Questions tagged [euler]
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22
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Option Price keeps decreasing as the time-steps increase
I have been writing a code in Python, trying to find a European Benchmark of the Gatheral Double-Mean Reverting model (since there is no available benchmark values online), using the Euler scheme.
For ...
- 13
3
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1
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965
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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 ...
- 443
3
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0
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70
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Verify mean-square convergence of the Euler-maruyama scheme numerically
I have a question about the order of convergence of the Euler-Maruyama scheme and how one verifes this numerically.
I have read that the Euler-Maruyama scheme is mean-squared convergent of order 1/2 ...
- 153
-1
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1
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199
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Capital Allocation, VaR, Expected Shortfall
Are there any serious drawbacks / weaknesses in the Euler allocation method, when used to allocate VaR capital (and potentially Expected Shortfall) to risk factors in a portfolio? I notice that ...
- 139
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1k
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Vasicek Short rate simulation - analytical formula vs discretization
I've been using two approaches to simulate Vasicek short rate paths and I'm wondering if one of them is more correct than the other.
The first approach is based on the analytical formula (see code ...
- 21
2
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0
answers
65
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Average individual consumption growth vs average aggregate consumption growth
Consumption growth is an essential thing in most asset pricing models and usually the Euler equation defines the return of an asset as a covariance between consumption frowth and the cash-flows of ...
- 8,456
3
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124
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Discretisation of OU (mean reverting) process with a jump process
I have a question about how to apply the Euler approximation on OU process with a jump process. The stochastic process $X_t$ has dynamic
$$dX_t=\alpha(\beta-X_t)dt+\sigma dW_t+dY_t$$
where $dY_t=...
- 107
2
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50
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How does this transformation for Euler Scheme in mean reverting SDEs alleviate instability?
I saw this text in the book - Interest Rate Modelling by Andersen volume 1 on Page 112:
I am unable to understand:
How does instability arise when we use the Euler scheme on X(t)?
What change does ...
- 31
4
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1
answer
685
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How to determine the order of convergence of the Euler-Maruyama method?
To make this simple let us consider the Geometric Brownian Motions.
My questions:
1. How can I show that the Euler-Maruyama Method is convergent using GBM?
2. How can I determine the order of ...
- 1,667
3
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112
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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 ...
- 31
3
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1
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4k
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Calculate drift of Brownian Motion using Euler method
I am working on a project to approximate numerically the solution $X_t$ of a stochastic differential equation (SDE) using the Euler method. I have do to this for the Brownian motion with drift. I am ...
- 31
6
votes
0
answers
907
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(C++) Monte Carlo pricer for SABR model to test Hagan / Paulot formulas
I'm trying to test the so-called Hagan formula (p.6 of this paper) and the Paulot formula, order 1 only (eq. (43) p.19 of this paper. For this, i'm trying to use both Euler and Milstein scheme ...
- 320
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369
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Problem of negative local volatility:
Consider the displaced log-normal process: $$dS(t) = \lambda(t)(a(t)+b(t)S(t))dW(t), S(0) = S_0>0, $$ where $W(t)$ is a one-dimensional Brownian motion.
We suppose that $(\forall t \ge 0) : \...
- 73
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452
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Euler discretization of SDE, combined with antithetic sampling
let's say we have a GBM $dS_t = r S_t dt + \sigma S_t dW_t$, where $W_t$ is standard Brownian motion, and we have an European option $C$ with payoff $f(S_T)$. I want to use an Euler discretization ...
- 175
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569
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Euler discretisation error for stochastic volatility model
Given the following model$$dS_t=S_t(\mu dt+\sigma(t,S_t)dW_t)$$
Using Monte Carlo Pricing method, I want to determine the price of the option. However I have been encountered the following problems:
...
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