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Questions tagged [jump-diffusion]

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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 ...
Lili M.'s user avatar
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3 votes
0 answers
154 views

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}\...
Alex's user avatar
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3 votes
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111 views

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 ...
jhon's user avatar
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2 votes
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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 $...
Kapes Mate's user avatar
2 votes
0 answers
180 views

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. ...
michael tancredi's user avatar
2 votes
0 answers
53 views

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 ...
Alexa's user avatar
  • 21
2 votes
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169 views

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 ...
Furqan Hashim's user avatar
2 votes
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186 views

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] \...
godric97's user avatar
2 votes
0 answers
775 views

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 ...
MrPefister's user avatar
2 votes
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137 views

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 ...
user155214's user avatar
1 vote
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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 ...
Steve Norkus's user avatar
1 vote
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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 ...
p.sibuea's user avatar
1 vote
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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,...
michael tancredi's user avatar
1 vote
0 answers
167 views

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 ...
na1201's user avatar
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162 views

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: $$dS = (r+\lambda*p)Sdt + \sigma*SdW+Sdq$$ $...
M00000001's user avatar
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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 ...
alexbougias's user avatar
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1 vote
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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 ...
confused's user avatar
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1 vote
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How are Levy driven SDE simulated?

Do you just use an Euler scheme as before? E.g. take this process, OU process with a Levy driver. \begin{equation} \text{d}V_t = -\lambda V_t\text{d}t + dZ_t \end{equation} Do you just have $V_{...
Lost1's user avatar
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Diffusive Limits for compound poisson process

I was reading about compounded Hawkes process and came across diffusive limit theorems. Where can I find diffusive limit theorems for Poisson processes. I am new to this area, is there a nice ...
user50123's user avatar
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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 ...
Frank's user avatar
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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 ...
Marc Allan's user avatar
0 votes
0 answers
37 views

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 ...
Oliver Mohr Bonometti's user avatar
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0 answers
483 views

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 ...
Paul's user avatar
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114 views

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 ...
HoldBreath's user avatar