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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20 views

Hindsight overhedge for pricing path dependent options

I understand how to use the longstaff schwartz method in Monte Carlo to compute the continuation value of path dependent options but someone recently mentioned another technique called "Hindsight ...
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33 views

Local Volatility with Monte Carlo Simulation

I am trying to implement a Monte Carlo Simulation using Local Volatility Model (Dupire’s Equation). I’m pretty sure I can build a very good LV surface, however, I do not know how to use it in the MC ...
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1answer
105 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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1answer
52 views

Control variate for pricing a best of assets option : $\mathop{{}\mathbb{E}}[ \max ( F^1_T,F^2_T, …,F^N_T )]$

I want to use Monte Carlo to price a best of assets derivative : $$\mathop{{}\mathbb{E}}[ \max ( F^1_T,F^2_T, ...,F^N_T )]$$ where the $F^i_T$ is the forward of the ith asset observed at expiry ...
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23 views

Monte Carlo Simulation with varying expected returns and volatilities

I have yearly CMAs which denote the 5-year forward looking returns and vols. These CMAs are updated every year. For example in 2004, the outlook for next 5 years is 11%, in 2005 the outlook is 10.8%. ...
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1answer
29 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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4answers
113 views

Python libraries for Monte Carlo simulations?

I am learning about monte carlo simulations and I have found many blogs explaining its implementation in python. Because its a widely known and an important technique for structuring asset prices. I ...
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1answer
107 views

Antithetic sampling Monte Carlo

In Peter Jaeckel, Monte Carlo in Finance book, I read the following sentence: Whenever the first realised moment of the underlying variate draws $\{z_i\}$ has a strong impact on the result of the ...
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1answer
29 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 ...
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2answers
252 views

What are some examples of non-solvable SDE where Monte Carlo discretization is necessary

Reading Glasserman - "Monte Carlo Methods in Finance" it says in the introduction to Chapter 6 - Discretization Methods, that moste models arising in derivatives pricing can be simulated only ...
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98 views

Least Squares Monte Carlo

Could you explain to me in words (no formulas) the concept of the Least Squares Monte Carlo method to price an American style option?
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1answer
101 views

How to compute estimate performance with variable returns and days held

I have a trading strategy that results in a number of holdings, each of which has a variable number of days held, and obviously, return. So, for example, suppose I run a Monte Carlo simulation, and ...
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2answers
357 views

Least-Squares-Monte-Carlo by Neural Network Estimator for pricing American Option Python [closed]

First I did the LSM (Longstaff-Schwartz) to understand how its work to price an American option. code for standard_normal ...
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31 views

Extreme Value Simulation from Copulas with Monte Carlo

I'm trying to simulate the tail values from a multivariate distribution using copulas. I'm using Vine Copula package of R to derive the suitable copula for my data and I generate random samples out of ...
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26 views

Solving the sde under the Bates Model

Can someone please help me to find a way to simulate or find an approximation for the sde? So far, I've come across some research papers that use the 'Markov Chain Monte Carlo' method. But are there ...
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32 views

Approximation of portfolio VaR (after mapping) when Delta and Gamma both equal zero

As titled, I am having trouble estimating the VaR of a portfolio mapped as a function of a single risk factor $S$, in the form : $$V(S) = S^3 - 30S^2 + 300S + 150$$ with current value $S = 10$. $S$...
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1answer
177 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 ...
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16 views

Longstaff Schwartz with future conditional coupons

I've implemented the L-S algorithm for a simple put option. I want to value a more complex derivative which has future conditional coupons which only occur if the option is in the money. How would I ...
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1answer
46 views

Multi-legged Swap pricing

can anyone guide me how to price a multi-legged swap and whether I need Monte Carlo / LMM based approach or if there is a closed form solution. Receive leg "Libor 3m +1%" Payment leg If Libor is ...
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29 views

Using Non-Risk Neutral (Risk Natural) Parameters to Price Options?

Please correct me if any of my following statements are false. My understanding as to why we use Risk Neutral Analysis is that it makes life easy, and ultimately, allows use to come to a closed form ...
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1answer
50 views

Generate scenarios of multiple related parameters

Assume I have three industry datasets: interest rates, inflation and unemployment. Data contains information of last ten years and it's monthly. Now, I would like to create N possible scenarios of ...
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0answers
39 views

Accuracy of Euler Monte Carlo discretization without knowing exact solution?

