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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554 views

(C++) Monte Carlo pricer for SABR model to test Hagan / Paulot formulas

I'm trying to test the so-called Hagan formula (p.6 of this paper) and the Paulot formula, order 1 only (eq. (43) p.19 of this paper. For this, i'm trying to use both Euler and Milstein scheme ...
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84 views

How to price lookback american option when its payment is distributed during its life

I would like to price a floating strike american lookback with a particular feature: I don't want to charge upfront the client, rather I would like to insert a "running fee", some sort of a dividend. ...
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51 views

Are radial basis functions popular in least squares monte carlo option pricing?

In a Longstaff-Schwarz setting option on several underlyings can be priced using least squares monte carlo. Using suitable set of basis functions, continuation values can be approximated using ...
3
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0answers
160 views

How can I estimate the time-varying θ term in the Hull-White one factor model?

I am trying to simulate the prices of bond indexes (e.g. Barclays Aggregate, IBOXX sovereign, IBOXX corporates) using Monte Carlo assuming that they follow the SDE given by the Hull-White model (one-...
3
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2answers
200 views

How to interpret and define statistics of GBM output

I am trying to model the future prices of a number of commodities. For this, I am applying geometric Brownian motion, writing a Monte Carlo code in Python. Given that I want to estimate tommorows ...
3
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0answers
2k views

Jamshidian's trick for Swaptions

Following Brigo$^1$ p.77, we can decompose the price of a swaption as a sum of Zero-Coupon bond options (Jamshidian's Trick). To do so, the authors suggest to find $r^*$ the value of the spot rate at ...
3
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0answers
89 views

Intraday Value at Risk approximations

We use full valuation of derivatives portfolios using scenarios from historical data. For simple contracts, this is relatively fast. For contracts requiring monte carlo simulation, this becomes ...
3
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0answers
872 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 ...
3
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0answers
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 ...
2
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0answers
53 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 ...
2
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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 ...
2
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0answers
60 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 ...
2
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0answers
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 ...
2
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0answers
77 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 ...
2
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1answer
132 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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510 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 $$...
2
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0answers
241 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 ...
2
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0answers
121 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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0answers
274 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, ...
2
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0answers
109 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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0answers
107 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). ...
2
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0answers
1k 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-...
2
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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 ...
2
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0answers
352 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 ...
2
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0answers
104 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 ...
2
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0answers
1k 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(-...
2
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0answers
4k 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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0answers
47 views

Hand coded algorithm for tangent algorithmic differentiation

I'm looking for a way to hand code the algorithm for the forward/tangent mode of algorithmic differentiation to calculate option Greeks with Monte Carlo simulations. The computational power is very ...
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0answers
50 views

Risk-Neutral covariance matrix of arbitrage-free Nelson Siegel

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 ...
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1answer
60 views

Heston Monte Carlo or FFT Pricing

I am trying to better understand the Heston model and its implementation. It seems like a lot of people use the FFT method for calculating the call prices during the Heston calibration, but the Monte ...
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0answers
40 views

Simulate correlated Brownian motions conditioned on future state(s)

Consider a model defined by 2 geometric Brownian motions $$dY_{1}(t) = \sigma_{2} Y_{1}(t)dW_{1}(t)$$ $$dY_{2}(t) = \sigma_{2} Y_{2}(t)dW_{2}(t)$$ with $Y_{1}(0) = y_{1}$, $Y_{2}=y_{2}$ and $dW_{1}(...
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0answers
20 views

Lognormal asymmetry implication on Value at Risk

To examine the Value at Risk implications for a portfolio consisting of a spot and futures time series I have generated a 1-day monte carlo simulation. I was long in the spot and short in the future (...
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1answer
93 views

Monte carlo delta calculation for Worst/Best Of Option

I try to calculate the Delta for WO by finite difference. For example, $K = 1.$ $$ S_t = S_0 e^{(r - d_1 - \frac{\sigma_1^2}{2})t + \sigma_1 W_t^1} $$ $$ F_t = F_0 e^{(r - d_2 - \frac{\sigma_2^2}{...
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1answer
118 views

Formula for quantiles of swaprates in the 1-factor Hull-White model

Is there a closed formula to approximate the quantiles of swaprates in the 1-factor Hull White model? Background The Hull-White is a Gaussian model for the short rate. Its mean and covariance ...
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0answers
55 views

