Option pricing with Legendre polynomials

Hok, Julien; Chan, Ron

doi:10.1016/j.cam.2017.03.027

Cited by 5 publications

(4 citation statements)

References 51 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Leippold and Scharer [10] develop a stochastic liquidity model, and they investigate discrete-time option pricing with stochastic liquidity. Hoka and Chanb [11] develop an option pricing method based on Legendre series expansion of the density function, and approximation formulas for pricing European type options are derived. Davison and Mamba [12] obtain a solution of the Black--Scholes equation with a nonsmooth boundary condition using symmetry methods.…”

Section: Introductionmentioning

confidence: 99%

European Option Pricing Formula in Risk-Aversive Markets

Wu¹,

Wang²

2021

Mathematical Problems in Engineering

View full text Add to dashboard Cite

In this study, using the method of discounting the terminal expectation value into its initial value, the pricing formulas for European options are obtained under the assumptions that the financial market is risk-aversive, the risk measure is standard deviation, and the price process of underlying asset follows a geometric Brownian motion. In particular, assuming the option writer does not need the risk compensation in a risk-neutral market, then the obtained results are degenerated into the famous Black–Scholes model (1973); furthermore, the obtained results need much weaker conditions than those of the Black–Scholes model. As a by-product, the obtained results show that the value of European option depends on the drift coefficient μ of its underlying asset, which does not display in the Black–Scholes model only because μ = r in a risk-neutral market according to the no-arbitrage opportunity principle. At last, empirical analyses on Shanghai 50 ETF options and S&P 500 options show that the fitting effect of obtained pricing formulas is superior to that of the Black–Scholes model.

show abstract

Section: Introductionmentioning

confidence: 99%

European Option Pricing Formula in Risk-Aversive Markets

Wu¹,

Wang²

2021

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…In [7], an adaptive sparse grid algorithm using the finite element method is employed for the solution of the Black-Scholes equation for option pricing. A Legendre series expansion of the density function is employed in [22] for option valuation. In [2], a proper orthogonal decomposition and non negative matrix factorization is employed to make pricing much faster within a given model parameter variation range.…”

Section: Introductionmentioning

confidence: 99%

Chebyshev reduced basis function applied to option valuation

Frutos

Gatón

2017

Comput Manag Sci

View full text Add to dashboard Cite

We present a numerical method for the frequent pricing of financial derivatives that depends on a large number of variables. The method is based on the construction of a polynomial basis to interpolate the value function of the problem by means of a hierarchical orthogonalization process that allows to reduce the number of degrees of freedom needed to have an accurate representation of the value function. In the paper we consider, as an example, a GARCH model that depends on eight parameters and show that a very large number of contracts for different maturities and asset and parameters values can be valued in a small computational time with the proposed procedure. In particular the method is applied to the problem of model calibration. The method is easily generalizable to be used with other models or problems.

show abstract

“…Various studies have been conducted about the linear Black-Scholes model [9][10][11][12][13][14][15] though it adopts the unrealistic assumption of no transaction costs. Several studies have been attempted to evaluate the price of European options [16][17][18][19][20][21][22][23], American options [24][25][26][27][28], Asian options [29,30], and Barrier options [31] in a completely friction-less market. Recently, the fractional Black-Scholes model [32][33][34] received some attention.…”

mentioning

confidence: 99%

Efficient Numerical Schemes for Computations of European Options with Transaction Costs

Hossan

Islam

Kamrujjaman

2022

Eur. J. Math. Anal.

View full text Add to dashboard Cite

This paper aims to find numerical solutions of the non-linear Black-Scholes partial differential equation (PDE), which often appears in financial markets, for European option pricing in the appearance of the transaction costs. Here we exploit the transformations for the computational purpose of a non-linear Black-Scholes PDE to modify as a non-linear parabolic type PDE with reliable initial and boundary conditions for call and put options. Several schemes are derived rigorously using the finite volume method (FVM) and finite difference method (FDM), which is the novelty of this paper. Stability and consistency analysis assure the convergence of these schemes. We apply these schemes to various volatility models, such as the Leland, Boyle and Vorst, Barles and Soner, and Risk-adjusted pricing methodology (RAPM). All the schemes are tested numerically. The convergence of the obtained results is observed, and we find that they are also reliable. Finally, we display all the approximate results together with the exact values through graphical and tabular representations.

show abstract

Option pricing with Legendre polynomials

Cited by 5 publications

References 51 publications

European Option Pricing Formula in Risk-Aversive Markets

European Option Pricing Formula in Risk-Aversive Markets

Chebyshev reduced basis function applied to option valuation

Efficient Numerical Schemes for Computations of European Options with Transaction Costs

Contact Info

Product

Resources

About