Black-Scholes Option Pricing Model

Exchange-traded currency options are a recent innovation in the Indian financial market and their pricing is as yet unexplored. The objective of this research paper is to empirically compare the pricing performance of two well-known option pricing models – the Black-Scholes-Merton Option Pricing Model (BSM) and Duan’s NGARCH option pricing model – for pricing exchange-traded currency options on the US dollar-Indian rupee during a recent turbulent period. The BSM is known to systematically misprice options on the same underlying asset but with different strike prices and maturities resulting in the phenomenon of the ‘volatility smile’. This bias of the BSM results from its assumption of a constant volatility over the option’s life. The NGARCH option pricing model developed by Duan is an attempt to incorporate time-varying volatility in pricing options. It is a deterministic volatility model which has no closed-form solution and therefore requires numerical techniques for evaluation. In this paper we have compared the pricing performance and examined the pricing bias of both models during a recent period of volatility in the Indian foreign exchange market. Contrary to our expectations the pricing performance of the more sophisticated NGARCH pricing model is inferior to that of the relatively simple BSM model. However orthogonality tests demonstrate that the NGARCH model is free of the strike price and maturity biases associated with the BSM. We conclude that the deterministic BSM does a better job of pricing options than the more advanced time-varying volatility model based on GARCH.

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Nonparametric Estimation of Fractional Option Pricing Model

Mathematical Problems in Engineering ◽

10.1155/2020/8858821 ◽

2020 ◽

Vol 2020 ◽

pp. 1-8

Author(s):

Qing Li ◽

Songlin Liu ◽

Misi Zhou

Keyword(s):

Option Pricing ◽

Stock Exchange ◽

Option Price ◽

Integral Function ◽

The State ◽

Pricing Model ◽

State Price ◽

Black Scholes ◽

Option Pricing Model ◽

State Price Density

The establishment of the fractional Black–Scholes option pricing model is under a major condition with the normal distribution for the state price density (SPD) function. However, the fractional Brownian motion is deemed to not be martingale with a long memory effect of the underlying asset, so that the estimation of the state price density (SPD) function is far from simple. This paper proposes a convenient approach to get the fractional option pricing model by changing variables. Further, the option price is transformed as the integral function of the cumulative density function (CDF), so it is not necessary to estimate the distribution function individually by complex approaches. Finally, it encourages to estimate the fractional option pricing model by the way of nonparametric regression and makes empirical analysis with the traded 50 ETF option data in Shanghai Stock Exchange (SSE).

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Predicting the stock price of frontier markets using machine learning and modified Black–Scholes Option pricing model

Physica A Statistical Mechanics and its Applications ◽

10.1016/j.physa.2020.124444 ◽

2020 ◽

Vol 555 ◽

pp. 124444 ◽

Cited By ~ 2

Author(s):

Reaz Chowdhury ◽

M.R.C. Mahdy ◽

Tanisha Nourin Alam ◽

Golam Dastegir Al Quaderi ◽

M. Arifur Rahman

Keyword(s):

Machine Learning ◽

Option Pricing ◽

Stock Price ◽

Pricing Model ◽

Black Scholes ◽

Option Pricing Model

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ItÔ's Calculus: Derivation of the Black–Scholes Option Pricing Model

Security Analysis, Portfolio Management, and Financial Derivatives ◽

10.1142/9789814343589_0027 ◽

2012 ◽

pp. 1081-1116

Keyword(s):

Option Pricing ◽

Pricing Model ◽

Black Scholes ◽

Option Pricing Model

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Improved Additive Operator Splitting Algorithms for Basket Option Pricing Model

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.756-759.2739 ◽

2013 ◽

Vol 756-759 ◽

pp. 2739-2743

Author(s):

Xiao Zhong Yang ◽

Gao Xin Zhou

Keyword(s):

Option Pricing ◽

Operator Splitting ◽

Stability And Convergence ◽

Pricing Model ◽

Explicit Schemes ◽

Basket Option ◽

Additive Operator ◽

Black Scholes ◽

Option Pricing Model ◽

Additive Operator Splitting

In order to solve Black-Scholes equation of basket option pricing model by numerical method. This paper used Additive Operator Splitting (AOS) algorithm to split the multi-dimensional Black-Scholes equation into equivalent one-dimensional equation set, and constructed 'Explicit-Implicit' and 'Implicit-Explicit' schemes to solve it. Then compatibility, stability and convergence of those schemes were analyzed. Finally, this paper compared computation time and precision of the schemes through numerical experiments. 'Explicit-Implicit' and 'Implicit-Explicit' schemes of AOS algorithms have both higher accuracy and faster computing speed and them have practical significance in solving basket option pricing model.

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