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.

Filter by
Sorted by
Tagged with
1
vote
2answers
301 views

Pricing Exotics: Monte-Carlo is too slow?

I want to price exotic options under the exponential VG model and Merton's model to compare both models. To price exotics under Merton's model, I have written the code below. The output is the price ...
7
votes
1answer
5k views

How to simulate a jump-diffusion process?

I would like to price Asian and Digital options under Merton's jump-diffusion model. To that end, I will have to simulate from a jump diffusion process. In general, the stock price process is given ...
4
votes
4answers
372 views

Web-based Backtesting for Options Traders [duplicate]

Is there a good web-based option for back-testing of equity options trading strategies.
3
votes
3answers
3k views

rate of convergence for Monte Carlo

I would like to show explicitly the rate of convergence of Monte Carlo method to be $O(\sqrt{n})$, where $n$ is the number of simulation paths. Assume I want to do that with a price of a European call ...
1
vote
1answer
125 views

Can someone check this boundary condition for me?

At the moment I'm comparing plots between the implicit numerical Black-Scholes PDE and the Monte-Carlo Method for the Black-Scholes equation. However, for the particular boundary condition I'm using I'...
1
vote
2answers
128 views

FTAP wih Heston Model

The Fundamental Theorem of Asset Pricing (FTAP) is invoked when we say the time $0$ price of a European option with payoff $g$ is $e^{-rT}E_Q(g(S_T))$, with the hypothesis that $e^{-rt}S_t$ is a $Q$-...
1
vote
1answer
195 views

Is Poisson Disk Sampling an alternative to crude Monte Carlo and QMC?

I recently stumbled over Poisson Disk Sampling (here and the meditative version). I wonder if it is an alternative to crude or quasi Monte Carlo for very high dimensional integrals. It is not ...
2
votes
2answers
769 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 ...
1
vote
2answers
162 views

Monte Carlo Accuracy - Antithetic Variate Method

I'm self studying for an actuarial exam and I am curious about a property of the antithetic variate method for increasing the Monte Carlo price accuracy (i.e. For every random draw of $z$, also ...
0
votes
2answers
634 views

Black scholes model for down and out European call option using Monte Carlo

I tried to implement Matlab program computing the price of the European down and out call option using Monte Carlo and Euler discretization scheme. I have initial price S0=50, strike K=50, barrier ...
2
votes
1answer
59 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 ...
1
vote
2answers
102 views

Finding optimal drift, importance sampling, least square monte carlo

I am working with Importance sampling for Least Squared monte carlo and have now problems understanding the implementation of the Robbins-Monro algorithm for finding the optimal drift for finding ...
2
votes
1answer
345 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 =...
4
votes
2answers
703 views

Importance Sampling for pricing options with longstaff and schwartz

I have been asking this similar question before. However, I really want to be concrete and get and concrete explanation. I have been reading the paper by Moreni and try to implement the same ...
2
votes
0answers
88 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). ...
3
votes
1answer
788 views

Choice of time increment in Monte Carlo/ Geometric Brownian Motion (GBM) stock price prediction

I am playing around with writing a daily stock price prediction algo in Python using a Monte Carlo/GBM methodology. I know there are many other questions on here about this topic (here, and here), but ...
2
votes
1answer
210 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 ...
3
votes
1answer
475 views

Importance Sampling for Least Square Monte Carlo [duplicate]

I am currently trying to implement and model an Importance Sampling estimator for Longstaff and Schwartz algorithm for pricing American put options. It is used such that more paths are in-the-money ...
1
vote
2answers
439 views

Conditional probability of geometric brownian motion

I created paths using GBM to implement The stochastic mesh method. But the method requires the conditional distribution, given some S(t) the probability of S(t+1). I've searched and can't find this ...
3
votes
1answer
250 views

Is This A Viable Alternative Options Pricing Method?

i'm currently a high school student who hasn't gone past Algebra II, and thus I have minimal Calculus knowledge. I know the basics of Integration and Derivation (drop the coefficient, raise to the ...
7
votes
2answers
573 views

Interpret simulation results ($P$ and $Q$ measures)

I am struggling in interpreting results of my simulations. I use Monte Carlo algorithm to simulate stock paths and calculate option price. The notation: $r$ is a risk free interest rate, $T$ is time ...
1
vote
0answers
402 views

Pricing back swaptions corresponding to underlying swaps of Bermudan Swaption in calibrated LMM

I do not know to which swaption volatility matrix I have to calibrate the LMM in order to price back correctly the swaptions corresponding to the underlying swaps of a Bermudan Swaption. My problem: ...
1
vote
1answer
919 views

how to derive critical values for augmented Dickey–Fuller test (ADF) using Monte Carlo method?

Can anybody explain in simple terms how the critical value of the ADF test can be derived using Monte Carlo simulation?
1
vote
1answer
341 views

Is this formula correct to estimate a knock out option price using monte-carlo?

I have a knock-out option with barrier $L>0$ and strike $K$ that pays at maturity $(S-K)_+$. So, positive payoff occurs only in case the price stays below the barrier over life of the option. I am ...
3
votes
1answer
339 views

Pricing a log-contract using Monte Carlo

Having a payoff of log-contract defined as $$ \Pi_T = \ln \left(\frac{S_T}{S_0} \right) $$ How would you express the MC-estimator for the price of this contract? The stock price dynamics here is ...
0
votes
0answers
69 views

Generating process for stock price paths in this paper?

