scholarly journals Diffusion Approximations of the Geometric Markov Renewal Processes and Option Price Formulas

2010 ◽  
Vol 2010 ◽  
pp. 1-21 ◽  
Author(s):  
Anatoliy Swishchuk ◽  
M. Shafiqul Islam
Keyword(s):  
Approximation Scheme ◽  
Option Price ◽  
Rates Of Convergence ◽  
Security Market ◽  
Renewal Processes ◽  
Call Option ◽  
Diffusion Approximations ◽  
European Call Option ◽  
Markov Renewal Processes ◽  
Diffusion Scheme

We consider the geometric Markov renewal processes as a model for a security market and study this processes in a diffusion approximation scheme. Weak convergence analysis and rates of convergence of ergodic geometric Markov renewal processes in diffusion scheme are presented. We present European call option pricing formulas in the case of ergodic, double-averaged, and merged diffusion geometric Markov renewal processes.

scholarly journals The Binomial Model for N-Period European Call Option Price

2019 ◽  
Vol 1341 ◽  
pp. 062037
Author(s):  
Marwan Musa ◽  
J Massalesse ◽  
Diaraya
Keyword(s):  
Option Price ◽  
Binomial Model ◽  
Call Option ◽  
European Call Option

Option pricing under multifractional Brownian motion in a risk neutral framework

2020 ◽  
Vol 38 (3) ◽  
Author(s):  
Fabrizio Di Sciorio
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Market Price ◽  
Option Price ◽  
Mathematical Framework ◽  
Call Option ◽  
Multifractional Brownian Motion ◽  
European Call Option ◽  
Black Scholes Model ◽  
Black Scholes

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

2020 ◽  
pp. 2150008
Author(s):  
Raffaele Mattera ◽  
Fabrizio Di Sciorio
Keyword(s):  
Brownian Motion ◽  
Probability Distribution ◽  
Option Pricing ◽  
Option Price ◽  
Long Range Dependence ◽  
Call Option ◽  
Closed Formula ◽  
Multifractional Brownian Motion ◽  
Put Option ◽  
European Call Option

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.

scholarly journals Non-Homogeneous Semi-Markov and Markov Renewal Processes and Change of Measure in Credit Risk

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 55
Author(s):  
P.-C.G. Vassiliou
Keyword(s):  
Markov Chain ◽  
Probability Measure ◽  
Renewal Process ◽  
Markov Chain Model ◽  
Markov Renewal Process ◽  
Renewal Processes ◽  
Chain Model ◽  
Markov Renewal Processes ◽  
Risky Bonds ◽  
Markov Structure

For a G-inhomogeneous semi-Markov chain and G-inhomogeneous Markov renewal processes, we study the change from real probability measure into a forward probability measure. We find the values of risky bonds using the forward probabilities that the bond will not default up to maturity time for both processes. It is established in the form of a theorem that the forward probability measure does not alter the semi Markov structure. In addition, foundation of a G-inhohomogeneous Markov renewal process is done and a theorem is provided where it is proved that the Markov renewal process is maintained under the forward probability measure. We show that for an inhomogeneous semi-Markov there are martingales that characterize it. We show that the same is true for a Markov renewal processes. We discuss in depth the calibration of the G-inhomogeneous semi-Markov chain model and propose an algorithm for it. We conclude with an application for risky bonds.

Option pricing under the fractional stochastic volatility model

2021 ◽  
Vol 63 ◽  
pp. 123-142
Author(s):  
Yuecai Han ◽  
Zheng Li ◽  
Chunyang Liu
Keyword(s):  
Brownian Motion ◽  
Option Pricing ◽  
Fractional Brownian Motion ◽  
Stochastic Volatility ◽  
Option Price ◽  
Stochastic Volatility Model ◽  
Option Prices ◽  
European Call Option ◽  
Volatility Model ◽  
The Impact

We 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. doi:10.1017/S1446181121000225

scholarly journals Limit Theorems for Markov Renewal Processes

1964 ◽  
Vol 35 (4) ◽  
pp. 1746-1764 ◽  
Author(s):  
Ronald Pyke ◽  
Ronald Schaufele
Keyword(s):  
Limit Theorems ◽  
Renewal Processes ◽  
Markov Renewal Processes
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