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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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1answer
80 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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2answers
2k views

Why do we need correlated random variables in a Monte Carlo simulation?

Question: I don't understand why a Monte Carlo simulation needs correlated random variables. Isn't each simulation thread independent? Background: Specifically, I'm referring to the below example on ...
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1answer
86 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
484 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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2answers
116 views

Is it possible to model path-dependent clauses using finite difference methods?

I'm trying to build a convertible bond pricer. In my case a convertible bond is a complex derivative with call, put and conversion price reset clauses, and all of the clauses are triggered in a path-...
2
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1answer
69 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 ...
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2answers
814 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 ...
2
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1answer
60 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 ...
2
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2answers
79 views

Sample from aggregate portfolio distribution versus individual asset distributions

Suppose I have three assets $x_1,x_2,x_3$ in a portfolio with weights $W=\begin{bmatrix} w_1 \\ w_2 \\ w_3 \end{bmatrix} $, expected returns $R=\begin{bmatrix} \mu_1 \\ \mu_2 \\ \mu_3 \end{bmatrix}$, ...
2
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1answer
279 views

Monte Carlo Simulation of price processes

before I ask my question I want to illustrate what I think I know about Monte Carlo simulation: say I want to simulate the price paths of one European Call Option with fixed strike and maturity in the ...
2
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1answer
207 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 $$...
2
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1answer
365 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
392 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
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 ...
2
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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 ...
2
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1answer
691 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
867 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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2answers
86 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 ...
2
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1answer
45 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 ...
2
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1answer
93 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
69 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 ...
2
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1answer
86 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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3answers
530 views

how to simulate FX forwards

My question is how to do Monte Carlo simulation for FX forward contracts. Just imagine you have bought a bunch of FX forwards (in various currencies and various tenors) for hedging purposes and you ...
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3answers
869 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
181 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
194 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 ...
2
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1answer
349 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
702 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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0answers
34 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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0answers
73 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
53 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
63 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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0answers
214 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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0answers
153 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 ...
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0answers
102 views

Control Variate Barrier Basket Option

I need to improve the speed of convergence of PRNG Monte Carlo. I'm opening a new thread for that purpose and I have question / need confirmation about the algorithm. I'm pricing options with Heston, ...
2
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2answers
414 views

Monte-Carlo simulation Hull-White process: physical and risk-neutral measure

From Monte-Carlo simulation Hull-White process I get paths in risk-neutal measure. How can I get paths in physical measure?
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0answers
195 views

Quasi Monte Carlo method and Heston model

I want to run a quasi monte carlo simulation for Heston model in matlab. Obviously there exists a lot of literature regarding the theoretical aspects of the topic, for example by Baldeaux and Roberts, ...
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0answers
106 views

Monte Carlo Simulation of Spread Strategy. Two correlated assets vs One spread simulation?

I am trying to simulate paths of a certain spread strategy such as a calendar spread between two futures ( May Crude vs Aug Crude) using a Monte Carlo simulation. My questions is there a difference ...
2
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3answers
205 views

Non-convergence in Monte Carlo

Trying to implement some monte carlo simulation for the first time. For the sabr model (http://www.javaquant.net/papers/managing_smile_risk.pdf), would this work? Here, a = volatility of volatility, ...
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0answers
97 views

Monte Carlo approach to RAN bonds in Quantlib or suggestions

This is a problem from Schlogl's book in the chapter on the HJM model: Price option of the RAN instrument with 3 month coupons and maturity 3 years using Monte Carlo(Exercise 4 Range Accrual Note). ...
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0answers
381 views

Local volatility grids - Monte carlo - Implementation [closed]

I read the paper "Monte Carlo pricing with local volatility grids" (authors: D.F. Abasto, B. Hientzsch and M.P. Kust) and I would like to know if anyone on this forum had a chance to implement it as I ...
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0answers
930 views

Forecast of ARMA-GARCH model in R

I managed to forecast a GARCH model yesterday and run a Monte Carlo simulation on R. Nevertheless, I can't do the same with an ARMA-GARCH. I tested 4 different method but without achieving an ARMA-...
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0answers
1k views

Simulation of Heston process

I am currently working on implementing Heston model in matlab for option pricing (in this case I am trying to price a European call) and I wanted to compare the results I obtain from using the exact ...
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0answers
304 views

Initial values for Heston Model calibration

I'm doing a Heston model in Matlab using simple Monte Carlo simulations (5.000 paths and 2 steps per day, simulating 360 days). When I try to calibrate the Heston parameters using fminsearch it takes ...
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0answers
101 views

Practitioner's criterion for MC pricing convergence

Let's say I have some Interest Rates (IR) pricing model which relies on Monte Carlo pricing and I'd like to benchmark its quality and find out optimal settings (time steps & iterations) per asset ...
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0answers
943 views

How to price zero coupon bonds with the Monte Carlo method?

Im trying to calculate monthly ZCB bond prices with a fixed maturity T, over a period of months via Monte Carlo methods. Here is my attempt: For the first month, the price is $P_{t_0}(0,T) = E[exp(-...
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0answers
3k views

Models for simulating FX movements

My goal is to develop a model to simulate long term FX movements. (I am not sure if long term makes any difference, but if it does I am more interested in long term fx movements) These Monte Carlo ...
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2answers
293 views

What would be a concise method to learn Monte Carlo methods?

Is there a concise way of learning the core Monte Carlo Methods from resources available online? This leads to my next question which is what are the core ideas to learn in Monte Carlo methods?
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1answer
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Pricing a double barrier option using Monte Carlo (C++ & Python code included)

I'm trying to price an option with upper and lower barriers using MC where the payoff is $B_u$ when $S_t > B_u$, $B_l$ when $S_t < B_l$ and $S_t$ when $B_l < S_t < B_u$. I have written ...
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2answers
748 views

Accuracy Rebonato Swaption Approximation Formula among Different Strikes

Can somebody explain me if the Rebonato swaption volatility approximation formula is accurate for only ATM strikes, and if yes why? Can it also be used for ITM and OTM strikes? My foundings: Let $0 &...