scholarly journals Efficacy of Nifty Index Options through BSM Model

2019 ◽  
Vol 8 (3S2) ◽  
pp. 947-949
Keyword(s):  
Options Pricing ◽  
Price Determination ◽  
Strike Price ◽  
Index Options ◽  
Put Options ◽  
Black Scholes Model ◽  
Exercise Price ◽  
Black Scholes ◽  
Long Time ◽  
Optimum Price

Options are one of the products in financial derivatives, which gives the rights to buy and sell the product to an option holder in pre-fixed price which known as the strike price or exercise price at certain periods. Options contract was existed in various countries for long time, but it became very popular among the investors when the Fisher Black, Myron Scholes and Robert Merton were introduced the Black-Scholes Model in the year of 1973. This model was formerly developed by these three economists who were also receiving the Nobel prize for finding this innovative model. This model is mainly used to deal with the theoretical pricing challenge in options price determination. In India the trading in Index Options commenced on 4th June 2001 and Options on individual securities commenced on 2nd July 2001. There are many types in options contracts like stock options; Index options, weather options, real options and etc. This study has mainly been focusing on Nifty 50 index options which are effectively trade at NSE. This paper goes to describe about the importance of options pricing and how the BSM model has effectively used to find the optimum price of the theoretical value of call and put options.

Modeling of implied volatility surfaces of nifty index options

2019 ◽  
Vol 06 (03) ◽  
pp. 1950028 ◽  
Author(s):  
Mihir Dash
Keyword(s):  
Implied Volatility ◽  
Strike Price ◽  
Index Options ◽  
Put Options ◽  
Call Options ◽  
Merton Model ◽  
Implied Volatility Surface ◽  
Black Scholes ◽  
Volatility Surface ◽  
Implied Volatility Surfaces

The implied volatility of an option contract is the value of the volatility of the underlying instrument which equates the theoretical option value from an option pricing model (typically, the Black–Scholes[Formula: see text]Merton model) to the current market price of the option. The concept of implied volatility has gained in importance over historical volatility as a forward-looking measure, reflecting expectations of volatility (Dumas et al., 1998). Several studies have shown that the volatilities implied by observed market prices exhibit a pattern very different from that assumed by the Black–Scholes[Formula: see text]Merton model, varying with strike price and time to expiration. This variation of implied volatilities across strike price and time to expiration is referred to as the volatility surface. Empirically, volatility surfaces for global indices have been characterized by the volatility skew. For a given expiration date, options far out-of-the-money are found to have higher implied volatility than those with an exercise price at-the-money. For short-dated expirations, the cross-section of implied volatilities as a function of strike is roughly V-shaped, but has a rounded vertex and is slightly tilted. Generally, this V-shape softens and becomes flatter for longer dated expirations, but the vertex itself may rise or fall depending on whether the term structure of at-the-money volatility is upward or downward sloping. The objective of this study is to model the implied volatility surfaces of index options on the National Stock Exchange (NSE), India. The study employs the parametric models presented in Dumas et al. (1998); Peña et al. (1999), and several subsequent studies to model the volatility surfaces across moneyness and time to expiration. The present study contributes to the literature by studying the nature of the stationary point of the implied volatility surface and by separating the in-the-money and out-of-the-money components of the implied volatility surface. The results of the study suggest that an important difference between the implied volatility surface of index call and put options: the implied volatility surface of index call options was found to have a minimum point, while that of index put options was found to have a saddlepoint. The results of the study also indicate the presence of a “volatility smile” across strike prices, with a minimum point in the range of 2.3–9.0% in-the-money for index call options and of 10.7–29.3% in-the-money for index put options; further, there was a jump in implied volatility in the transition from out-of-the-moneyness to in-the-moneyness, by 10.0% for index call options and about 1.9% for index put options.

