Questions tagged [pdf]

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Computing the Probability Density Function (PDF) for the Heston model

I am trying to compute the PDF for the Heston model using the Breeden Litzenberger formula. I have calculated the the Heston implied volatilities for a strike range (which i have interpolated using ...
3
votes
2answers
120 views

Interpretation of a uniform asset return distribution

Typically asset return distributions are bell-shaped with most mass occurring in and around the center, 0% returns, and less so in the tails, with the left tail representing the probability of large ...
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1answer
137 views

Which financial time series have a PDF and/or CDF?

Consider the following types of financial time series for a single publicly-listed stock: Price data Log returns Cumulative returns Each is computed from the item listed before it: log returns are ...
4
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2answers
180 views

Probability distribution of the stochastic process $\int_{0} ^{t}\frac{u}{t}dW_{u}$

I am wondering about the probability distribution of the stochastic process $$X_t=\int_0^t \frac{u} {t} dW_{u}$$ I thought of using the Kolmogorov equation but after converting this into An SDE $$...
1
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1answer
40 views

CDF&density of stock price modeled by standard brownian motion

Assume that the price of the stock follows the model $S(t) = S(0) exp ( mt − ((σ^2)/2 ) t + σW(t) )$ , (1) where W(t) is a standard Brownian motion; σ > 0, S(0) > 0, m are some constants. Derive the ...
4
votes
0answers
101 views

Alternative Method for Determining Option-Implied pdf

As I am refining a pricing model to incorporate skew, and not just ATM volatilities, I need to create random realizations of the underlying consistent with the skew-implied pdf. When searching, one ...