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.

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.

A RECOMBINING TREE METHOD FOR OPTION PRICING WITH STATE-DEPENDENT SWITCHING RATES

2016 ◽  
Vol 19 (02) ◽  
pp. 1650012 ◽  
Author(s):  
J. X. JIANG ◽  
R. H. LIU ◽  
D. NGUYEN
Keyword(s):  
Option Pricing ◽  
Regime Switching ◽  
Asset Price ◽  
Numerical Results ◽  
Price Process ◽  
State Dependent ◽  
Switching Models ◽  
Markovian Regime Switching ◽  
Tree Method ◽  
Markovian Regime

This paper develops simple and efficient tree approaches for option pricing in switching jump diffusion models where the rates of switching are assumed to depend on the underlying asset price process. The models generalize many existing models in the literature and in particular, the Markovian regime-switching models with jumps. The proposed trees grow linearly as the number of tree steps increases. Conditions on the choices of key parameters for the tree design are provided that guarantee the positivity of branch probabilities. Numerical results are provided and compared with results reported in the literature for the Markovian regime-switching cases. The reported numerical results for the state-dependent switching models are new and can be used for comparison in the future.

scholarly journals Geometric Average Asian Option Pricing with Paying Dividend Yield under Non-Extensive Statistical Mechanics for Time-Varying Model

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 828 ◽  
Author(s):  
Jixia Wang ◽  
Yameng Zhang
Keyword(s):  
Statistical Mechanics ◽  
Option Pricing ◽  
Asset Price ◽  
Closed Form Solution ◽  
Real Data ◽  
Form Solution ◽  
Asian Option ◽  
Time Varying ◽  
Dividend Yield ◽  
Geometric Average

This paper is dedicated to the study of the geometric average Asian call option pricing under non-extensive statistical mechanics for a time-varying coefficient diffusion model. We employed the non-extensive Tsallis entropy distribution, which can describe the leptokurtosis and fat-tail characteristics of returns, to model the motion of the underlying asset price. Considering that economic variables change over time, we allowed the drift and diffusion terms in our model to be time-varying functions. We used the I t o ^ formula, Feynman–Kac formula, and P a d e ´ ansatz to obtain a closed-form solution of geometric average Asian option pricing with a paying dividend yield for a time-varying model. Moreover, the simulation study shows that the results obtained by our method fit the simulation data better than that of Zhao et al. From the analysis of real data, we identify the best value for q which can fit the real stock data, and the result shows that investors underestimate the risk using the Black–Scholes model compared to our model.

scholarly journals Cross-section instability in financial markets: impatience, extrapolation, and switching

2021 ◽  
Author(s):  
Roberto Dieci ◽  
Xue-Zhong He
Keyword(s):  
Financial Markets ◽  
Cross Section ◽  
Asset Price ◽  
Asset Market ◽  
Long Run ◽  
Short Run ◽  
And Performance ◽  
Equilibrium Market ◽  
High Degree ◽  
Fundamental Price

AbstractThis paper presents a stylized model of interaction among boundedly rational heterogeneous agents in a multi-asset financial market to examine how agents’ impatience, extrapolation, and switching behaviors can affect cross-section market stability. Besides extrapolation and performance based switching between fundamental and extrapolative trading documented in single asset market, we show that a high degree of ‘impatience’ of agents who are ready to switch to more profitable trading strategy in the short run provides a further cross-section destabilizing mechanism. Though the ‘fundamental’ steady-state values, which reflect the standard present-value of the dividends, represent an unbiased equilibrium market outcome in the long run (to a certain extent), the price deviation from the fundamental price in one asset can spill-over to other assets, resulting in cross-section instability. Based on a (Neimark–Sacker) bifurcation analysis, we provide explicit conditions on how agents’ impatience, extrapolation, and switching can destabilize the market and result in a variety of short and long-run patterns for the cross-section asset price dynamics.

Fabrication of three-dimensional tissues with multilayer mesenchymal stem cell sheets: overcoming the diffusion limit

2008 ◽  
Vol 9 (2) ◽  
pp. 110 ◽  
Author(s):  
W Matsuda ◽  
Y Haraguchi ◽  
T Shimizu ◽  
S Miyoshi ◽  
A Umezawa ◽  
...  
Keyword(s):  
Stem Cell ◽  
Mesenchymal Stem Cell ◽  
Three Dimensional ◽  
Diffusion Limit ◽  
Cell Sheets

scholarly journals Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Tanki Motsepa ◽  
Chaudry Masood Khalique ◽  
Motlatsi Molati
Keyword(s):  
Option Pricing ◽  
Three Dimensional ◽  
Mathematical Finance ◽  
Group Classification ◽  
Lie Point Symmetries ◽  
Group Invariant ◽  
Black Scholes ◽  
Group Invariant Solutions ◽  
Bond Option

We carry out group classification of a general bond-option pricing equation. We show that the equation admits a three-dimensional equivalence Lie algebra. We also show that some of the values of the constants which result from group classification give us well-known models in mathematics of finance such as Black-Scholes, Vasicek, and Cox-Ingersoll-Ross. For all such values of these arbitrary constants we obtain Lie point symmetries. Symmetry reductions are then obtained and group invariant solutions are constructed for some cases.

scholarly journals A Medieval Bishop's Palace in Milicz: 3D Reconstruction as a Method of a Research Hypotheses Presentation

2017 ◽  
Vol 1 (2) ◽  
pp. 428-443 ◽  
Author(s):  
Justyna Kolenda ◽  
Małgorzata Markiewicz
Keyword(s):  
Three Dimensional ◽  
Long Run ◽  
Historical Monuments ◽  
Border Towns ◽  
History Of ◽  
The Will ◽  
Academy Of Sciences ◽  
The Church ◽  
Source Materials ◽  
Intensive Development

As a result of the intensive development of multimedia 3D visualizations of various kinds of historically, artistically or scientifically valuable objects became standard at the beginning of the 21st century. What triggered the construction of three-dimensional visualizations was the will to protect the cultural heritage – especially historical monuments which are in ruins and exposed to further destruction – as well as the need to disseminate the information about such objects not only among the small group of specialists. Another reason of that is to verify the existing proposals of reconstructions or research hypotheses. The bishop’s palace in Milicz was probably built in the late thirteenth or early fourteenth century. It was a brick building referring to the type of layout of princely buildings known in Silesia. Erection of the building in Milicz was connected with the creation of the Church castellany in this area. Visualisation of the oldest phase of the bishop’s palace in Milicz is part of the project: Regni custodiam et clavem – Santok and clavis regni Poloniae – Milicz as an example of two border towns, implemented by the Institute of Archaeology and Ethnology of the Polish Academy of Sciences and financed from the funds of the National Program for the Development of Humanities for the years 2011-2017 (number 11H 11 0184 80). Virtual reconstructions were based on the analysis and interpretation of source materials, in accordance with the guidelines contained in the London Charter. The purpose of the visualization is to introduce residents of Milicz and tourists to history of the building and, in the long run, to take steps by local authorities towards preservation and revitalization of the bishop’s palace.

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.

Sign in / Sign up

Export Citation Format

Share Document