Questions tagged [jump-diffusion]
The jump-diffusion tag has no usage guidance.
63
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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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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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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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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 ...
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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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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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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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Maximum Likelihood Estimation for Merton's Jump Diffusion Model
I'm wondering if there is a consensus about the
a) most accurate and
b) most computationally efficient
way to estimate parameters for Merton's (1976) jump diffusion model. In this model, the ...
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Characteristic Function Kou (2002) Model
I'm looking for the correct characteristic function for the Kou (2002) jump diffusion model.
Can someone help me? Because if I try to look at it online everyone forgot $r$ and $S_0$.
This is what I ...
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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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Variance of the log returns in jump diffusion with time-varying jump sizes
I'm trying to calculate the variance $\mathrm{var}\left(\log\frac{S\left(t\right)}{S\left(0\right)}\right)$, where the dynamics of the stock $S$ follows a jump-diffusion process given by $$\frac{dS\...
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How do I estimate volatility for MPR historical data
How can I estimate volatility with historical data for Monetary Policy Rate (MPR) to use in a short rate model?
I could use regular techniques like simple standard deviation or max likelihood, but the ...
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How to solve numerically the IDE of GUILBAUD & PHAM model?
By the Guilbaud & Pham model (Optimal high frequency trading with limit and market orders, 2011), the authors said that integro-differential-equation (IDE)
can be easily solved by numerical method....
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Separating jumps and diffusion
I want to model energy prices. I have two markets, lets say market 1 and 2.
Market 1 is continuously traded, and I will assume it follows brownian motion. So the value of the asset could be defined ...
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Jump Diffusion Process question
I have a European call option with time maturity $T=3$ years,$K=50$, and given that $S(t)$ refers to the derivative is being described by the geometric Brownian motion with $S_{0}=100$ and $r = 0.04$....
user57440
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Second variation of a Brownian motion under jump-diffusion process
I am trying to solve exercise 15.3 from the book The concepts and practice of mathematical finance where it is asked
Suppose the $\log S_t$ follows a Brownian motion over the period $[0, 1]$ except ...
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Euler Scheme for Jump-Diffusion models
Jump-diffusion models (as Merton) have following SDE:
$$dS_t=\mu S_tdt+\sigma S_t dW_t+S_tdJ_t$$
where
$$J_t=\sum_{i=1}^{N_t}(\xi_i - 1)$$
$\xi_i$ - i.i.dn $N_t$ - Poisson process
Do we in Euler ...
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The distribution of the jump diffusion process
In the Merton jump diffusion model the process of the share price can be expressed as $$S_{t}=S_{0}\cdot\exp\left\{ X_{t}\right\} ,$$ where $$X_{t}=\mu t+\sigma W_{t}+\sum_{i=1}^{N_{t}}Y_{i}.$$
Here $...
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Efficient way to perform MLE on Merton Jump Diffusion model parameters?
I understand that under Merton Jump Diffusion Model, if we are going to estimate the parameters $ \alpha, \sigma,\mu_J, \delta, \lambda $, we can use maximum likelihood estimation on the probability ...
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2
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Jump diffusion simulation
I want to simulate a geometric Brownian motion and we assume that the volatility of the stock can take just two values $\sigma_1=0.2$ and $\sigma_2=0.8$. We also assume that the jumps up from lower ...
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"Pricing European Options in a Stochastic-Volatility-Jump Diffusion Model" ,does anyone have this article?
I can't find the article "Pricing European Options in a Stochastic-Volatility-Jump Diffusion Model" of
Thomas Knudsen and Laurent Nguyen-Ngoc, Journal of Financial and Quantitative Analysis,...
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How option value default adjusted in jump diffusion model
According to the doc here: http://faculty.baruch.cuny.edu/jgatheral/JumpDiffusionModels.pdf.
Formula 7 specifies that the option value under jump diffusion model becomes:
So when the default ...
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Characteristic function for heston model with jumps in price and variance
I need the characteristic function of the Heston model with jumps in price and variance, or in other words, the characteristic function of the Bates model (1996) adding jumps in the variance dynamics.
...
