and indicate the time-changed [Formula: see text] is a satisfactory model.

Option pricing under the fractional stochastic volatility model

2021 ◽  
Vol 63 ◽  
pp. 123-142
Author(s):  
Yuecai Han ◽  
Zheng Li ◽  
Chunyang Liu
Keyword(s):  
Brownian Motion ◽  
Option Pricing ◽  
Fractional Brownian Motion ◽  
Stochastic Volatility ◽  
Option Price ◽  
Stochastic Volatility Model ◽  
Option Prices ◽  
European Call Option ◽  
Volatility Model ◽  
The Impact

We investigate the European call option pricing problem under the fractional stochastic volatility model. The stochastic volatility model is driven by both fractional Brownian motion and standard Brownian motion. We obtain an analytical solution of the European option price via the Itô’s formula for fractional Brownian motion, Malliavin calculus, derivative replication and the fundamental solution method. Some numerical simulations are given to illustrate the impact of parameters on option prices, and the results of comparison with other models are presented. doi:10.1017/S1446181121000225

scholarly journals High-frequency trading with fractional Brownian motion

2020 ◽  
Author(s):  
Paolo Guasoni ◽  
Yuliya Mishura ◽  
Miklós Rásonyi
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
High Frequency ◽  
Asset Price ◽  
Optimal Strategies ◽  
Trading Costs ◽  
Frequency Limit ◽  
Dynamic Optimisation ◽  
High Frequency Limit ◽  
Mean Variance

Abstract In the high-frequency limit, conditionally expected increments of fractional Brownian motion converge to a white noise, shedding their dependence on the path history and the forecasting horizon and making dynamic optimisation problems tractable. We find an explicit formula for locally mean–variance optimal strategies and their performance for an asset price that follows fractional Brownian motion. Without trading costs, risk-adjusted profits are linear in the trading horizon and rise asymmetrically as the Hurst exponent departs from Brownian motion, remaining finite as the exponent reaches zero while diverging as it approaches one. Trading costs penalise numerous portfolio updates from short-lived signals, leading to a finite trading frequency, which can be chosen so that the effect of trading costs is arbitrarily small, depending on the required speed of convergence to the high-frequency limit.

scholarly journals On the Return Time for a Reflected Fractional Brownian Motion Process on the Positive Orthant

2011 ◽  
Vol 48 (01) ◽  
pp. 145-153 ◽  
Author(s):  
Chihoon Lee
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Heavy Traffic ◽  
Queueing Network ◽  
Network Models ◽  
Return Time ◽  
Brownian Motion Process ◽  
Positive Orthant ◽  
Time Result ◽  
Heavy Tailed

We consider a d-dimensional reflected fractional Brownian motion (RFBM) process on the positive orthant S = R + d , with drift r 0 ∈ R d and Hurst parameter H ∈ (½, 1). Under a natural stability condition on the drift vector r 0 and reflection directions, we establish a return time result for the RFBM process Z; that is, for some δ, κ > 0, sup x∈B E x [τ B (δ)] < ∞, where B = {x ∈ S : |x| ≤ κ} and τ B (δ) = inf{t ≥ δ : Z(t) ∈ B}. Similar results are known for reflected processes driven by standard Brownian motions, and our result can be viewed as their FBM counterpart. Our motivation for this study is that RFBM appears as a limiting workload process for fluid queueing network models fed by a large number of heavy-tailed ON/OFF sources in heavy traffic.

scholarly journals Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs

2017 ◽  
Vol 22 (1) ◽  
pp. 161-180 ◽  
Author(s):  
Christoph Czichowsky ◽  
Rémi Peyre ◽  
Walter Schachermayer ◽  
Junjian Yang
Keyword(s):  
Brownian Motion ◽  
Transaction Costs ◽  
Fractional Brownian Motion ◽  
Portfolio Optimisation ◽  
Shadow Prices

scholarly journals Transaction Costs and Farm-to-Market Linkages in China: Empirical Evidence from Apple Producers

2020 ◽  
Vol 12 (9) ◽  
pp. 82
Author(s):  
Yu Wang ◽  
Lu Han ◽  
Kunda Qi ◽  
Jianyun Hou
Keyword(s):  
Information System ◽  
Transaction Costs ◽  
Empirical Evidence ◽  
Market Integration ◽  
Market Participation ◽  
Proportional Transaction Costs ◽  
Market Linkages ◽  
Monitoring Costs ◽  
Apple Production ◽  
The Impact

Using field surgveyed data from two apple production belts in China, this study estimates the impact of transaction costs on smallholders’ market participation and integration. The analysis is based on an innovative measurement of the transaction costs and a disaggregated analysis of sales, information, negotiation, and monitoring costs. The results reveal that farmers’ market participation levels are mainly determined by the proportional transaction costs and price, while their market integration depends on the fixed transaction costs and price. This suggests that, to lower the transaction costs and enable specialization and market participation, it is necessary to invest in and construct adequate farming infrastructure, update the rural information system, improve the structure of farmer households, and subsidize specialized rural cooperative organizations.

OPTION PRICING UNDER THE FRACTIONAL STOCHASTIC VOLATILITY MODEL

2021 ◽  
pp. 1-20
Author(s):  
Y. HAN ◽  
Z. LI ◽  
C. LIU
Keyword(s):  
Brownian Motion ◽  
Option Pricing ◽  
Fractional Brownian Motion ◽  
Stochastic Volatility ◽  
Option Price ◽  
Stochastic Volatility Model ◽  
Option Prices ◽  
European Call Option ◽  
Volatility Model ◽  
The Impact

Abstract We investigate the European call option pricing problem under the fractional stochastic volatility model. The stochastic volatility model is driven by both fractional Brownian motion and standard Brownian motion. We obtain an analytical solution of the European option price via the Itô’s formula for fractional Brownian motion, Malliavin calculus, derivative replication and the fundamental solution method. Some numerical simulations are given to illustrate the impact of parameters on option prices, and the results of comparison with other models are presented.

scholarly journals A Geometric Drift Inequality for a Reflected Fractional Brownian Motion Process on the Positive Orthant

2011 ◽  
Vol 48 (03) ◽  
pp. 820-831
Author(s):  
Chihoon Lee
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Heavy Traffic ◽  
Queueing Network ◽  
Network Models ◽  
Compact Set ◽  
Brownian Motion Process ◽  
Positive Orthant ◽  
Heavy Tailed ◽  
Necessary And Sufficient

We study a d-dimensional reflected fractional Brownian motion (RFBM) process on the positive orthant S = ℝ+ d , with drift r 0 ∈ ℝ d and Hurst parameter H ∈ (½, 1). Under a natural stability condition on the drift vector r 0 and reflection directions, we establish a geometric drift towards a compact set for the 1-skeleton chain Ž̆ of the RFBM process Z; that is, there exist β, b ∈ (0, ∞) and a compact set C ⊂ S such that ΔV(x):= E x [V(Ž̆(1))] − V(x) ≤ −βV(x) + b 1 C (x), x ∈ S, for an exponentially growing Lyapunov function V : S → [1, ∞). For a wide class of Markov processes, such a drift inequality is known as a necessary and sufficient condition for exponential ergodicity. Indeed, similar drift inequalities have been established for reflected processes driven by standard Brownian motions, and our result can be viewed as their fractional Brownian motion counterpart. We also establish that the return times to the set C itself are geometrically bounded. Motivation for this study is that RFBM appears as a limiting workload process for fluid queueing network models fed by a large number of heavy-tailed ON/OFF sources in heavy traffic.

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