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
-2 votes
0 answers
26 views

Historical vs Monte Carlo backtesting

Im developing a new strategy thats evaluated on a metric $Z$ (not necessarily sharpe) and for not falling into backtest overfitting , I created a lot of synthetic data (it can be parametric or non ...
NICOLÁS ZANNI's user avatar
-2 votes
0 answers
57 views

Monte Carlo simulation via Excel - a very basic question [closed]

I am learning about simulation modelling / Monte Carlo using Excel. I've never done this before. I am looking at the Microsoft page https://support.microsoft.com/en-us/office/introduction-to-monte-...
Alex's user avatar
  • 117
0 votes
0 answers
36 views

How can we simulate daily return based on multi-factor model?

This is an interesting question for simulation. The question is a bit lengthy but I'm trying my best to make it super clear here. Now I have some multi-factor model, say some US barra risk model from ...
xxxtttsss666's user avatar
0 votes
0 answers
50 views

Monte Carlo simulation with SABR model

I have to price European Options using only the classical Monte Carlo method. The models I have to select are Lévy models and SABR. Consider for instance the simplest Lévy model: a Geometric Brownian ...
FrederickLearner's user avatar
2 votes
0 answers
91 views

Antoine Savine's store

In his book "Modern Computational Finance, AAD and Parallel Simulation", Antoine Savine writes page 263 in the footnote : "We could have more properly implemented the store with GOF’s ...
11house's user avatar
  • 93
0 votes
0 answers
56 views

Satisfying put-call parity in Monte Carlo option valuation

I am trying to price European call and put options on a stock using the Monte Carlo method, given some dynamics for the underlying that may or may not have a closed-form solution (e.g. Black-Scholes, ...
SupSquark's user avatar
0 votes
1 answer
99 views

Clustering of Maximum Drawdown Values in Monte Carlo Simulations (Jaekle & Tomasini example)

Hope this question isn't too naive. I've been trying to replicate the Monte Carlo method using sampling without replacement as described in the Jaekle & Tomasini book (Trading Systems: A New ...
djhanson's user avatar
0 votes
0 answers
34 views

cap/floor valuation in a hypothetical scenario using monte carlo simulation

How can I do a cap/floor valuation in a hypothetical scenario using monte carlo simulations of some interest rate model? My conditions: (For example) I want to do valuation of a cap option under a ...
Jan Bas's user avatar
0 votes
0 answers
73 views

Monte Carlo option pricing

Can someone please confirm if I understood this correctly. The Monte Carlo method for pricing path-dependent options essentially gives you a multitude of price processes, which you use to determine ...
artemars's user avatar
0 votes
2 answers
104 views

Why do we use a simple average for pricing options in MonteCarlo?

I was recently reviewing my notes on the Binomial Trees and MonteCarlo (MC) methods for option pricing. I've taken this for granted and just used the method....but I started questioning why we take a ...
Chet's user avatar
  • 237
1 vote
2 answers
268 views

Why do we adjust the drift in the geometric brownian motion

I am building a monte carlo based on the GMB, and I am having a hard time understanding why we subtract 1/2 variance from the drift. If I have a drift of 12% and a volatility of 50%, that would give ...
John's user avatar
  • 11
0 votes
0 answers
36 views

Understanding the application of Asset-Correlation to credit risk models

Suppose we have a portfolio of $n$ credits. In order the estimate the Portfolio Value at Risk (99,9) we use a standard vasicek model with the Ability to pay variable $A_i=\sqrt{\rho}x+\sqrt{1-\rho}z_i$...
Alex's user avatar
  • 1
0 votes
1 answer
128 views

Monte Carlo methods: Choosing the best measure

When pricing derivatives using Monte Carlo methods, we take outset in the risk neutral pricing formula which states that we need to calculate the expected value of the discounted cashflows. To do this,...
Landscape's user avatar
  • 548
0 votes
2 answers
138 views

Method for using Historical Simulation method on an Instrument priced using Monte Carlo

