Price Of Call Option Research Articles

Alòs Type Decomposition Formula for Barndorff-Nielsen and Shephard Model

The objective is to provide an Al\`os type decomposition formula of call option prices for the Barndorff-Nielsen and Shephard model: an Ornstein-Uhlenbeck type stochastic volatility model driven by a subordinator without drift. Al\`os (2012) introduced a decomposition expression for the Heston model by using Ito's formula. In this paper, we extend it to the Barndorff-Nielsen and Shephard model. As far as we know, this is the first result on the Al\`os type decomposition formula for models with infinite active jumps.

Option pricing under a Markov-modulated Merton jump-diffusion dividend

In this paper, the valuation of European option is investigated when the discrete dividends are described by Markov-modulated Merton jump-diffusion process. According to the dividend discount theory, we regard the stock price as the net present value of all future dividends. The regime switching Esscher transform is applied to determine a risk-neutral measure. The closed form solution of European option is obtained under the condition that the dividend payments are announced in advance. Numerical simulations for the European call option prices are provided.

OPTION PRICING UNDER THE FRACTIONAL STOCHASTIC VOLATILITY MODEL

AbstractWe investigate the European call option pricing problem under the fractional stochastic volatility model. The stochastic volatility model is driven by both fractional Brownian motion and standard Brownian motion. We obtain an analytical solution of the European option price via the Itô’s formula for fractional Brownian motion, Malliavin calculus, derivative replication and the fundamental solution method. Some numerical simulations are given to illustrate the impact of parameters on option prices, and the results of comparison with other models are presented.

Bond Implied Risks Around Macroeconomic Announcements

Using a large panel of Treasury futures and options, I construct model-free measures of bond uncertainty and tail risks across different tenors from 2000 to 2020. I find that bond tail risk 1) negatively correlates with stock tail risk in general, but the correlation turns positive prior to and around three financial crises; 2) It increased dramatically before the 2008 Financial Crisis and in March 2020 foreshadowing the extreme challenges in the Treasury bond markets; 3) and has significantly decreased in recent years under zero-lower-bound and forward guidance. I then study the behavior of bond tail and uncertainty risk measures around FOMC announcements and document three novel findings: First, bond uncertainty increases three to two days prior to the announcements and reverts back upon release, due to an increase in call option prices rather than puts. Second, yields of 5, 10, and 30 year Treasuries decline by 1bps on the day before the announcement. Third, uncertainty risk cannot help explain the pre-FOMC announcement drift.

An efficient Monte Carlo simulation for new uncertain Heston–CIR hybrid model

In this paper, we consider two new stock models in which their differential equations are modeled by Liu process in uncertain environment. Firstly, we study the uncertain Schobel–Zhu–Hull–White hybrid model and obtain its closed European call option pricing using Liu calculus. Also, we solve this model by Monte Carlo simulation to ensure the performance of Monte Carlo method. Our main purpose is to present a new model, uncertain Heston–CIR hybrid model, in which its uncertain differential equations cannot be solved and so we can calculate the option value via Monte Carlo simulation. Finally, some examples are stated for illustrating these models to obtain successful results and show the efficiency of Monte Carlo method.

Option Pricing with Markov Switching

In this article, we consider a model of time-varying volatility which generalizes the classical Black-Scholes model to include regime-switching properties. Specically, the unobservable state variables for stock uctu- ations are modeled by a Markov process, and the drift and volatility pa- rameters take dierent values depending on the state of this hidden Markov process. We provide a closed-form formula for the arbitrage-free price of the European call option, when the hidden Markov process has nite number of states. Two simulation methods, the discrete diusion method and the Markovian tree method, for computing the European call option price are presented for comparison.

Application of the Generalized Laplace Homotopy Perturbation Method to the Time-Fractional Black–Scholes Equations Based on the Katugampola Fractional Derivative in Caputo Type

