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 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.

scholarly journals OPTIONS WRITTEN ON STOCKS WITH KNOWN DIVIDENDS

2004 ◽  
Vol 07 (07) ◽  
pp. 901-907
Author(s):  
ERIK EKSTRÖM ◽  
JOHAN TYSK
Keyword(s):  
Stock Price ◽  
Option Price ◽  
Option Prices ◽  
Strike Price ◽  
Call Options ◽  
Alternative Approach ◽  
Black Scholes ◽  
Market Practice ◽  
The Difference ◽  
Risk Free Rate

There are two common methods for pricing European call options on a stock with known dividends. The market practice is to use the Black–Scholes formula with the stock price reduced by the present value of the dividends. An alternative approach is to increase the strike price with the dividends compounded to expiry at the risk-free rate. These methods correspond to different stock price models and thus in general give different option prices. In the present paper we generalize these methods to time- and level-dependent volatilities and to arbitrary contract functions. We show, for convex contract functions and under very general conditions on the volatility, that the method which is market practice gives the lower option price. For call options and some other common contracts we find bounds for the difference between the two prices in the case of constant volatility.

scholarly journals Mean-Variance Analysis of Alternative Hedging Strategies

1972 ◽  
Vol 4 (1) ◽  
pp. 123-128 ◽  
Author(s):  
David Holland ◽  
Wayne D. Purcell ◽  
Terry Hague
Keyword(s):  
Futures Markets ◽  
Market Price ◽  
Theoretical Models ◽  
Spot Price ◽  
Hedging Strategies ◽  
Optimum Position ◽  
Futures Price ◽  
The Difference ◽  
Mean Variance ◽  
Over Time

Much of the research in commodity hedging has concentrated upon the development of theoretical models describing the optimum position in cash and futures markets. Other studies have shown that the difference between current spot price and futures price represents the market price for storage, processing services, or both. The revenue stabilizing potential of futures markets for commodities with continuous as opposed to noncontinuous inventories has also received attention. However, very little work or literature is publicly available on how different hedging strategies actually would have performed for a particular commodity over time.

Valuation of Covered Warrant Subject to Default Risk

2003 ◽  
Vol 06 (01) ◽  
pp. 21-44 ◽  
Author(s):  
Shen-Yuan Chen
Keyword(s):  
Default Risk ◽  
Market Price ◽  
Option Price ◽  
Option Value ◽  
Valuation Model ◽  
Black Scholes ◽  
Covered Warrant ◽  
The Difference ◽  
Vulnerable Option ◽  
Settlement Mechanism

There is no margin settlement mechanism for existing covered warrants in Taiwan, thus the credit risk of the warrant issuer must be considered when investors evaluate the price of a covered warrant. This paper applies the vulnerable option valuation model to empirically study the difference in the theoretical value of a vulnerable warrant, Black–Scholes option price and the market price of warrant by using the Taiwan warrant data. Empirical results show that the theoretical value of a vulnerable warrant is lower than the Black–Scholes non-vulnerable option value and its market value.

Implied Volatility of the KOSPI 200 Index Option Market

2015 ◽  
Vol 23 (4) ◽  
pp. 517-541
Author(s):  
Dam Cho
Keyword(s):  
Financial Crisis ◽  
Trading Volume ◽  
Implied Volatility ◽  
Spot Price ◽  
Strike Price ◽  
Market Pricing ◽  
Put Options ◽  
The Difference ◽  
Index Option ◽  
Option Market

This paper analyzes implied volatilities (IVs), which are computed from trading records of the KOSPI 200 index option market from January 2005 to December 2014, to examine major characteristics of the market pricing behavior. The data includes only daily closing prices of option transactions for which the daily trading volume is larger than 300 contracts. The IV is computed using the Black-Scholes option pricing model. The empirical findings are as follows; Firstly, daily averages of IVs have shown very similar behavior to historical volatilities computed from 60-day returns of the KOSPI 200 index. The correlation coefficient of IV of the ATM call options to historical volatility is 0.8679 and that of the ATM put options is 0.8479. Secondly, when moneyness, which is measured by the ratio of the strike price to the spot price, is very large or very small, IVs of call and put options decrease days to maturity gets longer. This is partial evidence of the jump risk inherent in the stochastic process of the spot price. Thirdly, the moneyness pattern showed heavily skewed shapes of volatility smiles, which was more apparent during the global financial crises period from 2007 to 2009. Behavioral reasons can explain the volatility smiles. When the moneyness is very small, the deep OTM puts are priced relatively higher due to investors’ crash phobia and the deep ITM calls are valued higher due to investors’ overconfidence and confirmation biases. When the moneyness is very large, the deep OTM calls are priced higher due to investors’ hike expectation and the deep ITM puts are valued higher due to overconfidence and confirmation biases. Fourthly, for almost all moneyness classes and for all sub-periods, the IVs of puts are larger than the IVs of calls. Also, the differences of IVs of deep OTM put ranges minus IVs of deep OTM calls, which is known to be a measure of crash phobia or hike expectation, shows consistent positive values for all sub-periods. The difference in the financial crisis period is much bigger than in other periods. This suggests that option traders had a stronger crash phobia in the financial crisis.

scholarly journals ON THE PROFIT AND LOSS DISTRIBUTION OF DYNAMIC HEDGING STRATEGIES

