# 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 ...
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### 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
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### 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
Accepted

### 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 + \...
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### 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]\\ &= \...
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### 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 ...

### 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 ...
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