Questions tagged [monte-carlo]

Monte Carlo simulation methods are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results.

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876 views

Law of a geometric brownian motion first hitting time (formula dont match Monte Carlo Simulation)

I posted this question before on MSE I need to use it in a small step in the middle of a simulation and I think I'm not getting correct results to this probabilities and so for my all ...
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119 views

Optimizing stochastic functions numerically

Is there an efficient and commonly used optimization method for "more complex" investment strategies. For instance, say you have a function $f(X_1,...,X_n,c,v)$ where the $X_k$'s are your random ...
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2answers
758 views

Risk Neutral and Real World Valuations using Monte Carlo

Assume I'm an investor that wants to sell exotic put options. No one else is selling my kind of put option, so I need to determine my own "Market Price" through Monte Carlo simulation. I know that by ...
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2answers
273 views

What are some examples of non-solvable SDE where Monte Carlo discretization is necessary

Reading Glasserman - "Monte Carlo Methods in Finance" it says in the introduction to Chapter 6 - Discretization Methods, that moste models arising in derivatives pricing can be simulated only ...
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1answer
567 views

Calibration by monte carlo, should I fix my seed?

I am calibrating a 3-parameter stochastic model to options market data via Monte Carlo simulation. Let the parameter set be denoted by $\bar{\theta}$. (this is not a simple Black-Scholes type model, ...
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1answer
333 views

Deep ITM Call Implied Vol via Monte Carlo

Let's say I've computed the price of a call using Monte Carlo with $S_0 = 100$ and $K = 80$, using $T = 0.1$ and $r = 0$ to be $\$20.00095$. This price estimate comes with a $95\%$ confidence ...
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1answer
4k views

How to generate simulated stock price from historical data using R?

I have created a strategy specifically for a particular stock which I backtested with its historical data. Now I want to forward test it with simulated stock price generated using Monte Carlo. I have ...
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1answer
257 views

Testing a Monte Carlo simulation independently

I'm building a Monte Carlo option pricing model in Python/SciPy. I want to test the results produced by the Python code by building the model independently in Excel and then comparing the results. Off ...
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1answer
2k views

How to explain the path dependency in binomial tree model to price options?

I'm new to quantitative finance, so I'm confused with the so-called path dependency in binomial tree model. Originally I thought the path dependency exists because in binomial tree model, we will ...
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2answers
141 views

Effect of correlation on a best-of rainbow option

EDIT 2: I found the problem(s) and the prices seem to behave as expected now. For anyone interested there was a bug when normalizing the dependant ranom normal variates used in the simulation, so ...
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3answers
279 views

VaR estimate with Monte Carlo simlation

i want to verify the theoretical VaR 99% for the following Random Variable: \begin{align*} X=\epsilon + \nu, \end{align*} $\epsilon \sim \mathcal{N}(0,1)$, \begin{align*} \nu= \begin{cases}\begin{...
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1answer
254 views

Using crude Monte Carlo

Background Information: The crude Monte Carlo algorithm for the arithmetic Asian call option is $$Y = e^{-rT}(\overline{S}_A - K)^{+}$$ and the control is $$C e^{-rT}(\overline{S}_G - K)^{+}$$ The ...
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1answer
82 views

Doing MC simulation using two different methods, are they the same?

I have learnt two versions of Monte Carlo simulations to do stock price, and can someone help check if I am thinking this right. The first one is the most common one: $\frac{\Delta S_t}{St}-1 = \mu ...
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1answer
99 views

Greeks: Estimate gamma by Monte Carlo finite difference

When I was using Monte Carlo to calculate the gamma of a vanilla call option by finite difference method, I stuck in this weird situation as below. Consider this, $$ Gamma = \frac{CallPrice(S^{up}_{T})...
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1answer
109 views

What is the annualized realized volatility of simulated Brownian motion paths?

