# Questions tagged [brownian]

The tag has no usage guidance.

7 questions
Filter by
Sorted by
Tagged with
45 views

### Derive the convexity adjustment for inflation YoY swap with unconventional payoff

I'm trying to solve for the convexity adjustment for an inflation YoY swap with unconventional payoff, where $I_i$ is CPI at time i: $Notional * ([I_i/I_{i-1}]^{Day Count Fraction} - 1)$ In the normal ...
49 views

### Brownian Motion for USD/EUR Exchange Rate [closed]

I'm writing in order to have a clear overview of the Brownian Motion applied to an Exchange Rate. Which elements would you take into account to calculate the Drift for an exchange rate? I re-mark the ...
• 19
1 vote
133 views

### How to prove that the following is still a Brownian motion [closed]

Given a Brownian motion $B_t$ on a filtered probability space, how can I prove that $W_t=B_t+\alpha t$ is still a Brownian motion, with $\alpha \in \mathbb{R}$? Is it always true? Do I need necessarly ...
• 33
243 views

### Proof: Brownian Motion Path Continious with Probability One [closed]

How can one show that the paths of the standard Wiener process are continuous in $T$ with probability one? Can we just proof it with the assumption of independence ? Thank You in advance!
185 views

### Itos Lemma Derivation notation

So in Hull (2012) the main point is that $\Delta x^2 = b^2 \epsilon ^2 \Delta t +$higher order terms has a term of order $\Delta t$ and can not be ignored as the Brownian motion exhibits the ...
138 views

### Ito formula for $Y_t=tB_t$

someone can help me to solve this problem: $B_t$ is a Standard Brownian Motion. Let $Y_t=tB_t$. Using Ito formula, find drift and volatility of $Y_t$. The result I found is $dY_t=B_tdt+t\cdot dB_t$ ...
1 vote
152 views

### SDE Parameter Estimation

Have a question about "How to estimate parameters for SDE with multiple Brownian Motions ?" Let's say $X_t$ follows the process: $dX_t=\mu dt+\sigma_1 dW_t^1 + \sigma_2 dW_t^2$ I think I've checked ...