# Questions tagged [jump-diffusion]

The tag has no usage guidance.

50 questions
Filter by
Sorted by
Tagged with
1 vote
82 views

### Separating jumps and diffusion

I want to model energy prices. I have two markets, lets say market 1 and 2. Market 1 is continuously traded, and I will assume it follows brownian motion. So the value of the asset could be defined ...
62 views

179 views

### Efficient way to perform MLE on Merton Jump Diffusion model parameters?

I understand that under Merton Jump Diffusion Model, if we are going to estimate the parameters $\alpha, \sigma,\mu_J, \delta, \lambda$, we can use maximum likelihood estimation on the probability ...
1 vote
198 views

### Jump diffusion simulation

I want to simulate a geometric Brownian motion and we assume that the volatility of the stock can take just two values $\sigma_1=0.2$ and $\sigma_2=0.8$. We also assume that the jumps up from lower ...
1 vote
69 views

### "Pricing European Options in a Stochastic-Volatility-Jump Diffusion Model" ,does anyone have this article?

I can't find the article "Pricing European Options in a Stochastic-Volatility-Jump Diffusion Model" of Thomas Knudsen and Laurent Nguyen-Ngoc, Journal of Financial and Quantitative Analysis,...
37 views

### How option value default adjusted in jump diffusion model

According to the doc here: http://faculty.baruch.cuny.edu/jgatheral/JumpDiffusionModels.pdf. Formula 7 specifies that the option value under jump diffusion model becomes: So when the default ...
101 views

### Characteristic function for heston model with jumps in price and variance

I need the characteristic function of the Heston model with jumps in price and variance, or in other words, the characteristic function of the Bates model (1996) adding jumps in the variance dynamics. ...
99 views

1 vote
108 views

237 views

### Barrier Option under Jump Diffusion

I am trying to price a Barrier Option under a model with jumps. I am using a brownian bridge approach but struggle with the jumps around these bridges and don't know how to handle this. My main ...
1 vote
125 views

### stochastic vol modelling not enough for smile

It seems in practice models that include Stochastic Volatility alone do not have enough power to produce actual observed implied vol surfaces. Is there recent empirical literature documenting this?
217 views

### Simulate double exponential process with correlated jumps?

So, I'm trying to simulate a correlated double exponential jump process for two assets, and I understand the pure exponential jump process ($\eta_1$ and $\eta_2$, the probability of an upward jump ...
1 vote
1k views

### How to estimate lambda for Jump-Diffusion Process from Empirical data?

So, I have really no idea how to go about this, but how would I go about choosing sensible parameter values for a basic jump-diffusion simulation, namely $\lambda$ ? For example, getting the average ...
758 views

### exercise on multivariate Ito's lemma + jumps (Poisson)

Given the two jump-diffusions: \begin{equation} \begin{aligned} dX_{1,t} &= a_1 dt + b_1 dW_t + c_1 dN_t(\lambda) \\ dX_{2,t} &= a_2 dt + b_2 dW'_t + c_2 dN_t(\lambda) \\ corr(dW,dW') &= \...
851 views

### Merton's jump diffusion

Can someone help me finding the expected value of the solution to Merton's jump diffusion model: \begin{align} S_t &= S_0 \exp \left( \left(r - \frac{\sigma^2}{2} - \lambda k \right) t + \sigma ...
175 views

### Cadlag Property of Jump Proccesses

I've recently started studying Cont & Tankov's "financial modelling with jump processes". I'm curious as to why that this assumption of the cadlag property (also called RCLL "right continuous ...
740 views

### Trouble understanding jump part in Kou double exponential jump diffusion model

I am trying to work with Kou's double exponential Jump-diffusion model and simulate a price path in a programming language. So the dynamics of the asset price in Kou's model follow: \begin{equation} ...