By using Euler Monte Carlo discretization (for a Hull-White model) we simulate $$r(t+\Delta t)=r(t)+\lambda(\theta(t)-r(t))\Delta t+\eta\sqrt{\Delta t}Z$$ with $Z\sim N(0,1)$, $\lambda$, $\eta$ ...
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How can I manually calculate the VAR of a call and put portfolio?

How would I solve the following question? Im unsure how to estimate the stock price using MCS.
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1answer
76 views

Ho-Lee short rate model under the Heath-Jarrow-Morton framework

Under the Heath-Jarrow-Morton (HJM) framework the dynamics of the Ho-Lee short rate model are defined as following: $$dr(t)=\theta(t)dt+\sigma dW^{\mathbb{Q}}(t)$$ with $\mathbb{Q}$ the risk-neutral ...
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47 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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1answer
71 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
544 views

Consistency of economic scenarios in nested stochastics simulation

I am interested in references on research regarding the consistency of economic scenarios in nested stochastics for risk measurement. Background: Pricing by Monte-Carlo: For pricing complex ...
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1answer
102 views

How can I conduct a basic Monte carlo simulation on 2 stocks?

I have 2 stocks in my portfolio A and B.A is currently at 50 dollars and B at 40 dollars. Correlation between A and B is 0. Let us say I bought the stocks today at 50 and 40 dollars. If I wish to use ...
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1answer
147 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 ...
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1answer
162 views

How to model High/Low prices for Stocks with Monte Carlo

I'm using monte carlo simulation to model stock paths and measure risk, but I was wondering if there is a way to simulate the full bar/candle chart with open, high, low and close prices , as I'm only ...
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1answer
71 views

How to price a barrier using monte carlo when return distribution is not iid?

this question is actually related to set the stop loss and stop return. Say after a liquidity shock, I want to place two stops, one being stop loss and another being stop return. If I use, say 10 ...
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43 views

Using variance reduction on only some models

I am pricing options with some copula based models using Monte Carlo simulation. I was looking up some easily implementable variance reduction methods and decided on antithetic variates. However, ...
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2answers
355 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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80 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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1answer
141 views

Monte Carlo Method for American Call Option (No Dividends)

I tried to pricing the American Call option using "Longstaff-Schwartz" least squares method. However, I found the American call option is always lower than the Monte Carlo European call option (they ...
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1answer
170 views

Implied volatility in Monte Carlo models

Suppose I want to get the implied volatility for a given option, whose process does not generate a closed-form formula. In that framework, how is the IV calculated, given the fact that bisection ...
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1answer
148 views

Hull white model Monte Carlo simulation Zero Coupon Bond

I am trying to use Hull White Model to price a zero coupon bond by Monte Carlo Simulation. The basic idea is under this equation: Under Hull White Model, I want to generate every short rate (r) and ...
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74 views

Numerical simulation of Heston model

I am trying to simulate on Python random paths for a general asset price as described by the Heston model: \begin{equation} \begin{aligned} dS_t &= \mu S_t dt + \sqrt{\nu_t} S_t dW^S_t \\ d\nu_t &...
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2answers
127 views

Do correlated assets affect the price of a portfolio of derivatives?

I need to compute the value at risk of a given portfolio as an exercise for a class at university but I have trouble understanding how correlated assets affect the price of the portfolio. Could you ...
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1answer
100 views

Monte Carlo computational cost

Hello. I'm reading the above paper and I do not understand how they managed to solve eq (17.35) -- i've seen many papers skip through this as trivial and didn't bother to show the method to get there. ...
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1answer
96 views

Monte Carlo for Asian Pricing

I'm trying to verify the accuracy of my Monte Carlo method for pricing mean options. I came across this paper that supposedly gives an 'exact' solution for the arithmetic mean option (asian). It's a ...
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2answers
99 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-...
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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}...
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101 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
111 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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1answer
159 views

Black's model and Monte Carlo

It is well know that one uses the Black 76 model to price commodity derivatives. I would however like to perform a Monte Carlo simulation that ties back to this number. How would one go about this ...
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1answer
66 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 ...
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1answer
109 views

How to calculate mean and volatility parameters for Geometric Brownian motion?

Say I have a time series $S_K$ for monthly asset prices for the last 30 years. I want to run a monte carlo simulation using geometric brownian motion $$S_t = S_0\exp\left(\left(\mu - \frac{\sigma^2}{...
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0answers
17 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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1answer
63 views

Monte Carlo simulated price and Black Scholes Price are giving a huge difference in my Matlab code

I have written a script for showing Monte Carlo Price for a increasing N. But comparing with BS results , This indicates a huge difference. Where is the error? Function : function [cpay,ppay] = ...