Entropy binomial tree method and calibration for the volatility smile

2020 ◽  
Vol 28 (11) ◽  
pp. 1591-1608
Author(s):  
Wenxiu Gong ◽  
Zuoliang Xu ◽  
Qinghua Ma
Keyword(s):  
Volatility Smile ◽  
Binomial Tree ◽  
Tree Method

scholarly journals PENENTUAN HARGA KONTRAK OPSI KOMODITAS EMAS MENGGUNAKAN METODE POHON BINOMIAL

2017 ◽  
Vol 6 (2) ◽  
pp. 99
Author(s):  
I GEDE RENDIAWAN ADI BRATHA ◽  
KOMANG DHARMAWAN ◽  
NI LUH PUTU SUCIPTAWATI
Keyword(s):  
Option Prices ◽  
European Option ◽  
Binomial Tree ◽  
Call Options ◽  
Option Contracts ◽  
Put Option ◽  
Black Scholes ◽  
Tree Method

Holding option contracts are considered as a new way to invest. In pricing the option contracts, an investor can apply the binomial tree method. The aim of this paper is to present how the European option contracts are calculated using binomial tree method with some different choices of strike prices. Then, the results are compared with the Black-Scholes method. The results obtained show the prices of call options contracts of European type calculated by the binomial tree method tends to be cheaper compared with the price of that calculated by the Black-Scholes method. In contrast to the put option prices, the prices calculated by the binomial tree method are slightly more expensive.

Convergence of the Binomial Tree Method for American Options in a Jump-Diffusion Model

2005 ◽  
Vol 42 (5) ◽  
pp. 1899-1913 ◽  
Author(s):  
Xiao-song Qian ◽  
Cheng-long Xu ◽  
Li-shang Jiang ◽  
Bao-jun Bian
Keyword(s):  
Diffusion Model ◽  
American Options ◽  
Jump Diffusion ◽  
Binomial Tree ◽  
Jump Diffusion Model ◽  
Tree Method

TREE METHOD FOR OPTION PRICING UNDER STOCHASTIC VARIANCE

2000 ◽  
Vol 03 (03) ◽  
pp. 557-557
Author(s):  
DRAGAN ŠESTOVIĆ
Keyword(s):  
Option Pricing ◽  
Asset Price ◽  
Three Dimensional ◽  
Diffusion Limit ◽  
Lattice Method ◽  
Binomial Tree ◽  
Long Run ◽  
Hedging Portfolio ◽  
Risk Neutral Probabilities ◽  
Tree Method

We develop a recombining tree method for pricing of options by using a general two-factor stochastic-variance (SV) diffusion model for asset price dynamics. We show that it is possible to construct a riskless hedge by including additional short-term options in the hedging portfolio. This procedure gives us Partial Differential Equation (PDE) that can be solved by using standard numerical techniques giving us a unique option's price. We show that the option's price does not depend on the long run volatility forecast but only on the parameters of the model, which are related to the volatility of variance. We show one particular transformation of PDE to the Finite Difference Equation (FDE) that leads to the three-dimensional lattice method similar to the standard binomial-tree method. Our tree grows in the price-variance space and similarly to the binomial-tree, the coefficients of the FDE can be interpreted as risk neutral probabilities for jumping between the tree nodes. By investigating an error accumulation in the tree we found the stability criterion and the method that can be applied in order to achieve a stabile procedure. Our option pricing method can be used for European and American options and various payoffs. Since the procedure converges quickly and can be easily implemented, we believe that it could be useful for practitioners. The SV model we used here was shown earlier to be a diffusion limit of various GARCH-type models giving the possibility of using parameters obtained in the discrete-time GARCH framework as an input for our option pricing method.

