Questions tagged [jump-diffusion]
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Discretising linear SDEs with jumps for forward curve simulation
I am working on discretising a general linear SDE with jumps and constructing the forward curve from it. The idea is to model the spot when it rolls over a contract expiry by using
$$
F(t,T) = \mathbb{...
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Pricing Barrier Option under Jump Diffusion
I'm currently building a Monte Carlo model to price a barrier option (specifically an Up-and-Out Call) under the Merton Jump-Diffusion model. I've written the simulation code and it runs without ...
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Variance of Poisson integral
I am looking for the solution to the expression
$$\text{Var}(\int_t^Te^{-a(T-s)}\ln(J)\text{d}N_s)$$
where $\ln(J)\sim N(\mu, \sigma^2)$ and $N$ has intensity $\lambda$. The term comes from a mean ...
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Volatility forecasting in presence of jumps
I have trained a GARCH(1,1) model that does a decent job of forecasting volatility (for real-world stock price time-series). For "known" events such as earnings announcements one can ignore ...
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Python implementation of the BNS (Barndorff-Nielsen & Shephard) jump test
Is there a reliable implementation in python of the BNS jump test available?
Barndorff-Nielsen & Shephard (2006) "Econometrics of Testing for Jumps in Financial Economics Using Bipower ...
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Simulating Kou's Asymmetric Double Exponential Random Variable
In Python, I import NumPy module to generate Kou's a vector of Asymmetric Double Exponential Random Variables (ADERV). I attempt to apply Glasserman's method for simulating the aforementioned from his ...
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How can one calculate third and fourth moments of a jump-diffusion process with time-varying parameters?
Suppose that $x_t$ is a random process that satisfies the mean-reversion jump-diffusion process governed by the stochastic differential equation
$$dx_t=\alpha(t)(\beta(t)-x_t),円dt+\sigma(t),円dW_t+J_t,円...
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What is the meaning of the difference of Q measures calibrated to prices vs. implied probabillities?
What's the meaning of the differences between Q measures (and calibrated parameters of a model) fit to prices vs market implied probabilities?
Updated and Clarified Question:
If I calibrate a Merton ...
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Ornstein-Uhlnbeck Process with Jumps
I am trying to simulate an OU Process (Vasicek version) with jumps and I would like to derive the drift and diffusion term when jumps are incorporated, which will enable me to perform monte carlo ...
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Modelling stocks with jump to default and recovery value
Jump to default models (eg Black-Scholes or SV with jump to default) are quite tractable models to model the possibility of default.
However, if a company defaults it doesn't always mean the stock ...
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Discretisation of Heston SV with Jumps (SVJ - Bates)
I want to simulate a price path of SVJ model (Bates) in Excel to see how it works in real time but I need help on how to discretise and construct the jump part with a Poisson process into Heston model ...
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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 ...
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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 ...