Options

2019 ◽  
pp. 231-248
Author(s):  
Alan N. Rechtschaffen
Keyword(s):  
Option Pricing ◽  
Strike Price ◽  
Over The Counter ◽  
Index Options ◽  
Underlying Asset ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Delta Hedging ◽  
Option Strategies ◽  
The Right

An option is a derivative that derives its value from another underlying asset, instrument, or index. Options “transfer the right but not the obligation to buy or sell the underlying asset, instrument or index on or before the option's exercise date at a specified price (the strike price).” A contract that gives a purchaser such a right is inherently an option even if it called something else. Options can trade over the counter or on an exchange. Regulatory jurisdiction will be defined by the underlying asset negotiated under the terms of the option, by the location where the options are traded, and by the counterparties to an option transaction. This chapter discusses the characteristics of options, how options work, the Black-Scholes model and option pricing, delta hedging, and option strategies.

scholarly journals Delta-gamma-theta Hedging of Crude Oil Asian Options

2015 ◽  
Vol 63 (6) ◽  
pp. 1897-1903
Author(s):  
Juraj Hruška
Keyword(s):  
Market Price ◽  
Options Pricing ◽  
Exotic Options ◽  
Asian Options ◽  
Hedging Strategy ◽  
Strike Price ◽  
Put Options ◽  
Hedging Strategies ◽  
Black Scholes ◽  
The Difference

Since Black-Scholes formula was derived, many methods have been suggested for vanilla as well as exotic options pricing. More of investing and hedging strategies have been developed based on these pricing models. Goal of this paper is to derive delta-gamma-theta hedging strategy for Asian options and compere its efficiency with gamma-delta-theta hedging combined with predictive model. Fixed strike Asian options are type of exotic options, whose special feature is that payoff is calculated from the difference of average market price and strike price for call options and vice versa for the put options. Methods of stochastic analysis are used to determine deltas, gammas and thetas of Asian options. Asian options are cheaper than vanilla options and therefore they are more suitable for precise portfolio creation. On the other hand their deltas are also smaller as well as profits. That means that they are also less risky and more suitable for hedging. Results, conducted on chosen commodity, confirm better feasibility of Asian options compering with vanilla options in sense of gamma hedging.

scholarly journals Determinants of Violations in the SET50 Index Options Pricing Relationships: Put-Call-Futures Parity and Box Spread Tests

2018 ◽  
Vol 14 (3) ◽  
pp. 1 ◽  
Author(s):  
Woradee Jongadsayakul
Keyword(s):  
Transaction Costs ◽  
Risk Premium ◽  
Tobit Model ◽  
Options Pricing ◽  
Options Market ◽  
Index Options ◽  
Exercise Price ◽  
Daily Data ◽  
Before And After ◽  
Contract Specification

Although SET50 Index Options, the only option product on Thailand Futures Exchange, has been traded since October 29, 2007, it has faced the liquidity problem. The SET50 Index Options market must offer a risk premium to compensate investors for liquidity risk. It may cause violations in options pricing relationships. This research therefore uses daily data from October 29, 2007 to December 30, 2016 to compare the violations in SET50 Index Options pricing relationships before and after change in contract specification on October 29, 2012 and investigate determinants of these violations using Tobit model. Two tests of SET50 Index Options pricing relationships, Put-Call-Futures Parity and Box Spread, are employed. The test results of Put-Call-Futures Parity show that the percentage and baht amount of violations in many cases are greater in the period before the modification of SET50 Index Options. Without transaction costs, we also see more Box Spread violations before contract adjustment. However, after taking transaction costs into account, there are more percentage and baht amount of Box Spread violations in the later time period. The estimation of Tobit model shows that the violation sizes of both Put-Call-Futures Parity and Box Spread, excluding transaction costs, depend on the liquidity of SET50 Index Options market measured by option moneyness and open interest. The SET50 Index Options contract specification, especially exercise price, also significantly affects the size of violations, though the direction of a relationship is not cleared.

