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 A modification term for Black-Scholes model based on discrepancy calibrated with real market data

2021 ◽  
Vol 1 (4) ◽  
pp. 313-326
Author(s):  
Xiaozheng Lin ◽  
◽  
Meiqing Wang ◽  
Choi-Hong Lai ◽  
Keyword(s):  
Option Pricing ◽  
Implied Volatility ◽  
Option Prices ◽  
Market Prices ◽  
Market Data ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Option Pricing Model ◽  
Real Market ◽  
S Model

<abstract><p>The Black-Scholes option pricing model (B-S model) generally requires the assumption that the volatility of the underlying asset be a piecewise constant. However, empirical analysis shows that there are discrepancies between the option prices obtained from the B-S model and the market prices. Most current modifications to the B-S model rely on modelling the implied volatility or interest rate. In contrast to the existing modifications to the Black-Scholes model, this paper proposes the concept of including a modification term to the B-S model itself. Using the actual discrepancies of the results of the Black-Scholes model and the market prices, the modification term related to the implied volatility is derived. Experimental results show that the modified model produces a better option pricing results when compare to market data.</p></abstract>

Arbitrage-free interpolation of call option prices

2020 ◽  
Vol 37 (1-2) ◽  
pp. 55-78
Author(s):  
Christian Bender ◽  
Matthias Thiel
Keyword(s):  
Implied Volatility ◽  
Reference Model ◽  
Interpolation Method ◽  
Call Option ◽  
Option Prices ◽  
One Dimensional ◽  
Black Scholes Model ◽  
Free Interpolation ◽  
Black Scholes ◽  
Special Case

AbstractIn this paper, we introduce a new interpolation method for call option prices and implied volatilities with respect to the strike, which first generates, for fixed maturity, an implied volatility curve that is smooth and free of static arbitrage. Our interpolation method is based on a distortion of the call price function of an arbitrage-free financial “reference” model of one’s choice. It reproduces the call prices of the reference model if the market data is compatible with the model. Given a set of call prices for different strikes and maturities, we can construct a call price surface by using this one-dimensional interpolation method on every input maturity and interpolating the generated curves in the maturity dimension. We obtain the algorithm of N. Kahalé [An arbitrage-free interpolation of volatilities, Risk 17 2004, 5, 102–106] as a special case, when applying the Black–Scholes model as reference model.

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.

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.

ON THE ASYMPTOTICS OF FAST MEAN-REVERSION STOCHASTIC VOLATILITY MODELS

2007 ◽  
Vol 10 (05) ◽  
pp. 817-835 ◽  
Author(s):  
MAX O. SOUZA ◽  
JORGE P. ZUBELLI
Keyword(s):  
Asymptotic Expansion ◽  
Stochastic Volatility ◽  
Implied Volatility ◽  
Correction Term ◽  
Option Prices ◽  
Stochastic Volatility Models ◽  
Black Scholes Model ◽  
Volatility Models ◽  
Asymptotic Formulae ◽  
Black Scholes

We consider the asymptotic behavior of options under stochastic volatility models for which the volatility process fluctuates on a much faster time scale than that defined by the riskless interest rate. We identify the distinguished asymptotic limits and, in contrast with previous studies, we deal with small volatility-variance (vol-vol) regimes. We derive the corresponding asymptotic formulae for option prices, and find that the first order correction displays a dependence on the hidden state and a non-diffusive terminal layer. Furthermore, this correction cannot be obtained as the small variance limit of the previous calculations. Our analysis also includes the behavior of the asymptotic expansion, when the hidden state is far from the mean. In this case, under suitable hypothesis, we show that the solution behaves as a constant volatility Black–Scholes model to all orders. In addition, we derive an asymptotic expansion for the implied volatility that is uniform in time. It turns out that the fast scale plays an important role in such uniformity. The theory thus obtained yields a more complete picture of the different asymptotics involved under stochastic volatility. It also clarifies the remarkable independence on the state of the volatility in the correction term obtained by previous authors.

scholarly journals The Performance of Skewness and Kurtosis Adjusted Option Pricing Model in Emerging Markets

2016 ◽  
Vol 5 (3) ◽  
pp. 70-84
Author(s):  
Özge Sezgin Alp
Keyword(s):  
Emerging Markets ◽  
Option Pricing ◽  
Option Prices ◽  
Pricing Model ◽  
European Options ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Option Pricing Model ◽  
Skewness And Kurtosis ◽  
Pricing Formula

In this study, the option pricing performance of the adjusted Black-Scholes model proposed by Corrado and Su (1996) and corrected by Brown and Robinson (2002), is investigated and compared with original Black Scholes pricing model for the Turkish derivatives market. The data consist of the European options written on BIST 30 index extends from January 02, 2015 to April 24, 2015 for given exercise prices with maturity April 30, 2015. In this period, the strike prices are ranging from 86 to 124. To compare the models, the implied parameters are derived by minimizing the sum of squared deviations between the observed and theoretical option prices. The implied distribution of BIST 30 index does not significantly deviate from normal distribution. In addition, pricing performance of Black Scholes model performs better in most of the time. Black Scholes pricing Formula, Carrado-Su pricing Formula, Implied Parameters

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