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2
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1answer
164 views

Distribution of Geometric Brownian Motion

Please let me know where I have been mistaken! Let the SDE satisfied by the GBM $S(t)$ be $$ \frac{dS(t)}{S(t)} = \mu dt + \sigma dW(t). $$ Then, the underlying BM $X(t)$ will satisfy $$ dX(t) = ...
4
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0answers
74 views

Does GARCH derived variance explain the auto-correlation in a time series?

Given a time series of $u_i$ returns where i=1 to t. $\sigma_i$ is calculated from GARCH(1,1) as $\sigma_i^2=w+\alpha u_{i-1}^2 +\beta \sigma_{i-1}^2$ . What is the mathematical basis to say that ...
3
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0answers
172 views

Kelly Capital Growth Investment Strategy (Example in R)

In the paper Response to Paul A Samuelson letters and papers onthe Kelly Capital Growth Investment Strategy pages 5 and 6 Dr William T Ziemba, gives a praticle example on Kelly Growth. I’m trying to ...
3
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0answers
54 views

Credit spreads vs default events dependence

Reading this note it strikes me that credit spreads and defaults seem not to be commonly modeled jointly (e.g. more or less directly in structural models), but at best with some kind of "ex post" ...
2
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0answers
62 views

Effective simulation of multi factor Heston model

Im looking for a quick way (as in runs quick, not necessarily is quick to implement) of simulating multiple square root processes for a stochastic volatility model, flexible enough to allow for ...
2
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0answers
141 views

Credit Valuation Adjustment Implementation

I am trying to help a friend with her thesis on Counterparty Credit Risk where she intends to have a somewhat lengthy treatment on Credit Valuation Adjustment (CVA). Specifically I am looking to help ...
1
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0answers
31 views

Order 1.5 strong SDE integration methods for systems with diagonal additive noise

I'm looking into simple-to-implement and efficient order 1.5 strong SDE integration schemes for my system. My noise is diagonal and additive (possibly time-varying). Thus methods designed for either ...
1
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0answers
662 views

Models for simulating FX movements

My goal is to develop a model to simulate long term FX movements. (I am not sure if long term makes any difference, but if it does I am more interested in long term fx movements) These Monte Carlo ...
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0answers
71 views

Problems with exact Heston simulations

I am just wondering if there is any problem with the so-called "exact" Heston simulations? So far what I have seen are the good things about it, what are the disadvantages? Because if it is so ...