Multiple layer Monte Carlo Option pricing

I have simulated 10000 price paths from the SVCJ model under $\mathbb{Q}$ from $S_{t0}$ until $S_{tm}$ and have computed one discounted option price $C_t$. I want to compute the numerical simulated ...
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0answers
389 views

Geometric Brownian Motion with Dividends

I am working on a problem and had a quick question. I understand that for Geometric Brownian Motion we use the formula: $$X_{t_n} = X_{t_{n-1}} + \mu X_{t_{n-1}} \Delta t + \sigma X_{t_{n-1}} \...
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0answers
111 views

Ultra Powerfull Vibrato Montecarlo for delta sensitivities of a not regular payoff

Ciao, I am working on a derivative with the following payoff at time $T$: $$ \sqrt{(S_T - K)^+} $$ where $S_T$ is the value of the stock at the expiring date. As usual we will assume $S_t$ to be a ...
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0answers
20 views

Benchmark values for exotic options with highly nonlinear boundaries

I have created some modifications of least squares monte carlo algorithm for pricing american options which gives me lower and upper bound. Now I want to test how good it works for options with highly ...
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0answers
142 views

Monte Carlo VAR with differente asset classes

I have found a very useful post regarding the use of Monte Carlo simulaton to obtain portfolio Value at risk, based on Cholesky decomposition, random variates, etc. This post I'm talking about is: Is ...
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0answers
30 views

Asian basket option variance reduction control variates monte carlo

I have priced an Asian put option with three underlying correlated stocks. Now I want to try to reduce the variance using control variates. I have found great ideas when there is one underlying (thus ...
1
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1answer
160 views

Simulating assets of different currencies

I have a situation as follows: One year call option on a Euro stock with a Euro denominated strike. Knock in feature as follows - The option can only pay out if the growth in the Euro stock over ...
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0answers
34 views

Determining the Relationship Between Monte Carlo Breaks and Model Volatility

I'm looking for a statistical test to understand the relationship (if any) between the model volatilities of a stochastic process, and the occurrence of 'break', defined as the instance when an ...
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0answers
81 views

Importance sampling procedure

I need someone to explain me the importance sampling method. There are several topics but the drift parameter $\theta$ when adjusting is never discussed. I read publications where $\theta$ was used ...
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0answers
109 views

Pricing a Path-Dependent Option with Heston

I want to price a path-dependent option (let's say for example an arithmetic average Asian option) under a Heston model. In a Black-Scholes setup, I use forward volatilities to do so. I want to apply ...
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0answers
124 views

Modelling VIX futures backwardation

I have VIX futures trading algorithm and would like to perform Monte-Carlo simulation of VIX and understand how my algorithm performs on each simulation. In this case, not only VIX should be modeled, ...
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0answers
112 views

Monte Carlo Simulation of correlated returns based on different frequencies

I am simulating through Monte Carlo, multivariate correlated returns of different products composing an Oil&Gas portfolio. The historical prices (from which I computed the log-returns) of the ...
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0answers
72 views

Monte Carlo Pricer for Express Certificate delivers wrong price [Mathematica]

So I wanted to price the following Express Certificate with this specific payout structure: If S1 > S0 -> 105.25 , else -> If S2 > 0.95*S0 -> 110.5 , else -> If S3 > 0.9*S0 -> 115.75 , else -> If ...
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0answers
57 views

Low estimator when valuing american option using Broadie and Glassermann Monte Carlo tree with antithetic branching (R)

I've been looking into Monte Carlo methods for valuing american options. Now, I found an R code by Stefano M. Iacus that values the option using a tree (based on Broadie and Glassermann) without use ...
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0answers
119 views

The last step of the Longstaff-Schwartz method

I'm reading An analysis of the Longstaff-Schwartz algorithm for American option pricing, by Clement, Lamberton and Protter. They define the stopping times (top of page 4) $$ \tau_j^{[m]} = \begin{...
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0answers
96 views

Monte Carlo convergence sample size

I'm studying Monte Carlo analysis but I find very counter-intuitive the computation of the minimum sample size in order to reach a certain level of precision. As stated in ...