scholarly journals On Option Pricing in Illiquid Markets with Jumps

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Youssef El-Khatib ◽  
Abdulnasser Hatemi-J
Keyword(s):  
Option Pricing ◽  
Continuous Process ◽  
Price Impact ◽  
Hedging Strategy ◽  
Illiquid Markets ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Random Jumps ◽  
Global Stock Markets ◽  
Recent Financial Crisis

One of the shortcomings of the Black-Scholes model on option pricing is the assumption that trading of the underlying asset does not affect the price of that asset. This assumption can be fulfilled only in perfectly liquid markets. Since most markets are illiquid, this assumption might be too restrictive. Thus, taking into account the price impact on option pricing is an important issue. This issue has been dealt with, to some extent, for illiquid markets by assuming a continuous process, mainly based on the Brownian motion. However, the recent financial crisis and its effects on the global stock markets have propagated the urgent need for more realistic models where the stochastic process describing the price trajectories involves random jumps. Nonetheless, works related to markets with jumps are scant compared to the continuous ones. In addition, those previous studies do not deal with illiquid markets. The contribution of this paper is to tackle the pricing problem for options in illiquid markets with jumps as well as the hedging strategy within this context, which is the first of its kind to the authors’ best knowledge.

scholarly journals PREFERENCES, LÉVY JUMPS AND OPTION PRICING

2007 ◽  
Vol 03 (01) ◽  
pp. 0750001 ◽  
Author(s):  
CHENGHU MA
Keyword(s):  
Option Pricing ◽  
Contingent Claims ◽  
Economic Variable ◽  
European Options ◽  
Jump Risk ◽  
Representative Agent ◽  
Potential Explanation ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Lévy Jumps

This paper derives an equilibrium formula for pricing European options and other contingent claims which allows incorporating impacts of several important economic variable on security prices including, among others, representative agent preferences, future volatility and rare jump events. The derived formulae is general and flexible enough to include some important option pricing formulae in the literature, such as Black–Scholes, Naik–Lee, Cox–Ross and Merton option pricing formulae. The existence of jump risk as a potential explanation of the moneyness biases associated with the Black–Scholes model is explored.

Option pricing models

1989 ◽  
Vol 116 (3) ◽  
pp. 537-558 ◽  
Author(s):  
D. Blake
Keyword(s):  
Option Pricing ◽  
Binomial Model ◽  
Pricing Models ◽  
Black Scholes Model ◽  
Black Scholes

ABSTRACTThe paper discusses two important models of option pricing: the binomial model and the Black—Scholes model. It begins with a brief description of options.

scholarly journals The Extended Black-Scholes Model with-LAGS-and “Hedging Errors”

2003 ◽  
Author(s):  
Mondher Bellalah
Keyword(s):  
Stock Price ◽  
Standard Form ◽  
Small Time ◽  
Market Model ◽  
Short Term ◽  
Hedging Strategy ◽  
Underlying Asset ◽  
Elapsed Time ◽  
Black Scholes Model ◽  
Black Scholes

The Black-Scholes model is derived under the assumption that heding is done instantaneously. In practice, there is a “small” time that elapses between buying or selling the option and hedging using the underlying asset. Under the following assumptions used in the standard Black-Scholes analysis, the value of the option will depend only on the price of the underlying asset S, time t and on other Variables assumed constants. These assumptions or “ideal conditions” as expressed by Black-Scholes are the following. The option us European, The short term interest rate is known, The underlying asset follows a random walk with a variance rate proportional to the stock price. It pays no dividends or other distributions. There is no transaction costs and short selling is allowed, i.e. an investment can sell a security that he does not own. Trading takes place continuously and the standard form of the capital market model holds at each instant. The last assumption can be modified because in practice, trading does not take place in-stantaneouly and simultaneously in the option and the underlying asset when implementing the hedging strategy. We will modify this assumption to account for the “lag”. The lag corresponds to the elapsed time between buying or selling the option and buying or selling - delta units of the underlying assets. The main attractions of the Black-Scholes model are that their formula is a function of “observable” variables and that the model can be extended to the pricing of any type of option. All the assumptions are conserved except the last one.