I was speaking to a very esteemed professional in Financial Risk and he mentioned that he always prefers to use Historical Simulation as the method for his VaR even if he prices his Exotic derivatives ...
jonathan's user avatar
  • 133
0 votes
0 answers
42 views

Commodity forward curve Monte-Carlo

I need to value an Asian commodity option using Monte Carlo and a log-normal model. The inputs are the commodity forward curve and the volatility surface for futures/options expiry. Unfortunately, all ...
Sergey Chigrinov's user avatar
0 votes
1 answer
71 views

Forward Black Implied Volatility For Within Risk Neutral European Option Pricing

Going to preface this question with an acknowledgement with how silly the ask is, but alas that is the working world; if anyone can share any ideas I'm all ears. We're pricing an exotic option in risk ...
TheOneTwoThreeForPumpkin's user avatar
1 vote
0 answers
57 views

asian geometric option valuation-- unable to get monte carlo simulation to converge to analytic value

I'm trying to price asian put options in which the averaging window begins immediately (T=0). currently, I'm trying to match up geometric averaging between my Monte Carlo simulations and my attempt at ...
donpicante's user avatar
1 vote
0 answers
105 views

Closed-form equation for geometric asian call option

I'm looking to use the geometric asian option as a control variable for a monte carlo simulation. However, I have an issue with the closed-form equation to get the geometric price. I'm using the ...
Vpaq's user avatar
  • 11
0 votes
2 answers
247 views

Pricing European Call Closed Form Spread Options in Python

I am currently trying to correctly price European Call Closed Form Spread Options using Python. The main problem I am currently running into is that I have nothing to compare the option price so that ...
Coco Garazzo's user avatar
2 votes
1 answer
148 views

Generating normally distributed random numbers using Sobol generator in QuantLib

I am trying use low discrepancy Sobol RNG to generate normally distributed random numbers and fill an Eigen matrix with those random numbers. The matrix represents a basket of 5 assets (rows) each ...
Yoshiro's user avatar
  • 21
1 vote
0 answers
134 views

How can I use Monte Carlo to price a Zero-coupon bond in the Cox-Ingersoll-Ross model?

Let me prefix this by saying that, yes, Cox-Ingersoll-Ross (C.I.R.) is deprecated when used to model interest rates. Yet integrals of the form $$P(0,T) = E\left(\exp\left(-\int_0^Tr_s ds\right)\right) ...
Martin Erhardt's user avatar
4 votes
0 answers
114 views

Black-Scholes implied volatility using a GARCH model

Why I'm not getting the same Black-Scholes implied volatility values as the ones given in the paper "Asset pricing with second-order Esscher transforms" (2012) by Monfort and Pegoraro? The ...
StochasticNewby's user avatar
2 votes
0 answers
109 views

Is it possible to calibrate Mertons Jump Diffusion Model such that it matches mean and vola from a normal process without jumps? [closed]

I'm currently playing around with Mertons version of jump diffusion processes where i'm testing the predicitions of a trading model given a time series with and without jumps to isolate the effects of ...
T123's user avatar
  • 543
0 votes
0 answers
25 views

Backward induction: equation including expected values of stochastic process

Given the following SDE: $$ d\psi_t = \rho dt + \mu \psi_t dX_t$$, where $G(t) = \rho t$, $\rho = \frac{1}{T}$ $\psi_0 =0$, $T=1$, $\mu > 0$ and $X_t$ is a standard Brownian Motion (assume we know ...
5ilver4rrow's user avatar
2 votes
1 answer
102 views

Derivatives without analytic expressions? [closed]

I was wondering if there exist options or other derivatives that do not have a known closed-form analytic expression (i.e., some sort of Black-Scholes PDE) and are usually priced using Monte Carlo ...
Physics Penguin's user avatar
2 votes
0 answers
49 views

Benchmark Model for Path-Dependant Monte Carlo Simulations?

