# Questions tagged [numerical-methods]

The tag has no usage guidance.

140 questions
Filter by
Sorted by
Tagged with
131 views

97 views

### 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
88 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 ...
141 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
53 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
55 views

### 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 ...
120 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 ...
164 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 ...
346 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 ...
236 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, ...
397 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 ...
185 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
63 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 ...
116 views

211 views

1 vote
126 views

### 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
157 views

### 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
69 views

For my thesis on a Bayesian sampling routine for a modification on arbitrage-free Nelson-Siegel I came across an equation that involves a matrix exponential within an integral, i.e. $\int_{0}^{\Delta ... 1 vote 0 answers 79 views ### Longstaff Schwartz method (LSM): how to increase accuracy? In the LSM method, I am currently (as they do in the paper) using weighted Laguerre polynomials as basis functions, about 3-5 of them. If I wish to increase the accuracy of my model, what should I do?... 1 vote 0 answers 109 views ### How is it possible that the measurement uncertainty in Kalman Filter is less than 0? In Euan Sinclair's Option Trading, Pricing and Volatility Strategies and Techniques, it mentions that the true value of the price can be estimated via Kalman Filter:$$S_\mathrm{new} = S + k (S_b − S)... 1 vote 1 answer 139 views ### L2 Assumptions of the Longstaff Schwartz method In page 121 of the original LS Paper they use the fact that the space of functions they are dealing with (payoffs of American options), belong to the$\mathcal L^2$space. They use this assumption ... 3 votes 0 answers 97 views ### 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 1 answer 365 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 ... 4 votes 1 answer 316 views ### In Carr-Madans option pricing method, why do they use FFT? In the famous fourier option pricing method by Carr-Madan, (http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.348.4044&rep=rep1&type=pdf), the crucial formula is They evaluate this by ... 2 votes 1 answer 3k views ### Simulation of Geometric Brownian Motion in R Using R, I would like to simulate a sample path of a geometric Brownian motion using \begin{equation*} S(t) = S(0) \exp\left(\left(\mu - \frac{\sigma^{2}}{2}\right)t + \sigma B_{t}\right), \end{... 3 votes 2 answers 225 views ### Produce the random variable for an asset from a uniformly distributed random varible I'm working on a quant interview question from the book called Quant Job Interview Questions And Answers (by Mark Joshi and other authors). I cannot understand the following question(not the answer, ... 1 vote 1 answer 80 views ### Calibrate a model parameter with an error function Suppose I want to find the implied volatility using an option model from market prices. Surely I can find the implied volatility for each strike price ($k\$ different strike prices) for a given ... 