I saw this following question in an exam. Take a Brownian motion simulation with drift 5% and annualized volatility of 20% for a period of 1 year. Then the annualized realized volatility of the ...
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2answers
2k views

Monte Carlo simulations in Python using quasi random standard normal numbers using sobol sequences gives erroneous values

I am trying to perform Monte Carlo Simulations using quasi random standard normal numbers. I understand that we can use sobol sequences to generate uniform numbers, and then use probability integral ...
2
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1answer
81 views

Day counts and time increment in Monte Carlo

Suppose the evolution of the stock price is given by Geometric Brownian Motion. Futher I assume that the risk free rate process is given by CIR model. In both models there is a time increment dt. To ...
2
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2answers
974 views

Pricing variance swaps using Monte Carlo

For pricing variance swaps there is the well-known formula as sum of OTM options weighted by the inverse of the squared strike (see e.g. here). Would it also be valid to derive the local-volatility ...
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1answer
63 views

Expected number of days inside a corridor

Is there a simple (ish) approximation for the expected number of steps a random walk is within a set of bounds over a given time period? - in particular if i presume log normal and constant vol. If i ...
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1answer
3k views

How to use Halton sequence in monte carlo simulation

Does anybody know how to use the Halton pseudo random technique in monte carlo simulation. I'm able to generate the sequences and I know they are correct. I checked a couple of numbers from different ...
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1answer
53 views

Implementation of Stratified Sampling in Monte Carlo

Background I am trying to implement Monte Carlo Simulation with Stratified Sampling for barrier option under Black Scholes Model. I understand there is an analytic formula for this instrument and we ...
2
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1answer
64 views

Multivariate MC: what am I doing wrong?

I am trying to generate multivariate MC results presented in this paper A Simple Generalisation of Kirk’s Approximation for Multi-Asset Spread Options by the Lie-Trotter Operator Splitting Method, by ...
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2answers
122 views

Single-step Monte Carlo in Excel

How do you simulate correctly using raw prices not returns? I have corresponding periods of earnings to Futures but the Excel call function =NORMINV(RAND(),mean,stdev) generates negative Futures ...
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1answer
226 views

How to price the American style Asian option with recent N day average

How to price the American style Asian option with recent N day average, for example, we exercise at t day, then the payment is $$...
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1answer
419 views

Monte Carlo and PDE results are different for a Call Option!

Okay so this might be a fairly trivial question but I'm having an issue with valuing a call option using both a Monte Carlo method and a PDE method. When I started I first used the parameters: Spot =...
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2answers
453 views

Deduce expected exposure profile from option/structure delta?

I am thinking about whether there exists a relationship between the delta of an option (or any structured derivative) and it's expected positive/negative exposure? An intuitive question would be the ...
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1answer
1k views

American Swaption Pricing with Monte-Carlo method

I want to price an American swaption but I am not sure about what I am doing. Tree methods and PDE discretization seem difficult to adapt to a swaption. I am trying a Monte-Carlo approach. (in ...
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1answer
741 views

Quasi Monte Carlo in Matlab

I want to use Quasi Monte Carlo to try and improve the convergence of a simulation I am running. The random numbers are simply to produce the observation errors for a standard linear regression model....
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1answer
917 views

Greeks of Basket

I am considering a product composed of 10 underlying assets. The maturity is 5 year. Each year if the performance of the equi-weighted portfolio reach a barrier, it pays a coupon. My question concern ...
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1answer
199 views

simulate volatility surface

Assuming I have a stochastic volatility model for an asset, if I wanted to use it for pricing I would proceed in the following way: Use Euler discretization to simulate a sample path of the price and ...
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1answer
59 views

Exact solution stock price with Vasicek interest rate model

Define two correlated stock price- and interest rate (Vasicek) processes, governed by the Wiener processes $W^{S}(t)$ and $W^{r}(t)$ $$dS(t)=r(t)S(t)dt+\sigma S(t)dW^{S}(t)$$ $$dr(t)=\kappa(\theta-r(...
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1answer
82 views

Multi-factor vs Single-factor interest rate model for XVA / CCR

When calculating XVA or Counterparty Credit Risk (CCR), you can choose to simulate your interest rate with a Multi-factor interest rate model or a Single-factor interest rate model. What are the pros ...
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1answer
148 views

Why do we have to use in-the-money paths in LSMC, and how?