As part of my research for my masters thesis, I'm testing out the effectiveness of some different models in Monte Carlo simulations for path dependant options. I will be attempting a model-free ...
Rudy S's user avatar
  • 21
0 votes
0 answers
66 views

LSMC for Out of The Money paths

In the Longstaff & Schawartz article they condition on using In-The-Money (ITM) paths only for the regression. The reason for this is to obtain more accurate results and also reduce the ...
Landscape's user avatar
  • 548
0 votes
1 answer
115 views

Pricing VIX derivatives using Monte Carlo

I am looking at pricing VIX options and futures using Monte Carlo simulation. Most papers recognise that VIX can be written in terms of the S&P500 index itself, namely as: $$ VIX_t = \sqrt{-\frac{...
Sinbad The Sailor's user avatar
3 votes
0 answers
123 views

Continuation value in Longstaff-Schwartz: Why the expected value?

In the paper by Longstaff and Schwartz on American option pricing, the continuation value at time $t_k$ is given by: \begin{align} F(\omega;t_k) = \mathbb{E}_Q\Big[\sum_{j=k+1}^Kexp\Big(-\int_{t_k}^{...
arni's user avatar
  • 571
2 votes
0 answers
103 views

Problem matching prices of Black-Scholes vs. GARCH(1,1) in Duan (1995)

In the paper of Duan (1995) the author compare European call option prices using Black-Scholes model vs. GARCH(1,1)-M model (GARCH-in-mean). To be brief, the author fits the following GARCH(1,1)-M ...
StochasticNewby's user avatar
2 votes
1 answer
89 views

Piecewise constant Heston model Monte Carlo simulation

I am studying this time dependent Heston model \begin{equation} dS_t=(r-q) dt +\sqrt{V_t} dW_t^1 \\ dV_t=\kappa_t(\theta_t-V_t) dt + \sigma_t dW_t^2 \\ S_0=s_0\\ V_0=v_0\\ ...
User2089's user avatar
0 votes
0 answers
49 views

Monte Carlo Derivative Pricing

In order to try and price some derivatives with payoff $H(S_T).$ I am going to calibrate a few models (BS, Heston and CEV) to some real world data. Then I will calculate option prices as follows: ...
oskar szarowicz's user avatar
0 votes
0 answers
40 views

Is it possible to estimate 'future zero curves' using Hull-White 1 factor model?

With regards to the following: https://www.mathworks.com/help/fininst/price-bermudan-swaptions-with-different-interest-rate-models.html It seems to me that the HW1 model is used to generate the ...
user160738's user avatar
0 votes
0 answers
66 views

Correlating multiple two-factor hull white processes in the context of CVA

Let's say we have two rates processes (EUR and USD) both following a 2-factor hull white. Since it is in the context of CVA calculation, we calibrate both processes using Cap/Floors and swaptions (or ...
oumda's user avatar
  • 1
2 votes
2 answers
148 views

Use `LocalVolTermStructureHandle` in Python QuantLib

I would like to simulate a local volatility underlying $$ dS_t = S_t\sigma(t, S_t)dW_t $$ and have looked at QuantLib's LocalVolTermStructureHandle to do so. So far:...
rwicl's user avatar
  • 21
0 votes
1 answer
278 views

How to simulate a delta hedged option strategy

I'd like to do a montecarlo simulation of a $\Delta$ hedged strategy (long OTM call) to see how the PnL distributes on cases like: $\sigma_{bought} < \sigma_{realized}$ $\sigma_{bought} > \...
Oliver Mohr Bonometti's user avatar
0 votes
0 answers
61 views

Simulating of short rate model

I'm trying to simulate the risk factor of PFE from the interest rate model. For example, under Vasicek model : $$dr_t = k(\theta-r_t)dt + {\sigma}dW_t$$ with the analytic solution, we can simulate N ...
cactus's user avatar
  • 1
0 votes
0 answers
114 views

