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 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.

The two best ways to derive the Black–Scholes PDE

2019 ◽  
Vol 10 (2) ◽  
pp. 168-174
Author(s):  
Paul Wilmott
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Design Methodology ◽  
Content Type ◽  
Technical Requirements ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Business Perspective ◽  
Big Picture ◽  
Complex Methods

Purpose The purpose of this paper is to explain the Black–Scholes model with minimal technical requirements and to illustrate its impact from a business perspective. Design/methodology/approach The paper employs simple accounting concepts and an argument part based on business need. Findings The Black–Scholes partial differential equation can be derived in many ways, some easy to understand, some hard, some useful and others not. The two methods in this paper are extremely insightful. Originality/value The paper takes a big-picture view of derivatives valuation. As such, it is a simple accompaniment to more complex methods and aims to keep modelling grounded in reality.

A new approach to the Scoreboard

2015 ◽  
Vol 42 (4) ◽  
pp. 659-688
Author(s):  
Cosimo Magazzino ◽  
Francesco Felici ◽  
Vanja Bozic
Keyword(s):  
European Commission ◽  
Design Methodology ◽  
Early Stage ◽  
Critical Issue ◽  
Added Value ◽  
Policy Makers ◽  
New Approach ◽  
Content Type ◽  
Starting Point ◽  
The Relationship

Purpose – The purpose of this paper is to investigate the information content of the variables that can help detecting external and internal imbalances in an early stage. The starting point is the Scoreboard, where nine indicators are chosen in order to increase macroeconomic surveillance of all member states. Design/methodology/approach – This paper provides an overview of the variables that could be informative for imbalances by focusing on EU-27 countries over the period 1960-2010. The number of chosen variables is 28, and they are aggregated in six macro-areas. Therefore, once an imbalance is observed in any of those areas, it is possible to detect in a simple way which specific variable is determining such outcome. Findings – In general, this approach provides reliable signal to the policy-makers about the indicators that can drive imbalances within the area, shedding light on the relationship among the variables included in the analysis, too. Research limitations/implications – In fact, the empirical results underline some well-known critical issue for several countries, and is largely in line with results obtained in a variety of EC and OECD studies. Originality/value – The main added value of the approach adopted in this paper is the introduction of more variables than those initially proposed by the European Commission in the construction of the Scoreboard. This provides more information about the macroeconomic situation in each country, preserving, however, the simplicity of the analysis as the variables are aggregated by homogeneous areas.

scholarly journals PREFERENCES, LÉVY JUMPS AND OPTION PRICING

2007 ◽  
Vol 03 (01) ◽  
pp. 0750001 ◽  
Author(s):  
CHENGHU MA
Keyword(s):  
Option Pricing ◽  
Contingent Claims ◽  
Economic Variable ◽  
European Options ◽  
Jump Risk ◽  
Representative Agent ◽  
Potential Explanation ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Lévy Jumps

This paper derives an equilibrium formula for pricing European options and other contingent claims which allows incorporating impacts of several important economic variable on security prices including, among others, representative agent preferences, future volatility and rare jump events. The derived formulae is general and flexible enough to include some important option pricing formulae in the literature, such as Black–Scholes, Naik–Lee, Cox–Ross and Merton option pricing formulae. The existence of jump risk as a potential explanation of the moneyness biases associated with the Black–Scholes model is explored.

Option pricing models

1989 ◽  
Vol 116 (3) ◽  
pp. 537-558 ◽  
Author(s):  
D. Blake
Keyword(s):  
Option Pricing ◽  
Binomial Model ◽  
Pricing Models ◽  
Black Scholes Model ◽  
Black Scholes

ABSTRACTThe paper discusses two important models of option pricing: the binomial model and the Black—Scholes model. It begins with a brief description of options.

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.

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