This paper assumes that jump process in underlying assets-stock price is more common than Poisson process and derive the pricing formulas of some exotic options under the stochastic interest rates by martingale method with the risk-neutral hypothesis.

We examine foreign exchange options in the jump-diffusion version of the Heston stochastic volatility model for the exchange rate with log-normal jump amplitudes and the volatility model with log-uniformly distributed jump amplitudes. We assume that the domestic and foreign stochastic interest rates are governed by the CIR dynamics. The instantaneous volatility is correlated with the dynamics.

Synonyms for martingale in Free Thesaurus. Antonyms for martingale. 1 synonym for martingale: dolphin striker. What are synonyms for martingale?Jump diffusion is a stochastic process that involves jumps and diffusion. It has important applications in magnetic reconnection, coronal mass ejections, condensed matter physics, in Pattern theory and computational vision and in option pricing. In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a family of random variables.T1 - A Multivariate jump diffusion process for counterparty risk in CDS rates. AU - Ramli, Siti Norafidah Mohd. AU - Jang, Jiwook. PY - 2015. Y1 - 2015. N2 - We consider counterparty risk in CDS rates. To do so, we use a multivariate jump diffusion process for obligors' default intensity, where jumps (i.e. magnitude of contribution of primary.

The HKU Scholars Hub has contact details for these author(s). Professor Yang, Hailiang. Optimal investment for insurer with jump-diffusion risk process. Show simple item record; Show full item record; Export item record; Title: Optimal investment for insurer with jump-diffusion risk process: Authors: Yang, H Zhang, L. Keywords: Hamilton-Jacobi-Bellman equations Ito's formula Jump-diffusion.

Jump diffusion models, Merton and Bates. Olivier Pradere 2016-04-14 We also expose a subset of jump diffusion models available into LexiFi Apropos. Underlying dynamics, European call pricing and calibration procedures are developed for the Merton and Bates models. For the sake of clarity, some theoretical aspects and figures are hidden, don't hesitate to expand them for having more information.

The method of Esscher transforms is a tool for valuing options on a stock, if the logarithm of the stock price is governed by a stochastic process with stationary and independent increments. The price of a derivative security is calculated as the expectation, with respect to the risk-neutral Esscher measure, of the discounted payoffs. Applying the optional sampling theorem we derive a simple.

A Simple Option Formula for General Jump-Diffusion and Other Exponential Levy Processes. 25 Pages Posted: 6 Sep 2001. See all articles by Alan L. Lewis Alan L. Lewis. OptionCity.net. Date Written: September 2001. Abstract. Option values are well-known to be the integral of a discounted transition density times a payoff function; this is just martingale pricing. It's usually done in 'S-space.

Option Pricing and hedging in Jump-diffusion Models. 1. Yu Zhou Advising professor: Johan Tysk. Department of Mathematics, Uppsala University. May, 2010. 2. Abstract. The aim of this article is to solve European Option pricing and hedging in a jump-diffusion framework. To better describe the reality, some major events, for example, may lead to dramatic change in stock price; we impose.

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Jump-diffusion process Martingale-duality approach abstract We consider the dynamic portfolio choice problem in a jump-diffusion model, where an investor may face constraints on her portfolio weights: for instance, no-short-selling constraints. It is a daunting task to use standard numerical methods to solve a constrained portfolio choice problem, especially when there is a large number of.

Stochastic Reaction-diffusion Equations Driven by Jump Processes 133 Our paper confirms an observation that has already been made in earlier papers (13, 42) that the theory of stochastic integration with respect to a Poisson random measure in martingale type pBanach spaces is, to a large extend, analogous to the theory of stochastic integration with respect to a cylindrical Wiener process in.

OPTION PRICING UNDER JUMP-DIFFUSION MODEL WITH Q PROCESS VOLATILITY1 Su Jun2 Xu Genjiu3 Abstract: In this paper, a financial market model is presented, where the underlying asset price is given by the combination of a two state Q process volatility and a compound Poisson process. The formula of European call option price under this model is derived. It generalizes the results of Hull and White.

This paper studies equilibrium equity premium in a semi martingale market when jump amplitudes follow a binomial distribution. We take n to be the number of times. An investor is trading in this market with p being the probability that there is a shift in the price at the trading time t. We find significant variations in the equilibrium equity premium for the martingale and semi martingale.

Dynamic Asset Allocation with Loss Aversion in a Jump-diffusion Model: Hui MI 1,2, Xiu-chun BI 2, Shu-guang ZHANG 2: 1 School of Mathematical Sciences and Institute of Finance and Statistics, Nanjing Normal University, Nanjing 210023, China; 2 Department of Statistics and Finance, University of Science and Technology of China, Hefei 230026, China.

We derive results similar to Bo et al. (2010), but in the case of dynamics of the FX rate driven by a general Merton jump-diffusion process. The main results of our paper are as follows: 1) formulas for the Esscher transform parameters which ensure that the martingale condition for the discounted foreign exchange rate is a martingale for a general Merton jump-diffusion process are derived.