# Tag Info

### Strictly local martingales: what is the intuition behind them?

I think to understand the martingale/local martingale distinction, it helps to bring in a third class of processes, the uniformly integrable martingale. I would argue that the local martingale and ...
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### 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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### Quantum Computing for Quantitative Finance

Try Quantum for Quants, which has contributions from people working actively in quantum computing, and some small scale examples solved on the D-Wave Systems Quantum Annealer. The picture below is ...
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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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### Historic Value at Risk - Ratios vs. Differences

As a short summary and adaption of the question: You better redefine $\hat{r}_i= \frac{S_{i-1}}{S_1}-1$ and $\hat{S}_i = (1+\hat{r}_i)S_0$. The above definition of $\hat{S}_i$ yields a sample of ...
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