scholarly journals Option Pricing by Probability Distortion Operator Based on the Quantile Function

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Luogen Yao ◽  
Gang Yang
Keyword(s):  
Option Pricing ◽  
Simulation Analysis ◽  
Quantile Function ◽  
Martingale Measure ◽  
Option Prices ◽  
New Class ◽  
Pricing Options ◽  
Black Scholes ◽  
Exponential Lévy Models

A new class of distortion operators based on quantile function is proposed for pricing options. It is shown that option prices obtained with our distortion operators are just the prices under mean correcting martingale measure in exponential Lévy models. In particular, Black-Scholes formula can be recuperated by our distortion operator. Simulation analysis shows that our distortion operator is superior to normal distortion operator and NIG distortion operator.

scholarly journals Empirical Performance of Black-Scholes and GARCH Option Pricing Models during Turbulent Times: The Indian Evidence

2016 ◽  
Vol 8 (3) ◽  
pp. 123
Author(s):  
Aparna Bhat ◽  
Kirti Arekar
Keyword(s):  
Option Pricing ◽  
Closed Form Solution ◽  
Time Varying ◽  
Pricing Model ◽  
Currency Options ◽  
Pricing Models ◽  
Pricing Options ◽  
Volatility Model ◽  
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.

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 Valuing Coca-Cola And PepsiCo Options Using The Black-Scholes Option Pricing Model And Data Downloads From The Internet

2012 ◽  
Vol 8 (6) ◽  
pp. 559-564
Author(s):  
John C. Gardner ◽  
Carl B. McGowan Jr
Keyword(s):  
Option Pricing ◽  
Stock Price ◽  
Option Price ◽  
Option Prices ◽  
Pricing Model ◽  
Black Scholes ◽  
Option Pricing Model ◽  
Risk Free Rate ◽  
Daily Returns ◽  
Free Rate

In this paper, we demonstrate how to collect the data and compute the actual value of Black-Scholes Option Pricing Model call option prices for Coca-Cola and PepsiCo.The data for the current stock price and option price are taken from Yahoo Finance and the daily returns variance is computed from daily prices.The time to maturity is computed as the number of days remaining for the stock option.The risk-free rate is obtained from the U.S. Treasury website.

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.

SHORT-TIME IMPLIED VOLATILITY IN EXPONENTIAL LÉVY MODELS

2015 ◽  
Vol 18 (04) ◽  
pp. 1550025
Author(s):  
ERIK EKSTRÖM ◽  
BING LU
Keyword(s):  
Implied Volatility ◽  
Upper And Lower Bounds ◽  
Gaussian Component ◽  
Option Prices ◽  
Strike Price ◽  
Short Time Asymptotics ◽  
Black Scholes ◽  
Exponential Lévy Models ◽  
Necessary And Sufficient ◽  
Short Time

We show that a necessary and sufficient condition for the explosion of implied volatility near expiry in exponential Lévy models is the existence of jumps towards the strike price in the underlying process. When such jumps do not exist, the implied volatility converges to the volatility of the Gaussian component of the underlying Lévy process as the time to maturity tends to zero. These results are proved by comparing the short-time asymptotics of the Black–Scholes price with explicit formulas for upper and lower bounds of option prices in exponential Lévy models.

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

scholarly journals Option Pricing And Monte Carlo Simulations

2011 ◽  
Vol 3 (9) ◽  
Author(s):  
George M. Jabbour ◽  
Yi-Kang Liu
Keyword(s):  
Monte Carlo ◽  
Option Pricing ◽  
Monte Carlo Simulations ◽  
Variance Reduction ◽  
Closed Form Solution ◽  
Form Solution ◽  
Price Convergence ◽  
Option Prices ◽  
Black Scholes ◽  
The Difference

The advantage of Monte Carlo simulations is attributed to the flexibility of their implementation. In spite of their prevalence in finance, we address their efficiency and accuracy in option pricing from the perspective of variance reduction and price convergence. We demonstrate that increasing the number of paths in simulations will increase computational efficiency. Moreover, using a t-test, we examine the significance of price convergence, measured as the difference between sample means of option prices. Overall, our illustrative results show that the Monte Carlo simulation prices are not statistically different from the Black-Scholes type closed-form solution prices.