In Longstaff's original LSMC paper (Valuing American Options by Simulation: A Simple Least-Squares Approach, 2001 (link)), it is claimed that one should only use in-the-money paths for regression at ...
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1answer
83 views

Monte Carlo simulations of stock price percentage change rather than stock price

Say we have a stock price time series $S_k$. We can do monte carlo simulations on the stock price to make predictions about future prices (e.g. through Geometric Brownian Motion SDE's). Does it make ...
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1answer
101 views

References for Monte Carlo in insurance

As the title suggests, I'm looking for reference works on Monte Carlo methods in insurance. Wikipedia tells me that the terminus technicus here is dynamic financial analysis. I'm about to start a ...
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1answer
630 views

Longstaff Schwartz Algrorithm in R

I recently discovered the LSMonteCarlo library in R which basically determines the price of American options via Longstaff Schwartz method. I tried the ...
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3answers
973 views

Cointegration pair trading - how to test a trading rule using Monte Carlo?

I am doing a research exercise where I have two price series $X_t, Y_t$ which I regress against each other and test for cointegration. Once I confirm that they are cointegrated (using CADF or ...
2
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3answers
206 views

Distribution of pay-off of an exotic option

Can any assumptions be made about the pay-off of an exotic option? For example, might we say the distribution of the pay-off a vanilla option would be Normal? I have built a valuation tool that ...
2
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1answer
202 views

Example of options that cannot be priced with least-square Monte Carlo

Can you give some example of options that cannot be priced with least-square Monte Carlo? Intuitively, this is any option for which a payoff depends on a previous exercise decision. It's relatively ...
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1answer
375 views

Correlated random variables with additional autocorrelation - multi dimensional Cholesky?

For my thesis I'm currently generating several time series of random numbers, so far so good. Now I realized some autocorrelation in the series as well and don't really know how to cope with it. Can I ...
2
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1answer
766 views

Get distribution for aggregate loss using Monte Carlo

I am given two data sets containing dates and losses (in some currency). Given a distribution for the amount of losses and an (a,b,0) distribution for frequency of losses, how can I use Monte Carlo ...
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43 views

Which infinite activity Levy process is the most popular for option pricing

Hey I heard about different Levy processes with infinite activity like VG, NIG, Meixner or CGMY process, but which proccesses are the most popular? And which processes can be simulated (as simple as ...
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55 views

What are the most difficult/computationally expensive/infeasible derivatives to price?

I'm not sure if this question has a concrete answer or if it's more of a fun game, but I suppose the question that does have a concrete answer is what's the most difficult instrument to value that has ...
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0answers
63 views

Beta estimates of Regressions on AR(1) Process

I am currently working through the paper The Myth of Long-Horizon Predictability [1] and I got stuck in reproducing the empirical results in Section 1.4. It is my understanding that time series of ...
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0answers
61 views

Stratified sampling in asian options

I am using the procedure of stratified sampling for variance reduction. In the Glasserman book the algorithm for stratified the terminal value of the Brownian motion is given for european options. For ...
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77 views

Can variance change over time?

I'm working on a toy project that involves fantasy basketball, I know this is the quantitative finance stackexchange, but it seemed like the best place to ask this question. My goal is to make ...
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0answers
73 views

Optimizing monte carlo code in python [closed]

What are they key points to use while coding a monte carlo simulation in python? I have the following monte carlo code : ...
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0answers
79 views

When to remove a trading strategy?

Every strategy has a limited lifespan. How do you decide when to stop a particular strategy as it has lost its edge? Few of things that can be thought is strategy crossing its maximum drawdown, net ...
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1answer
140 views

Simulation scheme for SABR beside the standard Euler discretization

QUESTION: Beside Euler Scheme, is there another more robust (and preferably easy to implement) way to simulate asset path with SABR dynamics? Simulation that will withstand even for high volatilities....
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540 views

Longstaff-Schwartz, special american option simulation using Python (numpy package)

I got a put option, which can be exercised 3 times, all at different times, which are each month of a year $$t_1 = \frac{1}{12}, t_2 = \frac{2}{12} ... t_{12} = 1$$. Respectively, if exercised at $$...

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