scholarly journals EUROPEAN OPTIONS SENSITIVITY WITH RESPECT TO THE CORRELATION FOR MULTIDIMENSIONAL HESTON MODELS

2014 ◽  
Vol 17 (03) ◽  
pp. 1450015 ◽  
Author(s):  
LOKMAN A. ABBAS-TURKI ◽  
DAMIEN LAMBERTON
Keyword(s):  
Stock Prices ◽  
Asymptotic Approximation ◽  
Heston Model ◽  
Option Prices ◽  
European Options ◽  
European Option ◽  
Price Function ◽  
Spread Option ◽  
Correlation Parameters ◽  
Theoretical Results

We study the sensitivity of European option prices with respect to correlation parameters in the multi-asset Heston model. The differentiability of the price function with respect to the correlation is proved by using the regularity of the flow of the Cox–Ingersoll–Ross model. In the bidimensional case and when the Feller condition is satisfied, we establish an asymptotic approximation for the derivative of the price with respect to the correlation for short maturities. This approximation is used to discuss monotony issues for exchange and spread option prices. Monotony properties are also obtained for some values of "the volatility of the volatility parameter" and of the correlation between stock prices and their volatilities. We conclude with a large number of simulations that confirm the theoretical results.

REPLICATION SCHEME FOR THE PRICING OF EUROPEAN OPTIONS

2021 ◽  
pp. 2150014
Author(s):  
HIDEHARU FUNAHASHI
Keyword(s):  
Diffusion Process ◽  
Density Function ◽  
Numerical Experiments ◽  
Analytical Formula ◽  
Option Price ◽  
Option Prices ◽  
European Options ◽  
European Option ◽  
Volatility Models ◽  
Replication Scheme

This paper proposes an efficient method for calculating European option prices under local, stochastic, and fractional volatility models. Instead of directly calculating the density function of a target underlying asset, we replicate it from a simpler diffusion process with a known analytical solution for the European option. For this purpose, we derive six functions that characterize the density function of a diffusion process, for both the original and simpler processes and match these functions so that the latter mimics the former. Using the analytical formula, we then approximate the option price of the target asset. By comparison with previous works and numerical experiments, we show that the accuracy of our approximation is high, and the calculation is fast enough for practical purposes; hence, it is suitable for calibration purposes.

Simulating from the Heston model: A gamma approximation scheme

2015 ◽  
Vol 21 (3) ◽  
Author(s):  
Jean-François Bégin ◽  
Mylène Bédard ◽  
Patrice Gaillardetz
Keyword(s):  
Stochastic Volatility ◽  
Gamma Distribution ◽  
Simulation Study ◽  
Approximation Scheme ◽  
Exact Method ◽  
Heston Model ◽  
Asian Option ◽  
Option Prices ◽  
European Options

AbstractThe Heston model is appealing as it possesses a stochastic volatility term as well as semi-closed formulas for pricing European options. Unfortunately, few simulation schemes for this model can handle the violation of the Feller Condition. An algorithm based on the exact scheme of Broadie and Kaya to simulate price paths under the Heston model is introduced. In order to increase the speed of their exact method, we use a gamma approximation. According to Stewart, Strijbosch, Moors and Batenburg, it is possible to approximate a complex gamma convolution (similar to the representation given by Glasserman and Kim) by a simple moment-matched gamma distribution. We also perform a review of popular simulation schemes for the Heston model and validate our approach through a simulation study. The gamma approximation scheme appears to yield small biases on European and Asian option prices when compared to the most popular schemes.

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.

scholarly journals Transformations of Telegraph Processes and Their Financial Applications

Risks ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 147
Author(s):  
Anatoliy A. Pogorui ◽  
Anatoliy Swishchuk ◽  
Ramón M. Rodríguez-Dagnino
Keyword(s):  
Differential Equation ◽  
Stock Prices ◽  
Option Prices ◽  
Linear Transformations ◽  
Financial Applications ◽  
Telegraph Process ◽  
Put Option ◽  
New Models ◽  
Non Linear ◽  
New Applications

In this paper, we consider non-linear transformations of classical telegraph process. The main results consist of deriving a general partial differential Equation (PDE) for the probability density (pdf) of the transformed telegraph process, and then presenting the limiting PDE under Kac’s conditions, which may be interpreted as the equation for a diffusion process on a circle. This general case includes, for example, classical cases, such as limiting diffusion and geometric Brownian motion under some specifications of non-linear transformations (i.e., linear, exponential, etc.). We also give three applications of non-linear transformed telegraph process in finance: (1) application of classical telegraph process in the case of balance, (2) application of classical telegraph process in the case of dis-balance, and (3) application of asymmetric telegraph process. For these three cases, we present European call and put option prices. The novelty of the paper consists of new results for non-linear transformed classical telegraph process, new models for stock prices based on transformed telegraph process, and new applications of these models to option pricing.

CALIBRATION OF STOCHASTIC VOLATILITY MODELS VIA SECOND-ORDER APPROXIMATION: THE HESTON CASE

2015 ◽  
Vol 18 (06) ◽  
pp. 1550036 ◽  
Author(s):  
ELISA ALÒS ◽  
RAFAEL DE SANTIAGO ◽  
JOSEP VIVES
Keyword(s):  
Term Structure ◽  
Implied Volatility ◽  
Order Approximation ◽  
Calibration Procedure ◽  
Computational Effort ◽  
Heston Model ◽  
Option Prices ◽  
Volatility Models ◽  
Short And Long Term ◽  
Long Term Behavior

In this paper, we present a new, simple and efficient calibration procedure that uses both the short and long-term behavior of the Heston model in a coherent fashion. Using a suitable Hull and White-type formula, we develop a methodology to obtain an approximation to the implied volatility. Using this approximation, we calibrate the full set of parameters of the Heston model. One of the reasons that makes our calibration for short times to maturity so accurate is that we take into account the term structure for large times to maturity: We may thus say that calibration is not "memoryless," in the sense that the option's behavior far away from maturity does influence calibration when the option gets close to expiration. Our results provide a way to perform a quick calibration of a closed-form approximation to vanilla option prices, which may then be used to price exotic derivatives. The methodology is simple, accurate, fast and it requires a minimal computational effort.

European Option Pricing under the Double Exponential Jump Model with Stochastic Interest Rate, Stochastic Volatility and Stochastic Intensity

2014 ◽  
Vol 631-632 ◽  
pp. 1325-1328 ◽  
Author(s):  
Jin Yan Sang ◽  
Na Zhang ◽  
Ming Jian
Keyword(s):  
Stochastic Volatility ◽  
Jump Process ◽  
European Options ◽  
European Option ◽  
European Option Pricing ◽  
Stochastic Intensity ◽  
Jump Model ◽  
Double Exponential ◽  
Stochastic Interest ◽  
Form Representation

This paper explores the valuation of European options when the underlying asset follows the double exponential jump process with stochastic rate, stochastic volatility and stochastic intensity. This model better describes market characteristics, such as the volatility smile, and jump behavior. By using FFT (Fast Fourier Transform) approach, a closed form representation of the characteristic function of the process is derived for the valuation of European options. Numerical results show that the FFT method is effective and competent.

Sign in / Sign up

Export Citation Format

Share Document