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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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 ...
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366 views

How to deal with extreme cases in normal random numbers generation?

In order to generate normal random numbers, one usually generates random numbers following a uniform distribution $Z \sim \mathcal{U}(0,1)$ and then applies the reverse CDF function on them $X=\Phi^{-...
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711 views

BDT model implementation

I am looking for a nice and readable description of how to implement BDT model: $d log(r(t)) = [\theta(t)-\frac{\sigma'(t)}{\sigma(t)}log(r(t))]dt + \sigma(t) dW$. I assume I already have steady-...
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491 views

Black-Scholes under stochastic interest rates

I'm trying to implement the Black-Scholes formula to price a call option under stochastic interest rates. Following the book of McLeish (2005), the formula is given by (assuming interest rates are ...
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99 views

(Re) normalisation of random variable in Monte-Carlo simulations

I have a very simple model (CIR) with a very simple discretisation scheme (Euler) and I use it to do Monte-Carlo Simulations. It is working. Someone insisted that renormalization of my random ...
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386 views

How to do a Brownian Bridge with quasi-random numbers in the Heston model?

I'm required to use the Euler Monte Carlo method to compute the option price under Heston model settings. I know from some paper that the convergence is volatile for the Heston model with a plain ...
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309 views

Estimating early exercise boundary for American put

I am trying to estimate the early exercise boundary for an American put option. I can find the put value through the Longstaff-Schwartz LSM method. How do I obtain the early exercise boundary within ...
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266 views

What sort of order submission strategy would result in a random walk of trade prices?

I have written a simulation that matches buy and sell orders, keeps track of an order book and simulates trades. My first pass at order submission was to generate random orders around the bid/ask ...
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376 views

Divergence issue with my monte carlo pricer…

I am trying to implement a vanilla European option pricer with Monte Carlo and compare its result to the BS analytical formula's result. I noticed that as I increase (from 1 million to 10 millions) ...
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124 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 ...
4
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94 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. ...
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143 views

Geometric Brownian Motion - increasing simulations or smaller step size

I am running Monte Carlo simulations to estimate future share prices of some stocks. For stock A, I need 1 share price exactly one year from now. For stock B, I need daily prices for each trading ...
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327 views

Practical implementation of Libor Market Model

I am trying to implement a project about the BGM model, suggested in the book "The Concepts and Practice of mathematical finance" by Mark Joshi. My question is related to the forward volatility ...
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312 views

Practical implementation of Least Squares Monte Carlo (tweaks and pittfalls)

The Longstaff-Schwartz LSM approach is nowadays ubiquitous(at least in the academic literature) in pricing path dependant derivatives. Up to now I have mostly worked with lattice methods. My ...
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436 views

How to compute greeks using the adjoint Monte Carlo approach?

Assume I have a stochastic ODE $$dS = a(S)dt + b(S)dW,$$ with Euler approximation $$\hat{S}_{n+1}=F_n(\hat{S}_n)=\hat{S}_n+a(\hat{S}_n)h+b(\hat{S}_n)Z_n\sqrt{h}.$$ This allows me to create sample ...
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160 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 ...
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145 views

Whites Reality Check for Pair Trading

I want to use the Monte Carlo Method described in Aronsons book Evidence based Technical Analysis to test if a given pairs trading strategy is useless. First step there is to randomize the returns of ...
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205 views

Monte Carlo, convexity and Risk-Neutral ZCB Pricing

I've built a simplistic Excel monte carlo model to price a zero-coupon bond, but it came up with a slightly unepxected result so I wanted to confirm whether my maths is just a little rusty or my model ...
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52 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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142 views

Stopping Monte Carlo simulation once certain convergence level is reached

I'm creating a Monte Carlo simulation model which I use to price an European option with various pay-off conditions, hence I can't use Black Scholes. I want to stop the simulation once I am 95% sure ...
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919 views

When to use the real world drift and when the risk neutral one for a Monte-Carlo simulation?

