Tagged Questions

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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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 $Q$-...
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How inplement monte carlo simulation in bdt model ? (interest rate)

I want to implement monte carlo method in Black–Derman–Toy model to preview short interest rates. $$d\ln r_t=(\theta_t+\frac{\sigma'_t}{\sigma_t}\ln r_t)dt+\sigma_tdW_t$$ Someone can explain what ...
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Black-Scholes PDE boundary condition question regarding limits

I'm working with the Black-Scholes PDE and I'm testing some things out by taking an initial condition for it as $\sin(S/50)$, where $S$ is the spot price. My issue comes with attempting to find the ...
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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 ...
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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 ...
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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 ...
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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 ...
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Why use Monte Carlo simulation?

I'm currently building a stress test that uses Monte Carlo simulation to generate the return profiles for the portfolio while applying static cash flows throughout the time series. The question is: ...
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Monte Carlo and volatility

I'm little confused with vol term used in MC projects. I want to calculate MC var for a 6M FX forward contract. I'm using the Cholesky decomposition to simulate different scenarios for the three risk ...
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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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Estimating VaR (Value At Risk) with only 3 days of data

I've been given daily stock prices on Day 1, 2 and 3 for 10 stocks (hence 30 data numbers in total) and asked to approximately the 1-day 95% VaR (Value at Risk) on Day 3. I'm not allowed to use any ...
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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 ...
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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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The difference between the binomial model and monte carlo simulation

In my project I have focused on the least squares method by Longstaff and Schwartz to find the lower bound of the American put option. I also focused on the dual method to find the upper bound of the ...
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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 ...
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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). ...
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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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measuring portfolio performance using monte carlo simulation

I have a financial portfolio comprising standard asset classes such as equities, bonds, and commodities. I developped a strategy (optimized) and I include it in the financial portfolio. I want to ...
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FX Counterparty Risk Modeling

We are building PFE model for FX derivatives including but not limited to outright and barrier options. For counterparty risk purpose, we are assessing whether black karasinski would be good for fx ...
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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. Can anybody help ...
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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 ...
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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 ...
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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 ...
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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-...
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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 ...
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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 ...
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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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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 !
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Simulating stock price with Monte Carlo under uncertainity

I'm trying to perform Monte Carlo simulation in order to check to what extent target price derived from Discounted Cash Flow(DCF) model may be influenced by changes in variables which are: EUR ...