# 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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### Exploding Libor Rates in Libor Market Model

this is a well-known problem. One solution is to make volatility zero when rates exceed a certain high level. It's less problematic than it looks because any cash-flows generated will be divided by ...
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### Model reference price of Limit order book

This reference price is also sometimes called intrinsic price. One of the simplest ways to improve it in regards to the mid-price (assuming you have the depth data) is the following: define a ...
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### How to generate simulated stock price from historical data using R?

This approach is rather crude. It only takes the mean and volatility of the historical returns and assumes a very simple model. I'm not sure if you have much experience with Time Series, but your ...

### Terminal Variance in the Heston Model

From the equations of the model it is clear that $v_t$ is the instantaneous variance of the log-returns, not the terminal annualised variance of the log-asset price. Put differently, you are you ...
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### Python libraries for Monte Carlo simulations?

Try Quantlib https://www.quantlib.org, it comes with everything you need.
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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 Dickey–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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### Monte Carlo - Multivariate Simulation of Returns

You should apply it to the covariance matrix and from that compute the correlation matrix. Here's an example correlating 3 random normal variables. Let: $$\bf Y \sim \mathcal N(0, \Sigma)$$ where ...
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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 ...