Questions tagged [jump-diffusion]
The jump-diffusion tag has no usage guidance.
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Simulating compound Poisson jump-diffusion process with time-changed jump frequency
I want to simulate a jump-diffusion process with compound Poisson jumps and a deterministic jump frequency function $\lambda(t)$.
The function should follow the following stochastic differential ...
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Levy process and random measure
I am wondering if random measures are used under a Levy process and how this connects to finance (particularly pricing). Any paper or books for suggestions is welcomed.
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Hedging jump models with a infinite number of derivatives
First of all, I inform you that I am not a financial mathematician and have vague knowledge about an incomplete market.
Stochastic volatility models are incomplete so derivatives cannot be ...
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Bond PDE under an Affine Jump Diffusion model
Under the Jump extended Vasicek model, the dynamics of the short rate are as follow :
$$dr_t=\kappa(\theta-r_t)dt+\sigma\sqrt{r_t}\,dW_t+d\left(\sum\limits_{i=1}^{N_t}\,J_i\right)$$
where $N_t$ ...
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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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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 $\frac{S_n}{S_{n-1}...
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Barrier Option under Jump Diffusion
I am trying to price a Barrier Option under a model with jumps. I am using a brownian bridge approach but struggle with the jumps around these bridges and don't know how to handle this.
My main ...
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stochastic vol modelling not enough for smile
It seems in practice models that include Stochastic Volatility alone do not have enough power to produce actual observed implied vol surfaces. Is there recent empirical literature documenting this?
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Simulate double exponential process with correlated jumps?
So, I'm trying to simulate a correlated double exponential jump process for two assets, and I understand the pure exponential jump process ($\eta_1$ and $\eta_2$, the probability of an upward jump ...
- 273
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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 ...
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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') &= \...
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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 ...
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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 ...
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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}
...
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Black-Scholes formula for Poisson jumps
For underlying asset
$$d S = r S dt + \sigma S d W + (J-1)Sd N$$
here $W$ is a Brownian motion, $N(t)$ is Poisson process with intensity $\lambda.$
Suppose $J$ is log-normal with standard deviation $\...
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