Understanding Monte Carlo Simulation with Stratified Sampling

I am studying Monte Carlo Simulation with Stratified Sampling following Martin Haugh's lectures notes. As is it explained the variance of the estimator is $$ Var(\hat{\theta}_{st,n}) = \sum_{j=1}^{m} \...
Hiram's user avatar
  • 1
5 votes
1 answer
161 views

Convergence rate of Bermudan to American option

When trying to value an American option we often use grid-based methods (e.g. Monte Carlo in combination with Longstaff Schwartz; or Finite Difference Methods). As such, we are in fact estimating the ...
Landscape's user avatar
  • 548
0 votes
0 answers
126 views

Quantlib Piece-wise Heston for Monte Carlo Path Generation

I am trying to use a piece-wise heston to generate paths for a Monte Carlo Simulation. I create and calibrate a ql.PiecewiseTimeDependentHestonModel as in the example on the ql doc python site: https:/...
vman's user avatar
  • 31
0 votes
0 answers
117 views

Quantlib Monte Carlo using regular Volatility Surface, not Local Volatility surface

I am trying to run a Quantlib Python Monte Carlo simulation using either the ql.BlackScholesMertonProcess or the ql.GeneralizedBlackScholesProcess. I have a vol surface that I have generated using ql....
vman's user avatar
  • 31
3 votes
1 answer
374 views

Quantlib vol surface issue 'the black vol surface is not smooth enough'

I create a vol surface from the market and do smoothing(interpolation and extrapolation), and explicitly correct for any total variance decreasing on a given strike as we increase maturity. I create a ...
vman's user avatar
  • 31
1 vote
0 answers
151 views

Adjoint Automatic Differentiation

I'm currently benchmarking several Monte Carlo computing methods for sensitivities computation purposes. I've already done some implementation in Python using Numpy and MyGrad libraries and it's ...
Hilbert's user avatar
  • 43
2 votes
1 answer
141 views

Price of a simple autocall - Sebastien Bossu Advanced Equity derivatives

I am reading Advanced Equity Derivates by Sebastien Bossu and trying to do the exercises. In chapter 1 we have the following question : Consider an exotic option expiring in one, two, or three years ...
Leon's user avatar
  • 21
0 votes
1 answer
207 views

Choosing a time step in Monte Carlo simulation of forward rates in LIBOR Market Model

Lets talk about the Monte Carlo simulation of forward rates in Euler discretization scheme under the $T_N$-forward measure, a so called terminal measure. Suppose that we have a number of time steps ...
Hasek's user avatar
  • 764
1 vote
0 answers
94 views

MonteCarlo Value At Risk for futures portfolio

I wanted to ask, suppose I have a portfolio of futures of gasoline and other oil products eg ULSD (Ultra Low Sulphur Diesel), WTI (West Texas Intermediate) for different months. I want to compute the ...
Hustler885's user avatar
1 vote
0 answers
102 views

Speeding up Cutting Edge Quantitative Models on GPUs? [closed]

I have a very strong interest in the use of GPUs in quantitative finance, and am in search of algorithms/simulations/models that can have their runtime heavily reduced by GPU computation. What models, ...
GPUMan's user avatar
  • 11
-1 votes
1 answer
147 views

Pricing options in underlying problem

Let us look at options, which are cash settled, but instead of receiving cash, you receive the proportion from underlying asset with the same value as cash. Moreover, you can pay for these options in ...
lukas kiss's user avatar
2 votes
1 answer
246 views

Optimize interest rate swap calculations in Monte Carlo Simulation

I’m running a simulation in which I want to calculate the NPV of 100 swaps over 1000 (or even much more) different interest rate curves. It looks like Quantlib is not really fast in performing these ...
Oamriotn's user avatar
  • 355
0 votes
0 answers
36 views

How do I estimate volatility for MPR historical data

How can I estimate volatility with historical data for Monetary Policy Rate (MPR) to use in a short rate model? I could use regular techniques like simple standard deviation or max likelihood, but the ...
Oliver Mohr Bonometti's user avatar

1
2 3 4 5
11