# Tag Info

Accepted

### Least Squares Monte Carlo

To compute the price of an American option or a callable instrument in general, at each potential exercise date, one is required to compare its continuation value (discounted risk-neutral expectation ...
• 14.7k
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### How to simulate Levy processes

You have many different options. Firstly, you know the characteristic function for the log stock price and, using inversion, you can recover the (inverse) distribution and density function and ...
• 16.2k
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### How are Brownian Bridges used in derivatives pricing in practice?

Yes, the term Brownian Bridge seems to be used loosely. I assume you are talking about continuously monitored barriers by the way, since you mention the probability of the barrier being crossed in ...
• 521
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### rate of convergence for Monte Carlo

The estimation error is a random variable and not a simple scalar. As such, when performing one-shot assessments, you could always end up observing that using $6400$ paths provides a "better" price ...
• 14.7k

### Least Square Monte Carlo - american Call Option

If implemented properly, least-squares Monte Carlo as originally suggested by Longstaff-Schwartz should allow you to identify sub-optimal exercise dates and a lower bound of the true option price. ...
• 14.7k
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### Multithreading Monte-Carlo pricing in QuantLib for a single product

Yes, it can work. However, keep in mind that: you'll be safer if you don't share any objects between threads; see my answer here, in particular the last point; even if you use different seeds, there'...
• 7,808
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### Why are Interest Rate Swaps not valued using Monte Carlo Simulations?

Forward rates are determined from current spot rates bootstrapped from traded instruments. The reason is that if the forwards were different from the ones inferred from the spot rates, there would be ...
• 5,835

### Limitations of Monte Carlo simulations in finance

The properties of standard Monte-Carlo are not determined solely by the underlying process. You need to include the instrument $f$ you want to price in your analysis as well. One measure for accuracy ...
• 2,023
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### Calibration by monte carlo, should I fix my seed?

It is not cheating. It allows you to make your results (e.g. prices, calibrated parameters) 'reproducible' which is good. However, fixing the seed can hide convergence issues. When the variance of ...
• 14.7k

### Limitations of Monte Carlo simulations in finance

When I was first tasked with implementing VaR using MC in the 1990s, I knew little about MC, and there were no good books. The draft manuscript of Reuven Y. Rubinstein, Dirk P. Kroese. Simulation and ...
• 12.6k
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### Understanding Monte Carlo to solve option price with local volatility

I'm going to go through a coded example to show how you might attempt this, using the python port of the QuantLib library. It will all seem a little mechanical, but hopefully it is instructive. There ...
• 3,056
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### Problem with pricing a call option using the Monte Carlo Vasicek model

To make sure that I understand the problem: you are trying to price a call option expiring at time 0.5, which will exercise into a unit notional zero-coupon bond with a maturity of 1.0 at a strike (...
• 845
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### How to perform Monte-Carlo simulations to price Asian options?

Instead of simulating the spot price, simulate its logarithm since the latter can be simulated exactly for any time step. \ln S_{t + \Delta t} = \ln S_t + \left( r - \frac{1}{2} \...
• 6,074
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### Pricing a double barrier option using Monte Carlo (C++ & Python code included)

Here are at least three mistakes in your code: p += s0 * exp(...) should be p *= exp(...). Your volatility and rates are per ...
• 6,074

### Local Volatility with Monte Carlo Simulation

Let the risk-neutral dynamics under your LV model be given by $$\frac{d S_t }{S_t } = \mu_t dt + \sigma(t,S_t) dW_t$$ Let's drop the drift contribution (not relevant here) and apply Itô's lemma to ...
• 14.7k

### Correct Monte Carlo simulation of local volatility models

[I think] the problem is with the SDE, rather than the numerical scheme At a glance, and as I commented, I think the issue you are coming up against stems more from the underlying SDE rather than the ...
• 1,399

### Monte Carlo approximation of call option on the maximum of two assets

I image you want to calculate the following payoff: $$\pi_T = \max\left[ \max(S_T^1, S_T^2) - K, 0 \right]$$ If dynamics are expressed with the following dynamic (from your code, it should be the case)...
Accepted

### Montecarlo pricing

Commonly, you do not use 'pure' matrix algebra when formulating a Monte Carlo valuation setup. If your options are of the European type, and you truly want to price all options in one go, you could go ...
• 7,035