scholarly journals A Note on Numerical Solution of a Linear Black-Scholes Model

2014 ◽  
Vol 33 ◽  
pp. 103-115 ◽  
Author(s):  
Md. Kazi Salah Uddin ◽  
Mostak Ahmed ◽  
Samir Kumar Bhowmilk
Keyword(s):  
Time Integration ◽  
Weighted Average ◽  
Financial Mathematics ◽  
European Options ◽  
Average Scheme ◽  
Put Options ◽  
Weighted Average Method ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Solution Methods

Black-Scholes equation is a well known partial differential equation in financial mathematics. In this article we discuss about some solution methods for the Black Scholes model with the European options (Call and Put) analytically as well as numerically. We study a weighted average method using different weights for numerical approximations. In fact, we approximate the model using a finite difference scheme in space first followed by a weighted average scheme for the time integration. Then we present the numerical results for the European Call and Put options. Finally, we investigate some linear algebra solvers to compare the superiority of the solvers. GANIT J. Bangladesh Math. Soc. Vol. 33 (2013) 103-115 DOI: http://dx.doi.org/10.3329/ganit.v33i0.17664

The Constant Elasticity of Variance Models: New Evidence from S&P 500 Index Options

2004 ◽  
Vol 07 (02) ◽  
pp. 173-190 ◽  
Author(s):  
C. F. Lee ◽  
Ta-Peng Wu ◽  
Ren-Raw Chen
Keyword(s):  
European Contract ◽  
Chi Square ◽  
Index Options ◽  
Market Prices ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Option Model ◽  
New Evidence

The seminal work by Cox (1975, 1996), MacBeth and Merville (1979, 1980) and Emanuel and Macbeth (1982) show that, both theoretically and empirically, the constant elasticity of variance option model (CEV) is superior to the Black–Scholes model in explaining market prices. In this paper, we extend the MacBeth and Merville (1979, 1980) research by using a European contract (S&P 500 index options). We find supportive evidence to the MacBeth and Merville results although our sample is not subject to American premium biases. Furthermore, we reduce the approximation errors by using the non-central chi-square probability functions proposed by Shroder (1989).

UNCERTAINTY IN PRICING TRADABLE OPTIONS

2003 ◽  
Vol 06 (02) ◽  
pp. 103-117 ◽  
Author(s):  
JORGE R. SOBEHART ◽  
SEAN C. KEENAN
Keyword(s):  
Interest Rates ◽  
Market Equilibrium ◽  
Expected Value ◽  
Options Pricing ◽  
Options Market ◽  
Pricing Model ◽  
Random Delays ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Random Fluctuations

In this paper we introduce an options pricing model consistent with the level of uncertainty observed in the options market. By assuming that the price at which an option can be traded is intrinsically uncertain, either because of the inability to hedge continuously or because of errors in the estimation of the security's volatility and interest rates, random delays in the execution of orders or information deficiencies, we show that the Black-Scholes model produces a biased estimate of the expected value of tradable options. Information deficiencies lead to a call-put relationship that reduces to the standard call-put expression on average but shows random fluctuations consistent with the concept of market equilibrium. The same information deficiencies can contribute to the volatility skew that affects the Black-Scholes model.

scholarly journals On a Free Boundary Problem for American Options Under the Generalized Black–Scholes Model

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1563
Author(s):  
Jung-Kyung Lee
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
American Options ◽  
Closed Form Solution ◽  
Numerical Results ◽  
Put Options ◽  
Optimal Exercise Boundary ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Exercise Boundary

We consider the problem of pricing American options using the generalized Black–Scholes model. The generalized Black–Scholes model is a modified form of the standard Black–Scholes model with the effect of interest and consumption rates. In general, because the American option problem does not have an exact closed-form solution, some type of approximation is required. A simple numerical method for pricing American put options under the generalized Black–Scholes model is presented. The proposed method corresponds to a free boundary (also called an optimal exercise boundary) problem for a partial differential equation. We use a transformed function that has Lipschitz character near the optimal exercise boundary to determine the optimal exercise boundary. Numerical results indicating the performance of the proposed method are examined. Several numerical results are also presented that illustrate a comparison between our proposed method and others.

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