In the finance market, the Black–Scholes equation is used to model the price change of the underlying fractal transmission system. Moreover, the fractional differential equations recently are accepted by researchers that fractional differential equations are a powerful tool in studying fractal geometry and fractal dynamics. Fractional differential equations are used in modeling the various important situations or phenomena in the real world such as fluid flow, acoustics, electromagnetic, electrochemistry and material science. There is an important question in finance: “Can the fractional differential equation be applied in the financial market?”. The answer is “Yes”. Due to the self-similar property of the fractional derivative, it can reply to the long-range dependence better than the integer-order derivative. Thus, these advantages are beneficial to manage the fractal structure in the financial market. In this article, the classical Black–Scholes equation with two assets for the European call option is modified by replacing the order of ordinary derivative with the fractional derivative order in the Caputo type Katugampola fractional derivative sense. The analytic solution of time-fractional Black–Scholes European call option pricing equation with two assets is derived by using the generalized Laplace homotopy perturbation method. The used method is the combination of the homotopy perturbation method and generalized Laplace transform. The analytic solution of the time-fractional Black–Scholes equation is carried out in the form of a Mittag–Leffler function. Finally, the effects of the fractional-order in the Caputo type Katugampola fractional derivative to change of a European call option price are shown.

Option pricing under time interval driven model

A new model which we called time driven model for option pricing is proposed. In this model, the price of underlying asset is driven by different random driving source in different time interval. Explicit option pricing formulas for the European call option are obtained by using the Mellin transform. Moreover, some numerical illustrations are given by computing European call option prices.

Option Pricing under Double Heston Model with Approximative Fractional Stochastic Volatility

We establish double Heston model with approximative fractional stochastic volatility in this article. Since approximative fractional Brownian motion is a better choice compared with Brownian motion in financial studies, we introduce it to double Heston model by modeling the dynamics of the stock price and one factor of the variance with approximative fractional process and it is our contribution to the article. We use the technique of Radon–Nikodym derivative to obtain the semianalytical pricing formula for the call options and derive the characteristic functions. We do the calibration to estimate the parameters. The calibration demonstrates that the model provides the best performance among the three models. The numerical result demonstrates that the model has better performance than the double Heston model in fitting with the market implied volatilities for different maturities. The model has a better fit to the market implied volatilities for long-term options than for short-term options. We also examine the impact of the positive approximation factor and the long-memory parameter on the call option prices.

Calculation of call option using trinomial tree method and black-scholes method case study of Microsoft Corporation

Options are one of the most commonly known financial instrument used in financial market. Options are expected to minimize risk or even increase profits in stock trading. Therefore, it is important for options traders to take into account the contract price of options. This study discusses the determination of call option prices using the Trinomial Tree method and the Black-Scholes method with the data of Microsoft Corporation’s stock price and strike price. From the result of the calculations, a conclusion will be drawn from the comparison of the use of the two methods. In conclusion, the call option price using the trinomial tree method is close to the call option price using the Black-Scholes method. Therefore, the Trinomial tree method and the Black-Scholes method is worth using for the base calculation of option pricing.

Option Pricing Model with Transaction Costs and Jumps in Illiquid Markets

Option pricing model is a wildly interested topic in an area of financial Mathematics. The pioneer model was introduced by Fischer Black and Myron Scholes which is known as the Black-Scholes model. This model was derived under various assumptions such as liquidity and no transaction costs for which a underlying asset price in stock market might not be satisfied. With this fact, the underlying asset price models were remodeled, in order to determine an option value. This research aims to extend the Black-Scholes model by relaxing the assumption of no transaction costs in illiquid markets. Also, jumps of asset price are considered in this work. To do this, a differential form of asset price with transaction costs and jumps in illiquid markets is introduced and then used to construct the extended option pricing model. Furthermore, a numerical result of a call option price under a new situation is provided.

Put Options with Linear Investment for Hull-White Interest Rates

We derive a Put Option price associated with selling strategy of the underlying security in a random interest rate environment. This extends Put Option pricing under linear investment strategy from the Black-Scholes setting to Hull-White stochastic interest rate model. As an application, Call Option price for the linear investment strategy in the Hull-White model is established. Our results address recent emergence of developing dynamic investment strategies for the purpose of reducing the investor risk exposure associated with European-type options.

