# Tag Info

### Risk neutral measure for jump processes

Assume a constant risk-free rate $r$ and no dividends. Generalisation is straightforward. To preclude arbitrage opportunities, under the risk-neutral measure $\Bbb{Q}$, the discounted asset price ...
Accepted

### Basic book on stochastic calculus, Itô and jump processes and Brownian Motion

Consider “Paul Wilmott Introduces Quantitative Finance” if you look for an enjoyable read, good intuition and a not too academic approach

### Understanding and simulating the jumps in Merton's Jump-Diffusion SDE?

For anyone else searching for good Merton Jump Diffusion examples, found a much better notated reference here: https://www.codearmo.com/python-tutorial/merton-jump-diffusion-model-python
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### Bond PDE under an Affine Jump Diffusion model

Let $P(t, r_t, T)$ be the bond price at time $t$, where $0 \leq t \leq T$. Then, by Ito's formula, \begin{align*} &\ P(t, r_t, T) \\ =& P(0, r_0, T) + \int_0^t\partial_s P(s, r_s, T) ds + \...

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

As a complement to @ir7’s comprehensive derivation, in the case of Burgard and Kjaer’s the jump process $J_t$ models the default of the issuer. You specialize the process by setting $Z_1=-1$, while ...
Accepted

### SDE Jump-Diffusion

$dJ_{t}$ can be understood as a Steljes measure , when you want to define jumps using bounded variation function , but you can simply understand it as $J_{t}-J_{t-}$ Those processes belong to a more ...
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### Expected Value of Mean-Reverting Jump Process

First, we need to be careful about putting the condition at the right place: \begin{align} e^{kt}\mathbb{E}[\mu_t] -\mu_0 &= \mathbb{E}\bigg[\sum_{m=1}^{N_t} e^{k\tau_m}\eta_m\bigg]\\ &= \...
Accepted

### Vanilla Call Option Priced Using Jump Diffusion Model

No arbitrage means that you can't have a portfolio with a positive expectation without risk. let's suppose that the value of option with jumps is lower than $C_{BS}(0,S_0)$ Please consider the ...

### Predicting time series using Jump Diffusion model and Neural Networks

Most of the work you will find on jump diffusion models will be in derivative pricing or related work on insurance. In essence, they tend to be interesting ways to think about future distributions. ...

### Basic book on stochastic calculus, Itô and jump processes and Brownian Motion

If you're interested in learning about stochastic calculus outside of the context of quant finance (which I think is a better approach than learning about it solely in the context of finance), check ...
This not possible. The compensated Poisson process $N_t-\lambda t$ converges in the limit of large intensity $\lambda$ to a Brownian motion with variance rate $\lambda\,.$ Therefore, the pure jump ...