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American Options in Merton's (1976) Jump Model
@LocalVolatility proves in this stellar answer that European call option prices in the Merton jump diffusion model are given by
$$ C_{Merton}(S_0,r,q,\sigma,K,T) = \sum_{n=0}^\infty e^{-\lambda T}\...
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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 ...
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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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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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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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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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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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Expected Value of Mean-Reverting Jump Process
I cant see the link between my method of calculation and the method done in the book Cartea and Jaimungal (Algorithmic and High Frequency Trading, page 220.) We have a mean-reverting process
$$d\mu_t=-...
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Greeks for Pricing Convertible Bond Using Jump Diffusion Model
I'm learning the jump diffusion model used to price a convertible bond, and got the following stochastic differential equation under risk neutral measure:
$$dS = (r+\lambda*p)Sdt + \sigma*SdW+Sdq$$
$...
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Vanilla Call Option Priced Using Jump Diffusion Model
I'm reading a book called Quant Job Interview Questions and Answers and came across the following question and its answer, but cannot make sense of it, so I really appreciate your advice:
Question 2....
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What is the intuition behind "jumps" causing volatility skew?
Some models use jumps as a way to explain volatility skew. I understand that if jumps exist, then you are "mishedged" as you no longer can continuously hedge. Options have a gamma component and ...
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B-S derivative with another boundary condition
I want to use the derivation of BS for another type of derivative, not an option. Known the derivation of the Black-Scholes differential equation, is it possible to use in the same equation when my ...
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Pricing barrier option under Levy process: Biased estimate?
I want to price a down and out call, barrier option, with the underlying asset following a Levy process. I am interest on the Kou double exponential model or the NIG process, to capture asymmetric ...
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Why can't we create a "magic" basket of options to sell for no-arbitrage pricing in SVJ model?
I am learning how to price SVJ options and am reading some stuff on no-arbitrage pricing for SVJ model using the typical approach you would use (like in BSM option pricing) of creating a risk free ...
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Predicting time series using Jump Diffusion model and Neural Networks
I am trying to understand the difference between using Jump diffusion model and Neural Networks or more precisely LSTM to predict time series data regardless what that data contains for example a ...
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Jump Diffusion Model - Volatility and Mean of Jumps
I am trying to understand the concept of jump diffusion model. So far what I've understood is that by adding a Jump parameter to a GBM (Geometric Brownian Motion) we can generate a Jump diffusion ...
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Poisson parameter in Merton's Jump-Diffusion Model to price call option
I've been taught the following European call valuation formula under jump-diffusion model:
\begin{equation}
price = E[e^{-rT}max(S_T-K,0)] =\sum_{j = 0}^\infty e^{-rT}P_j(\lambda)E[max(S_T-K,0)|J=j]
\...
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Basic book on stochastic calculus, Itô and jump processes and Brownian Motion
I was looking for a good book that explains at beginner-level the basic of stochastic calculus, probability and random variables, Itô and jump processes as well as Brownian Motion.
At university we ...
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Formal proof market incompleteness under jump diffusion
Does anyone have formal proof of markets incompleteness under jump diffusion ?
I am familiar with the intuitive approach as mentioned in Tankov (delta), yet I am looking for a formal approach and ...
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Understanding and simulating the jumps in Merton's Jump-Diffusion SDE?
I found this great post deriving the solution to the Merton Jump-Diffusion SDE
$$S_t = S_0\exp\left(\left(\mu - \frac{\sigma^2}{2}\right)t + \sigma W_t\right)\prod_{j=0}^{N_t}V_j$$
The first part of ...
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Simulating compound Poisson jump-diffusion process with time-changed jump frequency
I want to simulate a jump-diffusion process with compound Poisson jumps and a deterministic jump frequency function $\lambda(t)$.
The function should follow the following stochastic differential ...
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Levy process and random measure
I am wondering if random measures are used under a Levy process and how this connects to finance (particularly pricing). Any paper or books for suggestions is welcomed.
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Hedging jump models with a infinite number of derivatives
First of all, I inform you that I am not a financial mathematician and have vague knowledge about an incomplete market.
Stochastic volatility models are incomplete so derivatives cannot be ...
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Bond PDE under an Affine Jump Diffusion model
Under the Jump extended Vasicek model, the dynamics of the short rate are as follow :
$$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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