I am reading Longstaff and Schwartz Valuing Aerican Options by Simulation because monte carlo simulations, especially their use in option pricing, is interesting to me. However, I am having some ...
2
votes
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 ...
0
votes
2answers
128 views

Stochastic Simulation vs percentile-to-percentile map

I was wondering why someone would go to the trouble to generate random variables in scenarios that are not path dependent. Let me provide a simple (although somewhat contrived) example. Lets say that ...
3
votes
2answers
314 views

Convergence of the distribution of 0.05 quantiles through Monte-Carlo simulation

I am trying to get admitted to a masters in quantitative finance (I come from a computer science background), so next week I will have 3h to solve an exam in statistical computing using my favourite ...
1
vote
1answer
115 views

Andersen Broadie American/Bermudan Put

I'm trying to implement Andersen and Broadie's dual method for an upper bound (here) of a regular American Put. I understand the process to compute it, but I have a conceptual issue : everything ...
1
vote
2answers
675 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 &...
3
votes
1answer
264 views

American option - Upper bound

I have computed a lower bound for an american option through longstaff and schwartz's algorithm. Now I have to compute the upper bound as andersen and broadie does in their article linked. Can anybody ...
2
votes
2answers
171 views

Monte Carlo Methods for Pricing Derivatives

can someone please suggest a good book on Monte Carlo Simulation for Pricing Derivatives? Don't want a book which is too complicated like a PhD level. A Masters level should be good. Thanks a lot in ...
2
votes
3answers
176 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
votes
0answers
356 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 ...
8
votes
3answers
3k views

Simulate correlated Geometric Brownian Motion in the R programming language

In response to this question: How to simulate correlated Geometric brownian motion for n assets? One of the responses provides an implementation in MATLAB: http://www.goddardconsulting.ca/matlab-...
1
vote
1answer
169 views

Monte Carlo Option Pricing: Averaging Price Per Path

In Glasserman's book, he computes the price of an option by first computing the average price over each simulated price path. Once all the paths have been simulated, the average of all the payoffs is ...
5
votes
3answers
374 views

Can call options be priced with Least-Squares Monte Carlo?

I have been reading about Least-Squares Monte Carlo (using Longstaff & Schwartz algorithm) for option pricing. So far, I have only read examples that uses LSMC for american/bermudan PUT options ...
1
vote
0answers
107 views

Las vegas method?

In one of his winning paper, backward induction for future values, A. Antonov, quant of the year 2016, refer to the American Monte-Carlo method as the Las Vegas method. Is this name used appart from ...
1
vote
0answers
266 views

Is this a GARCH Monte-Carlo simulation?

I tried this as a simulation for a GARCH(1,1) model. Is it correct? (I'm not speaking about the code itself, which works, but the underlying idea). Here is plot (of ...
6
votes
2answers
8k views

Two correlated brownian motions

Is it true (see here, footnote 2, p.22 / p.14, without proof) that we can obtain two discretized brownian motions $W_t^1, W_t^2$ with correlation $\rho$ by doing $$d W_t^1 \sim \mathcal N(0,\sqrt{dt}...
4
votes
2answers
785 views

Monte Carlo based mean variance optimization

I was asked this question in an interview some years ago. It struck me as a poorly formed question. I thought I would put it out there to the community to see if I just simply missed something. ...
-1
votes
1answer
279 views

Payoff of a butterfly c++

I would like to price options (call, put,, butterfly) with monte-carlo method, but actually I need the expression of the butterflay payoff; Could you ^please help me !
7
votes
1answer
721 views

Libor Market Model Calibration

Currently I am doing a research on the plain vanilla multi-curve framework Libor Market Model meaning that no stochastic volatility is involved. I had the idea to calibrate to the swaption market. In ...
1
vote
2answers
1k views

Discrepancy between binomial model, Black-Scholes and Monte-Carlo Simulation

I try to use Monte-Carlo Simulation to price a 10-year call option. Based on below parameter, S = 1, X = 1, volatility = 80%, T = 10, risk-free rate = 0.22% The option value based on Monte-Carlo ...
2
votes
1answer
187 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 ...
1
vote
1answer
408 views

Timesteps in Vasicek model

When simulating stocks one can easily use GBM with only one random variable per simulation to create a new stock price in say 5 years, you don't need to create the whole asset paths if you don't need ...
1
vote
0answers
33 views

Optimizing Monte Carl integral calculation with control variate

For an exercise I am asked to calculate an integral with a monte carlo simulation, after that I need to optimize the results with a control variate. This was the given integral: $\int_0^1 \! \frac{\...
1
vote
1answer
214 views

Calculate control variate for monte carlo simulation

For an exercise I need to calculate $\mathbb{E}[X]$ with a Monte Carlo simulation. I need to use control variate $Y$ with $\text{Var}(Y)=2$ and $\text{Cov}(X,Y)=1$. I am asked to give the optimale ...
1
vote
1answer
112 views

Martingale correction for Andersen scheme with Interest Rate

I have implemented martingale correction to my Andersen scheme for Heston model, as it is in the paper (page 19-22): http://www.ressources-actuarielles.net/EXT/ISFA/1226.nsf/0/...