scholarly journals Markov Chain Monte Carlo Method for Estimating Implied Volatility in Option Pricing

2018 ◽  
Vol 10 (6) ◽  
pp. 108
Author(s):  
Yao Elikem Ayekple ◽  
Charles Kofi Tetteh ◽  
Prince Kwaku Fefemwole
Keyword(s):  
Option Pricing ◽  
Implied Volatility ◽  
Call Option ◽  
Option Prices ◽  
Options Market ◽  
European Call Option ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Real Market ◽  
Independent Path

Using market covered European call option prices, the Independence Metropolis-Hastings Sampler algorithm for estimating Implied volatility in option pricing was proposed. This algorithm has an acceptance criteria which facilitate accurate approximation of this volatility from an independent path in the Black Scholes Model, from a set of finite data observation from the stock market. Assuming the underlying asset indeed follow the geometric brownian motion, inverted version of the Black Scholes model was used to approximate this Implied Volatility which was not directly seen in the real market: for which the BS model assumes the volatility to be a constant. Moreover, it is demonstrated that, the Implied Volatility from the options market tends to overstate or understate the actual expectation of the market. In addition, a 3-month market Covered European call option data, from 30 different stock companies was acquired from Optionistic.Com, which was used to estimate the Implied volatility. This accurately approximate the actual expectation of the market with low standard errors ranging between 0.0035 to 0.0275.

scholarly journals Finite Difference/Fourier Spectral for a Time Fractional Black–Scholes Model with Option Pricing

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Juan He ◽  
Aiqing Zhang
Keyword(s):  
Option Pricing ◽  
Dynamic Behavior ◽  
Numerical Scheme ◽  
Step Size ◽  
Spatial Direction ◽  
Discrete Method ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Difference Fourier ◽  
The Impact

We study the fractional Black–Scholes model (FBSM) of option pricing in the fractal transmission system. In this work, we develop a full-discrete numerical scheme to investigate the dynamic behavior of FBSM. The proposed scheme implements a known L1 formula for the α-order fractional derivative and Fourier-spectral method for the discretization of spatial direction. Energy analysis indicates that the constructed discrete method is unconditionally stable. Error estimate indicates that the 2−α-order formula in time and the spectral approximation in space is convergent with order OΔt2−α+N1−m, where m is the regularity of u and Δt and N are step size of time and degree, respectively. Several numerical results are proposed to confirm the accuracy and stability of the numerical scheme. At last, the present method is used to investigate the dynamic behavior of FBSM as well as the impact of different parameters.

From the Black Atlantic to Black-Scholes

2020 ◽  
Vol 16 (1) ◽  
pp. 92-110
Author(s):  
Luke Munn
Keyword(s):  
Eighteenth Century ◽  
Option Pricing ◽  
Financial Market ◽  
Stochastic Equation ◽  
Black Atlantic ◽  
Slave Ship ◽  
Historical Continuity ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Slave Ships

Rather than being unprecedented, contemporary technologies are the most sophisticated instances of a long-standing dream: if space could be more comprehensively captured and coded, it could be more intensively capitalized. Two moments within this lineage are explored: maritime insurance of slave ships in the eighteenth century, and the Black-Scholes model of option pricing from the twentieth century. Maritime insurance rendered the unknown space of the ocean knowable and therefore profitable. By collecting information at Lloyds, merchants developed a map of threat within the Atlantic, and by writing a 10 percent buffer into slave-ship contracts they internalized contingency. This codification of risk pressured captains and established a logic for the violence enacted on the ship’s human “cargo.” The Black-Scholes formula of option pricing sought to codify the ocean of risk represented by the financial market. The formula mapped stock movements into a knowable stochastic equation. Traders could quantify and hedge against the unpredictable, rendering the stock market a space of riskless profit. However, the 2008 financial crash demonstrated the limits of spatial calculation. Taken together, these two moments demonstrate the historical continuity of a core imperative to exhaustively capitalize space. This historicization also foregrounds the racialized inequalities coded within these informatic logics. Against the bright innovation narratives of technology, this article stresses a longer and darker lineage based on inequality and dispossession.

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