# Tag Info

### Do basket options have a closed form valuation formula?

I'm not completely certain from your question, but I'm going to assume you have a basket of $n$ stocks with prices $S_0(t)$ to $S_n(t)$, and you want to price an option with payoff at $C(\tau)$ at ...
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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 ...
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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 ...
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### Pricing a log-contract using Monte Carlo

By definition, the payoff of a log-contract of maturity $T$ writes $$\phi(S_T) = \ln\left(\frac{S_T}{S_0}\right)$$ Let $\Pi_t$ denote the $t$-value of such a contingent claim. We are interested in ...
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Is there a place online where you can simulate strategies programmatically? Your best choice is most likely a service such as Quantopian or QuantConnect. Quantopian provides equity and futures data ...
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### negative values in geometric brownian motion

I agree with wrong formula in simulation, but think i understand the question. Here's my take on it: The reason SDE may seem to allow a negative value of x is because dW can be a large negative ...
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### What is actually going on in Monte-Carlo simulation for Mortgage backed securities?

In my understanding, the mortgage prepayment option, at any point in time, is a function of the value of the mortgage from that point in time forward. This value, in turn, is a function of the future ...
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### Reliable random number generation for Monte Carlo

You have misunderstood the statement in Matsumotos original paper. The original Mersenne twister guarantees, over its period of $2^{19937}-1$ (a number which I am sure you will agree is larger than ...

### 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 ...
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### Optimize interest rate swap calculations in Monte Carlo Simulation

Yes, it's possible. You can create the 100 swaps and their engines beforehand and only change the curves. If you're using the same discount curve for all swaps, you can even create just one engine ...
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### how to derive critical values for augmented Dickeyâ€“Fuller test (ADF) using Monte Carlo method?

The ADF test assumes the DGP $$\Delta y_t = \alpha +\beta t +\gamma y_t +\delta_1 \Delta y_{t-1}+\cdots +\delta_k \Delta y_{t-k}+\epsilon_t$$ The parameters are estimated using OLS on a sample of ...
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### Simulating a path of bond yields by Monte Carlo (Python)

I do not know Python but this is what I would do in Excel (I am assuming you are familiar with Excel and can then translate the steps into Python: Pick a time series of Bond Yields which has $n$ ...
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### How to model High/Low prices for Stocks with Monte Carlo

Some time ago I wrote an Octave C++ function to do just what you want and blogged about it on my blog. The link to the relevant post is https://dekalogblog.blogspot.com/2011/08/creation-of-synthetic-...
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### Shifted Log-Normal model

Let us assume we are interested in some (forward) rate $F_t=F(t,T)$ which we assume is log-normally distributed: $$\text{d}F_t=\sigma F_t\text{d}W_t$$ However, we observe market rates can in practice ...
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### Monte Carlo simulations in Python using quasi random standard normal numbers using sobol sequences gives erroneous values

It is happening because you're using the same (psuedo/quasi) random numbers for each time step. in your code here: ...
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