Pricing S&P500 barrier put option of American type under Heston–CIR model with regime-switching

2019 ◽  
Vol 06 (02) ◽  
pp. 1950014 ◽  
Author(s):  
Farshid Mehrdoust ◽  
Idin Noorani
Keyword(s):  
Expectation Maximization ◽  
Regime Switching ◽  
Likelihood Estimation ◽  
Least Square ◽  
Hidden Markov Chain ◽  
Cir Model ◽  
Binomial Tree ◽  
Put Option ◽  
Rate Processes ◽  
Tree Method

In this paper, we consider the regime-switching Heston–CIR model, where the parameters of the volatility process are modulated by a Hidden Markov chain and the unobserved regimes. Then, we calibrate the parameters of the volatility and interest rate processes by the expectation maximization (EM) and maximum likelihood estimation (MLE) algorithms, respectively. Next, we use the least square Monte-Carlo (LSM) algorithm to determine the S&P500 American barrier put option under the Heston–CIR model. Finally, by the binomial tree method as a benchmark, we provide some numerical experiments to illustrate the accuracy of the achieved results.

Binomial tree method for option pricing: Discrete Carr and Madan formula approach

2021 ◽  
pp. 2150024
Author(s):  
Yoshifumi Muroi ◽  
Ryota Saeki ◽  
Shintaro Suda
Keyword(s):  
Option Pricing ◽  
Broad Class ◽  
Asset Price ◽  
Option Prices ◽  
European Option ◽  
Tree Model ◽  
Binomial Tree ◽  
Tree Models ◽  
Binomial Tree Model ◽  
Tree Method

This paper suggests a new Fourier analysis approach to evaluate the option prices and its sensitivities (Greeks) using the binomial tree model. In the last half of this paper, we show that option prices are efficiently and effectively evaluated using a semi-closed form formula for European option prices. We can compute option prices in a broad class of jump-diffusion models because we calculate the characteristic function for an underlying asset price numerically. Furthermore, we also compute the price of European options in the exp-Levy model. This numerical experiment gives new insights into option pricing in the nonparametric Levy model. The option prices and sensitivities can be computed very accurately and efficiently, even in binomial tree models with jumps.

scholarly journals PENERAPAN METODE BINOMIAL TREE DALAM MENGESTIMASI HARGA KONTRAK OPSI TIPE AMERIKA

2016 ◽  
Vol 5 (4) ◽  
pp. 156
Author(s):  
I GUSTI AYU MITA ERMIA SARI ◽  
KOMANG DHARMAWAN ◽  
TJOKORDA BAGUS OKA
Keyword(s):  
Stock Price ◽  
Price Movement ◽  
Binomial Tree ◽  
Option Contracts ◽  
Black Scholes ◽  
Risk Neutral ◽  
Price Option ◽  
Tree Method

Binomial tree is a method that can be used to determine price option contracts. In this method, the stock price movement is presented in the form of a  tree with each branch representing the probability of the stock price to move up or move down. The purpose of this paper was to determine the price of the options contracts with the American type on Binomial Tree method and compare the three methods that is variance matching, proportional , and risk neutral of determining the value of price option contracts used in Binomial Tree method with Black-Schole method. The result of this research was the value of the options contract using the variance matching more similar with the value of the Black-Scholes contract.

scholarly journals Pricing arithmetic asian options under the cev process

2010 ◽  
Vol 15 (29) ◽  
pp. 7-13
Author(s):  
Bin Peng ◽  
◽  
Fei Peng ◽  
Keyword(s):  
Stock Price ◽  
Numerical Results ◽  
Asian Options ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Binomial Tree ◽  
Cev Process ◽  
Parameter Values ◽  
Tree Method

This paper discusses the pricing of arithmetic Asian options when the underlying stock follows the constant elasticity of variance (CEV) process. We build a binomial tree method to estimate the CEV process and use it to price arithmetic Asian options. We find that the binomial tree method for the lognormal case can effectively solve the computational problems arising from the inherent complexities of arithmetic Asian options when the stock price follows CEV process. We present numerical results to demonstrate the validity and the convergence of the approach for the different parameter values set in CEV process.

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