1999 ◽  
Vol 02 (02) ◽  
pp. 131-152 ◽  
Author(s):  
SERGEI ESIPOV ◽  
IGOR VAYSBURD
Keyword(s):  
Monte Carlo ◽  
Probability Distribution ◽  
Present Value ◽  
Hedging Strategy ◽  
Loss Distribution ◽  
Time Dynamics ◽  
Hedging Strategies ◽  
Black Scholes ◽  
Risk Neutral ◽  
Stop Loss

Hedging a derivative security with non-risk-neutral number of shares leads to portfolio profit or loss. Unlike in the Black–Scholes world, the net present value of all future cash flows till maturity is no longer deterministic, and basis risk may be present at any time. The key object of our analysis is probability distribution of future P & L conditioned on the present value of the underlying. We consider time dynamics of this probability distribution for an arbitrary hedging strategy. We assume log-normal process for the value of the underlying asset and use convolution formula to relate conditional probability distribution of P & L at any two successive time moments. It leads to a simple PDE on the probability measure parameterized by a hedging strategy. For risk-neutral replication the P & L probability distribution collapses to a delta-function at the Black–Scholes price of the contingent claim. Therefore, our approach is consistent with the Black–Scholes one and can be viewed as its generalization. We further analyze the PDE and derive formulae for hedging strategies targeting various objectives, such as minimizing variance or optimizing distribution quantiles. The developed method of computing the profit and loss distribution for a given hedging scheme is applied to the classical example of hedging a European call option using the "stop-loss" strategy. This strategy refers to holding 1 or 0 shares of the underlying security depending on the market value of such security. It is shown that the "stop-loss" strategy can lead to a loss even for an infinite frequency of re-balancing. The analytical method allows one to compute profit and loss distributions without relying on simulations. To demonstrate the strength of the method we reproduce the Monte Carlo results on "stop-loss" strategy given in Hull's book, and improve the precision beyond the limits of regular Monte-Carlo simulations.

A new method to solve fuzzy stochastic finance problem

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Jayanta Kumar Dash ◽  
Sumitra Panda ◽  
Golak Bihari Panda
Keyword(s):  
Option Pricing ◽  
Market Price ◽  
Pricing Model ◽  
Strike Price ◽  
Content Type ◽  
Fuzzy Environment ◽  
Black Scholes ◽  
Option Pricing Model ◽  
A New Technique ◽  
Log Normal

PurposeThe authors discuss the value of portfolio and Black–Scholes (B–S)-option pricing model in fuzzy environment.Design/methodology/approachThe B–S option pricing model (OPM) is an important role of an OPM in finance. Here, every decision is taken under uncertainty. Due to randomness or vagueness, these uncertainties may be random or fuzzy or both. As the drift µ, the degree of volatility s, interest rate r, strike price k and other parameters of the value of the portfolio V(t), market price S_0 (t) and call option C(t) are not known exactly, so they are treated as positive fuzzy number. Partial expectation of fuzzy log normal distribution is derived. Also the value of portfolio at any time t and the B–S OPM in fuzzy environment are derived. A numerical example of B–S OPM is illustrated.FindingsFirst, the authors are studying some various paper and some stochastic books.Originality/valueThis is a new technique.

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.

scholarly journals ANALISIS SENSITIVITAS HARGA OPSI MENGGUNAKAN METODE GREEK BLACK SCHOLES

2018 ◽  
Vol 7 (2) ◽  
pp. 148
Author(s):  
DEVI NANDITA. N ◽  
KOMANG DHARMAWAN ◽  
DESAK PUTU EKA NILAKUSMAWATI
Keyword(s):  
Sensitivity Analysis ◽  
Stock Price ◽  
Price Change ◽  
European Option ◽  
Strike Price ◽  
Expiry Date ◽  
Hedging Strategies ◽  
Black Scholes

Sensitivity analysis can be used to carry out hedging strategies. The sensitivity value measures how much the price change of the option influenced by some parameters. The aim of this study is to determine the sensitivity analysis of the buying price of European option by using the Greek method on Black Scholes Formula. From this study we get the values of delta, gamma, theta, vega, and rho. The values of deltas, gamma, vega, and rho are positive, which means that the value of the option is more sensitive than the corresponding parameter. The most sensitive value of gamma is obtained when the stock price approaches the strike price and approaches the expiry date. The value of theta obtained is negative and hence the most sensitive theta value is when the value is getting smaller. While, the most sensitive value of vega is obtained when the stock price is close to the strike price and is far from the expiry date. The most sensitive value of rho is obtained when the stock price gets bigger and farther from the expiry date.

The Use of Martingale Theory for the Superreplication of Exotic Options in Incomplete Markets

2003 ◽  
Vol 23 (2) ◽  
pp. 323
Author(s):  
Christian Johannes Zimmer
Keyword(s):  
Incomplete Markets ◽  
Realistic Model ◽  
American Option ◽  
Exotic Options ◽  
Martingale Theory ◽  
Hedging Strategy ◽  
Black Scholes ◽  
Exotic Option

In this article we show the importance of modern martingale theory for the pricing and hedging of exotic options, especially in incomplete markets. When emitting an exotic option, the seller firstly has to ask himself whether there exists a hedging strategy for this title or not. Especially, when he wants to use a more realistic model than the simple Black-Scholes framework, the answer is not always obvious. We show in this article how to analyze this problem in the case of an exotic option, the Generalized Bermudian Option, which will turn out to be a generalization of the American option.

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