Questions tagged [stochastic-integral]
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7
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Path integral approach to price call option on zero coupon bonds
I am given the following identities:
$$
Z[J,t_1,t_2]=\int D W e^{\int_{t_1}^{t_2}dtJ(t)W(t)}e^{S}=e^{\frac{1}{2}\int_{t_1}^{t_2}dtJ(t)^2}
$$
$$
\int_t^Tdx\alpha(t,x)=\frac{1}{2}\left[\int_t^Tdx\sigma(...
- 133
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Calculate value of Integral of Wiener process $\int_{0}^t e^{\lambda u } dZ_u$
I am not quite sure how to solve this integral to be able to do numerical calculations with it. $\lambda$ is a constant, $u$ is time, and $Z_u$ is a wiener process. Can anyone provide some direction ...
- 131
1
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Integral of brownian motion wrt. time over [t;T]
From the post Integral of Brownian motion w.r.t. time we have an argument for
$$\int_0^t W_sds \sim N\left(0,\frac{1}{3}t^3\right).$$
However, how does this generalise for the interval $[t;T]$? I.e. ...
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Why this stochastic integral is calculated with Riemann integral
This picture is from Neftci's textbook, 'An Introduction to the Mathematics of Financial Derivatives, Third Edition'
What makes me uncomfortable is equation [10.61] In above picture.
In this equation,$...
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Parametric Stochastic Integral
I need help.
Defining the parametric stochastic integral
$$
F_t = \int_t^T\xi(t,s)g(s)ds
$$
$\\\\$
with $\xi$ a generic stochastic process such that $d\xi(t,s) = \mu(t,s)dt + \sigma(t,s)dW_t$, I'm ...
- 61
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What does it mean to "compute" an Itô integral?
I'm reading Shreve's Stochastic Calculus for Finance II. On page 191, Exercise 4.6, we are given the problem
Exercise 4.6. Let $S(t)=S(0)\exp\Big \{\sigma W(t)+(\alpha-\frac{1}{2}\sigma^2)t\Big\}$ be ...
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1
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Regression of stochastic integral on Wiener process
This question is a follow-up from the following: conditional expectation of stochastic integral
so I won't repeat myself regarding assumptions and notation.
Using Brownian bridge approach, we know ...
- 690