scholarly journals Relativistic Option Pricing

2021 ◽  
Vol 9 (2) ◽  
pp. 32
Author(s):  
Vitor H. Carvalho ◽  
Raquel M. Gaspar
Keyword(s):  
Option Pricing ◽  
High Speed ◽  
Reference Frames ◽  
Proper Time ◽  
Relativistic Effects ◽  
Theory Of Relativity ◽  
Market Participants ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Spatial Arbitrage

The change of information near light speed, advances in high-speed trading, spatial arbitrage strategies and foreseen space exploration, suggest the need to consider the effects of the theory of relativity in finance models. Time and space, under certain circumstances, are not dissociated and can no longer be interpreted as Euclidean. This paper provides an overview of the research made in this field while formally defining the key notions of spacetime, proper time and an understanding of how time dilation impacts financial models. We illustrate how special relativity modifies option pricing and hedging, under the Black–Scholes model, when market participants are in two different reference frames. In particular, we look into maturity and volatility relativistic effects.

scholarly journals Relativistic Effects in Reference Frames

1980 ◽  
Vol 56 ◽  
pp. 43-58 ◽  
Author(s):  
H. Moritz
Keyword(s):  
Gravitational Constant ◽  
Reference Frames ◽  
Relativistic Effects ◽  
Point Of View ◽  
Field Theories ◽  
Reference Systems ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
The Impact ◽  
Inertial Systems

AbstractThe impact of relativistic theories of space, time and gravitation on the problem of reference systems is reviewed.First, the concept of inertial systems is discussed from the point of view of the special and the general theory of relativity. Then, relativistic corrections of Doppler, laser and VLBI, and similar effects are reviewed; they are usually on the order of 10-8. Finally, the problem of a possible variation of the gravitational constant G (on the order of 10-11/year) is outlined; such a variation does not occur in special and general relativity, but is implied by certain generalized field theories which are less commonly accepted.

Time, Topology, and the Twin Paradox

2011 ◽  
Author(s):  
Jean‐Pierre Luminet
Keyword(s):  
High Speed ◽  
Reference Frames ◽  
Thought Experiment ◽  
Flat Space ◽  
Space Time ◽  
Twin Paradox ◽  
Theory Of Relativity ◽  
Apparent Paradox ◽  
Curved Space ◽  
Gravitational Fields

This chapter notes that the twin paradox is the best-known thought experiment associated with Einstein's theory of relativity. An astronaut who makes a journey into space in a high-speed rocket will return home to find he has aged less than his twin who stayed on Earth. This result appears puzzling, as the homebody twin can be considered to have done the travelling with respect to the traveller. Hence, it is called a “paradox”. In fact, there is no contradiction, and the apparent paradox has a simple resolution in special relativity with infinite flat space. In general relativity (dealing with gravitational fields and curved space-time), or in a compact space such as the hypersphere or a multiply connected finite space, the paradox is more complicated, but its resolution provides new insights about the structure of space–time and the limitations of the equivalence between inertial reference frames.

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 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.

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