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# Questions tagged [jump-diffusion]

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### The continuous-time limit of asset price processes where there is more than one asset

I've read Merton's article "On the Mathematics and Economics Assumptions of Continuous-Time Models" (Reprinted in Continuous-time Finance, Chapter 3), where Merton proved that the price of ...
0 votes
0 answers
29 views

### Diffusive Limits for compound poisson process

I was reading about compounded Hawkes process and came across diffusive limit theorems. Where can I find diffusive limit theorems for Poisson processes. I am new to this area, is there a nice ...
0 votes
1 answer
230 views

### Kou model — solving PIDE for European and American options in Python

Toivanen proposed$^\color{magenta}{\star}$ a method to solve the partial integro-differential equation (PIDE) with a numerical scheme based on Crank-Nicolson. In particular, he proposed an algorithm ...
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2 votes
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### Kou model - can't reproduce prices of European Option from Toivanen and Forsyth [duplicate]

I have implemented the Kou option model for pricing vanilla option. I have checked that my program can replicate the price of the option in the original paper of 2002. However, when I use it to price ...
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0 votes
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### What would be the practitioner way of hedging jump risks?

I have developed a keen interest in volatility strategies and have implemented various approaches based on practitioner delta. This delta is meticulously calibrated using a no-arbitrage implied ...
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0 votes
1 answer
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### Pure jump process in Duffie, Pan and Singleton's paper

In page 1349 or Section 2.1 of "Duffie, D., Pan, J., & Singleton, K. (2000). Transform Analysis and Asset Pricing for Affine Jump-Diffusions. Econometrica, 68(6), 1343-1376" the pure ...
2 votes
0 answers
166 views

### Is it possible to calibrate Mertons Jump Diffusion Model such that it matches mean and vola from a normal process without jumps? [closed]

I'm currently playing around with Mertons version of jump diffusion processes where i'm testing the predicitions of a trading model given a time series with and without jumps to isolate the effects of ...
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3 votes
2 answers
96 views

### Does discretizing a diffusion model make it look like a jump diffusion model?

Can we distinguish a sample generated from a diffusion model with large time steps from a sample generated from a jump diffusion model. Not mathematically but numerically (if we ask a computer to tell ...
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### Affine Jump Diffusion

I'm currently looking into affine jump-diffusions. I would like to get to know the literature better and I know the paper by Duffie, Pan, and Singleton (2000) is a very celebrated paper. Although I ...
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1 vote
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129 views

### Stochastic volatility with jumps [closed]

I'm reading the Duffie, Pan, and Singleton (2000) paper now and I've stumbled upon something that seems to me as an inconsistency. Whenever I look up the SVJJ model, I see that its log-transform is ...
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1 vote
0 answers
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### Mixing formula for SVJ models

I am trying to understand the mixing formula (Hull and White formula) for stochastic volatility models with jumps in the asset price. One article which discusses this is Lewis, The mixing approach to ...
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5 votes
1 answer
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2 votes
1 answer
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### What can the area under a GBM jump curve tell you

So I used matlab and simulated stock prices with the Merton diffusion model. Now I want to take the integral of the area. Now would there be any financial insight by taking the integral of a stock ...
-1 votes
2 answers
93 views

### I just got Matlab, what are some options that I should model in a jump diffusion

Don't worry I understand mathematics: ito's calc, martingales, etc. I am just curious what options I should test, and from what indices. Is there stuff I can test from the 2008 crash to measure their ...
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6 votes
2 answers
211 views

### Solution for a SDE for a Bond found in Bugard & Kjaer

I'm going over the paper -Partial Differential Equation Representation of Derivatives with Bilateral Counterparty Risk and Funding Costs- from Burgard and Kjaer. There the following SDE is given for ...
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1 vote
0 answers
167 views

### Unique risk neutral measure for jumps or incomplete markets for jumps

I wanted to understand why the market is incomplete in jump-diffusion models. whereas if we have a model following geometric Brownian motion then we can get a risk-neutral measure and hence a complete ...
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3 votes
2 answers
812 views

### SDE Jump-Diffusion

If you combine the compound Poisson process with the Brownian motion you obtain the simplest case of a Jump-diffusion. Let’s define $$X_t = \mu t + \sigma W_t + J_t$$ where $W_t$ is a Wiener process ...
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3 votes
1 answer
200 views

### Binomial tree with jumps

I am struggling with developing a binomial tree with jumps. although there are models such as CRR, could you suggest a book or have any idea to proceed? Thanks, Amir
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5 votes
1 answer
323 views

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3 votes
0 answers
111 views

### Euler discretization with jumps

There is a process $B_t = B_0\prod_{i=1}^{N_t}(1-Z_n)$, where $Z_n=e^{-ξ_n}$ for i.i.d exponentially distributed random variables $(ξn)_{n≥1}$ with rate $ρ=20$. ${N_t}$ is a counting process ...
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2 votes
1 answer
1k views

### Crash cliquet price

Denote by $n$ the n-th trading day in a year and by $S_n$ the stock price on that day. An instrument expirying in 1 year pays $\max(0,1-\frac{S_n}{S_{n-1}})$ and early terminates if \$\frac{S_n}{S_{n-1}...
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