Pricing options on a mean-reverting asset by the analytical operator splitting method

2021 ◽  
pp. 2150002
Author(s):  
C. F. Lo ◽  
Y. W. He
Keyword(s):  
Operator Splitting ◽  
Splitting Method ◽  
Dynamical Symmetry ◽  
Call Option ◽  
Option Prices ◽  
Pricing Options ◽  
Operator Splitting Method ◽  
European Call Option ◽  
Price Formula ◽  
Black Scholes

In this paper, we propose an operator splitting method to valuate options on the inhomogeneous geometric Brownian motion. By exploiting the approximate dynamical symmetry of the pricing equation, we derive a simple closed-form approximate price formula for a European call option which resembles closely the Black–Scholes price formula for a European vanilla call option. Numerical tests show that the proposed method is able to provide very accurate estimates and tight bounds of the exact option prices. The method is very efficient and robust as well.

scholarly journals Analytical Solution of Black-Scholes Equation in Predicting Market Prices and Its Pricing Bias

2020 ◽  
pp. 17-23
Author(s):  
Azor, Promise Andaowei ◽  
Amadi, Innocent Uchenna
Keyword(s):  
Analytical Solution ◽  
Goodness Of Fit ◽  
Call Option ◽  
Option Prices ◽  
Goodness Of Fit Test ◽  
Market Prices ◽  
European Call Option ◽  
Black Scholes

This paper is geared towards implementation of Black-Scholes equation in valuation of European call option and predicting market prices for option traders. First, we explained how Black-Scholes equation can be used to estimate option prices and then we also estimated the BS pricing bias from where market prices were predicted. From the results, it was discovered that Black-Scholes values were relatively close to market prices but a little increase in strike prices (K) decreases the option prices. Furthermore, goodness of fit test was done using Kolmogorov –Sminorvov to study BSM and Market prices.

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.

A simple closed-form approximation for constant elasticity of variance spread options

2020 ◽  
Vol 07 (04) ◽  
pp. 2050047
Author(s):  
C. F. Lo ◽  
X. F. Zheng
Keyword(s):  
Operator Splitting ◽  
Splitting Method ◽  
Option Price ◽  
Analytical Approximation ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Spread Options ◽  
Operator Splitting Method ◽  
Black Scholes ◽  
Closed Form Approximation

By applying the Lie–Trotter operator splitting method and the idea of the WKB method, we have developed a simple, accurate and efficient analytical approximation for pricing the constant elasticity of variance (CEV) spread options. The derived option price formula bears a striking resemblance to Kirk’s formula of the Black–Scholes spread options. Illustrative numerical examples show that the proposed approximation is not only extremely fast and robust, but it is also remarkably accurate for typical volatilities and maturities of up to two years.

scholarly journals Nonuniform Finite Difference Scheme for the Three-Dimensional Time-Fractional Black–Scholes Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Sangkwon Kim ◽  
Chaeyoung Lee ◽  
Wonjin Lee ◽  
Soobin Kwak ◽  
Darae Jeong ◽  
...  
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Experiments ◽  
Operator Splitting ◽  
Three Dimensional ◽  
Nonuniform Grid ◽  
Call Option ◽  
Splitting Scheme ◽  
European Call Option ◽  
Black Scholes

In this study, we present an accurate and efficient nonuniform finite difference method for the three-dimensional (3D) time-fractional Black–Scholes (BS) equation. The operator splitting scheme is used to efficiently solve the 3D time-fractional BS equation. We use a nonuniform grid for pricing 3D options. We compute the three-asset cash-or-nothing European call option and investigate the effects of the fractional-order α in the time-fractional BS model. Numerical experiments demonstrate the efficiency and fastness of the proposed scheme.

scholarly journals Finite Difference Method for the Multi-Asset Black–Scholes Equations

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 391 ◽  
Author(s):  
Sangkwon Kim ◽  
Darae Jeong ◽  
Chaeyoung Lee ◽  
Junseok Kim
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Operator Splitting ◽  
Splitting Method ◽  
Three Dimensional ◽  
Closed Form Solutions ◽  
Operator Splitting Method ◽  
Black Scholes ◽  
The One

In this paper, we briefly review the finite difference method (FDM) for the Black–Scholes (BS) equations for pricing derivative securities and provide the MATLAB codes in the Appendix for the one-, two-, and three-dimensional numerical implementation. The BS equation is discretized non-uniformly in space and implicitly in time. The two- and three-dimensional equations are solved using the operator splitting method. In the numerical tests, we show characteristic examples for option pricing. The computational results are in good agreement with the closed-form solutions to the BS equations.

scholarly journals The Operator Splitting Method for Black-Scholes Equation

2011 ◽  
Vol 02 (06) ◽  
pp. 771-778 ◽  
Author(s):  
Yassir Daoud ◽  
Turgut Öziş
Keyword(s):  
Operator Splitting ◽  
Splitting Method ◽  
Operator Splitting Method ◽  
Black Scholes
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