All Questions
Tagged with finance probability
218
questions
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Is there a notion of approximation of continuous-time Markov processes by finite-valued Markov processes?
Recall that in practice, to simulate a Brownian motion on $[0,1]$, we usually use the interpolated process $X^n=(X^n_t)_{t\in[0,1]}$ between the jumps of a random walk $(S_k)_{k=1,...,n}$ with $n$-...
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38
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Should I consider the price for "option pricing" problem?
I'm trying to solve the following problem from "Probability and Statistics" book by Morris H. DeGroot and Mark J. Schervish.
Suppose that common stock in the up-and-coming company A is ...
- 81
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29
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Analyzing Expected Profit in a Symmetric Random Walk with Trading Actions
Problem Formalization:
I am examining a problem where a stock price $X_t$ follows a symmetric random walk starting at 10, and increments or decrements by 1 unit at each step with equal likelihood. The ...
2
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60
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Deriving the CAPM pricing kernel from the general SDF and consumption-based kernel
I'm reading the paper "Quality minus junk" by Asness et al. (2019) and trying to understand the pricing kernel definition they provide on page 6. The authors present the following pricing ...
- 21
3
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72
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Characteristic function of a random variable by Fourier transform
this is character function in probability theory
$$\phi(u)=\int_{-\infty}^{\infty}\mathrm{e}^{\mathrm{i}ux}f(x)\mathrm{d}x$$
Let an asset price $S_t$ (e.g. a stock) be modeled with a Geometric ...
- 33
2
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1
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88
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Heaviside under Geometric Brownian Motion
I'm new to using Geometric Brownian Motion, so I'm not sure if what I've done is correct.
Be the Geometric Brownian Motion $dS_t = \mu S_tdt + \sigma S_t dW_t$, $H$ a Heaviside, and $p_r, r_k$ ...
- 43
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1
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94
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The partial derivative of a call option with respect to $t$ [closed]
In Black-Scholes related computations, why do we not treat the stock price $S$ as a function of $t$ when taking partial derivatives with respect to $t$? For example, if
$$c(t,T)=SN(d_1)-Ke^{-r(T-t)}N(...
- 285
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78
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How to self-learn probabilities [closed]
Bit of background: I’m 27, graduated 4 years ago with a bachelors in Computer Science in which I did well. Since I graduated, I’ve been working as an algo trader for a bank. I’d like to start applying ...
1
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1
answer
51
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Interpretation of Value at Risk and its relationship with the upper percentile
I found this definition of VaR (Value at Risk) in a paper:
VaR is defined as the “possible maximum loss over a given holding period within a fixed confidence level”. That is, mathematically, VaR at ...
0
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1
answer
88
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Brownian motion X(t) is with probability 1 a continuous function of t
Here is an excerpt from "An Elementary Introduction to Mathematical Finance" by Sheldon Ross, 3rd edition:
I understand this is not meant to be rigorous, but I'm having trouble ...
- 303
1
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1
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102
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European Option Delta derivation
With the Black-Scholes formula for a call option:
$$P= S e^{-\delta T } \Phi(d_{1}) - K e^{-rT} \Phi(d_{2}) $$
With $d_{1}$ and $d_{2}$ as:
$$ d1 = \frac{\ln\left(\frac{S}{K}\right) + \left(r - \delta ...
- 39
1
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0
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54
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Foreign Exchange Fallacy
Suppose that:
\$1 is worth €1 now;
For next year, there's 50% chance that \$1 is worth €1.25 and 50% chance that \$1 is worth €0.8.
Then the expected value of \$1 in terms of euros is 1.025. However,...
- 119
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142
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Using the Kelly criterion, what is the maximum amount you should wager when the odds are unknown?
Thinking from a general, layman's perspective, when one cannot properly assess the risks of a particular situation, but still wants to apply probability to maximize chance of gains, how can one use ...
- 121
3
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1
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43
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Determine all values $\lambda$ for which $\mu \succ 0 \succ \upsilon$
Suppose an investor has a preference represented by the relation $\succ$ for which there is a von-Neumann Morgenstern representation with the utility function $u$: $$u(x)=\begin{cases} x & x\ge 0 \...
- 307
1
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1
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40
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Extracting a conditional density from a formula involving 2 stochastic integrals
I have a problem coming from a financial maths application, that involves trying to
extract the conditional density of a variable expressed as an integral over a Brownian motion, conditioned on ...
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