# Questions tagged [numerical-methods]

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### Antoine Savine's store

In his book "Modern Computational Finance, AAD and Parallel Simulation", Antoine Savine writes page 263 in the footnote : "We could have more properly implemented the store with GOF’s ...
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### State-of-the-art grid construction techniques

I am wondering what the state-of-the-art regarding grid definition and construction, for solving PDEs using finite differences. I know some techniques are described in Duffy's Finite difference ...
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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 ...
1 vote
396 views

I am reading the article, where different approximations for the pricing of basket options are presented. I have tried to reproduce the result obtained by the Gentle's method in Python. We define the ...
178 views

### Choosing a time step in Monte Carlo simulation of forward rates in LIBOR Market Model

Lets talk about the Monte Carlo simulation of forward rates in Euler discretization scheme under the $T_N$-forward measure, a so called terminal measure. Suppose that we have a number of time steps ...
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### How to identify between Analytical, Numerical and ML Model based option pricing? [closed]

I am new to Quantitiative Finance. Coming from Computer Science domain, I wanted to clear the key distinguishing factor between analytical, numerical and ML based models for option pricing. As far as ...
1 vote
120 views

### Method to retrieve implied density for a mixture of local volatility model

Given a mixture model of two local volatility models, the price for an option is given by: $$V(K,T) = p V_{loc1}(K,T) + (1-p) V_{loc2}(K,T)$$ where $V_{loc}(K,T)$ is the price of the option given a ...
378 views

### Importance sampling for Monte Carlo with local volatility in practice

I am given a diffusion with a local volatility to price barrier options: $$dX(t)=X(t)\mu dt+X(t)\sigma(t,X)dW_t$$ I want to use Importance Sampling to price barrier options "far" out of the ...
1 vote
173 views

### Programming the Milstein method and computing the increments

In the wikipedia article on the Milstein method, the following python code to simulate a geometric Brownian motion is presented: ...
1 vote
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### Fitting parameters given an inverse function. (Orosi, 2015)

In trying to replicate Orosi's (2015) 5-parameter implied volatility model, but I can't wrap my head around the parameter fitting procedure Orosi proposes. My main goal is to calibrate the model to my ...
144 views

### Integrated Delta does not seem to be smooth (ATM, Heston)

I am interested in an integrated call option that removes the dependence on time, $$I(S)=\int_0^\infty C(S,t)\text{d}t.$$ Because the value of a call option is a smooth function, I expect this ...
276 views

### Likelihood ratio and pathwise sensitivity method for coupled SDEs

I have two coupled SDEs \begin{align*} dS_t=rS_tdt+V_tdW_t^{(1)},\\ dV_t=aV_tdt+b(V_t)dW_t^{(2)},\\ \end{align*} where $W_t^{(1)}$ and $W_t^{(2)}$ are independent Brownian motions, initial input data ...
874 views

### Quasi Monte Carlo and Brownian bridge (how to combine them)

I am trying to understand how quasi Monte Carlo (QMC) and the Brownian bridge (BB) can be combined to price an asset, but I am having a hard time understanding how. I am just considering a European ...
369 views

### Implementation of solvers for curve construction

I'd be really interested to hear people's experiences of implementing global solvers for curve construction, especially with regard to how robust the approach is in practice, numerical performance, ...
951 views

### Hyperbolic and Elliptic PDEs in Quant Finance

Parabolic PDEs (e.g. heat equation) are closely linked to finance via the Feynman Kac Theorem. Do other types of PDEs appear in quant finance? Elliptic PDEs don't contain a time dimension (so perhaps ...
286 views

### Asymptotics of Call Option as $S\to0$

Let $C(S)$ denote the (initial) value of a call option with underlying spot price $S$. I assume that the underlying has continuous sample paths (not necessarily a geometric Brownian motion though). As ...
1 vote
139 views

### Implicit Scheme for Cox-Ingersoll-Ross Model PDE

I am considering the PDE for the price of a bond $V(r,t)$ with maturity $T$ under the Cox-Ingersoll-Ross model, $$V_t+\frac12\sigma^2rV_{rr}+\nu(\theta-r)V_r-rV=0\quad r>0, t\in(0,1)$$ with ...
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1 vote
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### Overview of frequentist, likelihood and Bayesian approaches to finance problems

In quantitative finance tasks (asset pricing, portfolio optimization, option pricing, volatility forecasting, etc), there are frequentist, likelihoodist and Bayesian approaches or interpretations to ...
1 vote
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### Are asset return means difficult to predict because they have no lower bound?

In finance, it is widely known that the volatility of asset returns ($\sigma$) are easier to predict than the expected value of asset returns ($\mu$) , otherwise known as the average return or mean. ...
1 vote
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### Optimized search for yield-to-worst of a callable bond

Suppose that I need to find the yield-to-worst of a callable bond, and that the option is American (call any time). The bond may have step-up coupons and/or non-constant call price (oprion strike). ...
1 vote
533 views

### QuantLib returns slightly different bondYield when backtested

I am just starting to get familiar with QuantLib (in particular, fixed rate bond pricing functions). I read a number of examples, from which I am able to calculate bond price and bond yield. The ...