Under what conditions should the drift be real world and when risk neutral when simulating Delta Hedging option pricing trading strategy any other? For 2. it should be risk neutral. For 1., it ...
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53 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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67 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 ...
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86 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 ...
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96 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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153 views

What is wrong in this GBM simulation?

I am trying to generate a few samples of GBM using the following very simple MATLAB code: ...
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386 views

Monte Carlo for MultiFactor Ornstein Uhlenbeck

I'm following loosely the exposition given in "Monte Carlo Methods in Financial Engineering by Glasserman. For a multifactor OU process: $dX(t)=C(b-X(t))dt+DdW(t)$ Where C and D are d*d matrices ...
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223 views

Picking from two correlated distributions

Can anyone provide a simple example of picking from two distributions, such that the two generated time series give a specified value of Pearson's correlation coefficient? I would like to do this in ...
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133 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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118 views

Sobol numbers in monte Carlo simulation

I wanted to figure how how much faster the Sobol quasi random numbers convergence to the B&S call price compared with pseudo random numbers. To generate the Sobol numbers I used the randtoolbox in ...
3
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118 views

QuantLib C++: Monte Carlo Engine with SequenceStatistics

I'm trying to implement a Monte Carlo PricingEngine that stores multidimensional statistics. I have done the following: Defined a Monte Carlo Trait that among other things stores as the ...
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106 views

Evaluation of the semi-closed Heston pricing formula for call options

I'd like to know, how the integral part of the semi-closed Heston pricing formula for call options can be simulated for a given set of model parameters. Monte Carlo simulations shoud work for this ...
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61 views

How do you deal with Inflation lag in a MC simulation?

Consider the UK RPI index. This index is published every month around the 15th (give or take a few days). The publication refers to the RPI index of the month before, so there is a lag of a few weeks ...
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350 views

How to simulate a CIR process using GPU and Matlab

I am trying to simulate a CIR process using Matlab and my GPU for effeciency. At the moment i run into some implementation problems due to the recursive nature of the discretization. The sheme I ...
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216 views

Convergence of GBM mean after simulation?

As a follow up of my previous question, I am now simulating the GBM step by step for $n$ steps. I am using the following implementation for the simulation: $$S_{t+1} = S_t \exp \left[ \left(\mu-\...
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295 views

Valuation of barrier options in Jump diffusion model

I am trying to evaluate the value of a Barrier option using Monte carlo method. The stock follows a jump diffusion model. I am using the method described in Metwally and Atiya. The authors describe ...
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269 views

How to Calculate a Monte Calo VaR estimation error

I'm performing a Monte Carlo to calculate value at risk (with a 3 dimension risk factor) Now, I would like to calculate the error of the estimation of the VaR with respect to the number of simulations ...
3
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47 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
140 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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549 views

Why does changing the time step size in my Monte Carlo simulation change my result a lot?

I have written some software to price a call option using Monte Carlo simulation. It produces a price which is consistent with the model when I set the time step as recommended in a tutorial that I ...
3
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137 views

Which quantitative tools are actually used for hedging energy price and volume risk?

I'm a finance professor and I am looking for someone with actual trading and risk management knowledge within the energy sector who can tell me about pricing and hedging energy (especially electricity ...
3
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216 views

Fitting stochastic variance distributions to index return data

I want to calculate option prices based on a realistic distribution of the underlying. The underlying is a liquid index such as Eurostoxx50. I think of two aproaches, both of them incorporate ...
3
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1answer
88 views

Monte Carlo Convergence

Let $\{X_i\}$ be an i.i.d. sample of $X$ with $E(X) = \mu$ and $Var(X) = \sigma^2$. We know a MC estimate converges to the true value almost surely by the SLLN. That is, $$ \bar{X}_n \to \mu, \...
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33 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
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1answer
77 views

Importance Sampling for Least Square Monte Carlo

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 ...
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45 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 ...
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592 views

Portfolio Optimization with Monte Carlo Simulation - How to do it with Excel?

If I have three asset classes and their historical weekly returns for five years, how can I construct a minimum variance portfolio and an efficient frontier plot with Excel? To do that do I have to ...
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382 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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94 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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66 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 ...