scholarly journals Application of the Trefftz method for option pricing

2020 ◽  
Vol 2020 (146) ◽  
pp. 37-49
Author(s):  
Katarzyna BRZOZOWSKA-RUP ◽  
◽  
Sylwia HOŻEJOWSKA ◽  
Leszek HOŻEJOWSKI ◽  
◽  
...  
Keyword(s):  
Option Pricing ◽  
Design Methodology ◽  
Number Of Solutions ◽  
Trefftz Method ◽  
New Approach ◽  
Pricing Options ◽  
Black Scholes Model ◽  
Starting Point ◽  
Black Scholes ◽  
Computational Simplicity

Purpose: Option pricing is hardly a new topic, however, in many cases they lack an analytical 11 solution. The article proposes a new approach to option pricing based on the semi-analytical 12 Trefftz method. 13 Design/methodology/approach: An appropriate transformation makes it possible to reduce the 14 Black-Scholes equation to the heat equation. This admits the Trefftz method (which has shown 15 its effectiveness in heat conduction problems) to be employed. The advantage of such 16 an approach lies in its computational simplicity and in the fact that it delivers a solution 17 satisfying the governing equation. 18 Findings: The theoretical option pricing problem being considered in the paper has been solved 19 by means of the Trefftz method, and the results achieved appear to comply with those taken 20 from the Black-Scholes formula. Numerical simulations have been carried out and compared, 21 which has confirmed the accuracy of the proposed approach. 22 Originality/value: Although a number of solutions to the Black-Scholes model have appeared, 23 the paper presents a thoroughly novel idea of implementation of the Trefftz method for solving 24 this model. So far, the method has been applied to problems having nothing in common with 25 finance. Therefore the present approach might be a starting point for software development, 26 competitive to the existing methods of pricing options.

scholarly journals Option Pricing Under GARCH Models Applied to the SET50 Index of Thailand

2021 ◽  
Vol 20 ◽  
pp. 112-121
Author(s):  
Somphorn Arunsingkarat ◽  
Renato Costa ◽  
Masnita Misran ◽  
Nattakorn Phewchean
Keyword(s):  
Historical Data ◽  
Stock Exchange ◽  
Garch Models ◽  
Option Prices ◽  
Pricing Options ◽  
Black Scholes Model ◽  
Stock Exchange Of Thailand ◽  
Black Scholes ◽  
Neutral Models ◽  
Changes Over Time

Variance changes over time and depends on historical data and previous variances; as a result, it is useful to use a GARCH process to model it. In this paper, we use the notion of Conditional Esscher transform to GARCH models to find the GARCH, EGARCH and GJR risk-neutral models. Subsequently, we apply these three models to obtain option prices for the Stock Exchange of Thailand and compare to the well-known Black-Scholes model. Findings suggest that most of the pricing options under GARCH model are the nearest to the actual prices for SET50 option contracts with both times to maturity of 30 days and 60 days.

scholarly journals Comparing Two Different Option Pricing Methods

Risks ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 108
Author(s):  
Alessandro Bondi ◽  
Dragana Radojičić ◽  
Thorsten Rheinländer
Keyword(s):  
Option Pricing ◽  
Financial Markets ◽  
Stock Exchange ◽  
Calibration Method ◽  
Call Option ◽  
Option Prices ◽  
Penalty Term ◽  
Pricing Options ◽  
Percentage Difference ◽  
Using Data

Motivated by new financial markets where there is no canonical choice of a risk-neutral measure, we compared two different methods for pricing options: calibration with an entropic penalty term and valuation by the Esscher measure. The main aim of this paper is to contrast the outcomes of those two methods with real-traded call option prices in a liquid market like NASDAQ stock exchange, using data referring to the period 2019–2020. Although the Esscher measure method slightly underperforms the calibration method in terms of absolute values of the percentage difference between real and model prices, it could be the only feasible choice if there are not many liquidly traded derivatives in the market.

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