Stochastic pricing formulation for hybrid equity warrants

<abstract> <p>A warrant is a financial agreement that gives the right but not the responsibility, to buy or sell a security at a specific price prior to expiration. Many researchers inadvertently utilize call option pricing models to price equity warrants, such as the Black Scholes model which had been found to hold many shortcomings. This paper investigates the pricing of equity warrants under a hybrid model of Heston stochastic volatility together with stochastic interest rates from Cox-Ingersoll-Ross model. This work contributes to exploration of the combined effects of stochastic volatility and stochastic interest rates on pricing equity warrants which fills the gap in the current literature. Analytical pricing formulas for hybrid equity warrants are firstly derived using partial differential equation approaches. Further, to implement the pricing formula to realistic contexts, a calibration procedure is performed using local optimization method to estimate all parameters involved. We then conducted an empirical application of our pricing formula, the Black Scholes model, and the Noreen Wolfson model against the real market data. The comparison between these models is presented along with the investigation of the models' accuracy using statistical error measurements. The outcomes revealed that our proposed model gives the best performance which highlights the crucial elements of both stochastic volatility and stochastic interest rates in valuation of equity warrants. We also examine the warrants' moneyness and found that 96.875% of the warrants are in-the-money which gives positive returns to investors. Thus, it is beneficial for warrant holders concerned in purchasing warrants to elect the best warrant with the most profitable and more benefits at a future date.</p> </abstract>

CVaR-hedging and its applications to equity-linked life insurance contracts with transaction costs

<p style='text-indent:20px;'>This paper analyzes Conditional Value-at-Risk (CVaR) based partial hedging and its applications on equity-linked life insurance contracts in a Jump-Diffusion market model with transaction costs. A nonlinear partial differential equation (PDE) that an option value process inclusive of transaction costs should satisfy is provided. In particular, the closed-form expression of a European call option price is given. Meanwhile, the CVaR-based partial hedging strategy for a call option is derived explicitly. Both the CVaR hedging price and the weights of the hedging portfolio are based on an adjusted volatility. We obtain estimated values of expected total hedging errors and total transaction costs by a simulation method. Furthermore,our results are implemented to derive target clients’ survival probabilities and age of equity-linked life insurance contracts.</p>

Pricing Options in a Delayed Market Driven by Le’vy Noise

In this paper we studied stochastic delayed differential equations driven by Le’vy noise. The analogue of Ito formula is considered. The Black-Scholes formula analogue for Vanilla call option price formula is derived.

HARGA OPSI CALL TIPE EROPA MENGGUNAKAN SIMULASI MONTE CARLO STANDAR DAN TEKNIK ANTITHETIC VARIATES

The European call option is a contract that gives the contract holder the right to buy a certain asset at a price and a certain period of time, which is the execution time at maturity. This study aims to determine the accuracy of the simulation results of stock prices to determine the price of European call options from simulation of standardMonte Carlo and the antithetic variates technique using R-Studio software. The results of the simulation of the two methods will approach the option price of the analytic solution. Analytical solutions in this study use the Black-Scholes model to obtain a standard price that serves to compare the two methods. The call option price of the European type uses the Black-Scholes model as a benchmark is $ 14.20281. In the 1.000.000th standard Monte Carlo simulation, the call option price converges to $14.69786 with a standard error of 0.019, while the 100.000thMonte Carlo-antithetic variates produces a call option price converges at $14.69801 with a standard error of 0.043. The results of this study indicate that Monte Carlo simulation with antithetic variates technique is more accurate because it produces an option value faster to converge with a relatively smaller standard error

Option Pricing with Transaction Costs under the Subdiffusive Mixed Fractional Brownian Motion

This paper probes into the issue of option pricing with transaction costs under the subdiffusive mixed fractional Brownian motion. Under reasonable economic assumptions, and by applying the strategy of the mean-self-financing delta hedging in the discrete-time setting, the generalized European call option pricing formula is further developed to capture the certain property of financial time series and better observe the law of finance market.

Comparing Two Different Option Pricing Methods

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.

Option pricing under multifractional Brownian motion in a risk neutral framework

In this paper, we introduce a new method to compute the European Call Option price (ct) under multi-fractional Brownian motion (mBm) with deterministic Hurst function. We build a mathematical framework using a Lebovits et al. study to approximate mBm to fractional Brownian motion (fBm). As a result we obtain ct , through the simulation of the logarithmic price under mBm, using a Vasicek model for the discount factor. Finally, we compare the results with those computed with the Black Scholes model and Call market price (SPX).

Option Pricing Under Multifractional Process and Long-Range Dependence

We introduced a new method to compute the European Call (and Put) Option price under the assumption of multifractional Brownian motion (mBm). The reason why we need a procedure for estimating the Option price is due to the absence of a closed formula for this process. To compute the Option price, we first simulated the logarithmic price under mBm and, by using a discount factor, we computed the option’s pay-off. Then, we fitted the best probability distribution associated to the discounted pay-off, computing the European Call Option price as its average.