The tag has no wiki summary.

learn more… | top users | synonyms

1
vote
1answer
34 views

Desperate for help with simple derivative

Can someone help explain how differentiating the following with respect to $x$: $$ \frac{1}{2} \alpha \mathbf{x}^T \Sigma \mathbf{x} + (\mathbf{\mu} - R\mathbf{1})\mathbf{x} $$ Yields the following: ...
2
votes
2answers
42 views

Conditional expectation of a non stochastic process

In an example I was working through it was shown that $W_{t}^{2} - t$ was a martingale with respect to the Brownian motion filtration $\mathcal{F}_{s}^{W}$ with $t>s$. Everything was fine except a ...
1
vote
1answer
41 views

Is it possible that some types of financial systems can resonate?

Financial systems can certainly be modeled using the same tools physicists use to model dynamic physical systems. The validity of such is evidenced by models such as that developed by Black and ...
0
votes
1answer
40 views

How can we write swap as a chain of FRA's

For the rest of my question I use the notation from Brigo. The discounted payoff of a receiver interest rate swap (RFS) at $t<T_{\alpha}$, where $T_{\alpha}$ is the first resetting date, is given ...
2
votes
1answer
51 views

$\frac{1}{p(T_{i-1},T_i)}(A-p(T_{i-1},T_i))^+$ at time $T_i$ is equivalent to a payment of $(A-p(T_{i-1},T_i))^+$ at time $T_{i-1}$

How can I show that payment of $\frac{1}{p(T_{i-1},T_i)}(A-p(T_{i-1},T_i))^+$ at time $T_i$ is equivalent to a payment of $(A-p(T_{i-1},T_i))^+$ at time $T_{i-1}$ ? Where A is a deterministic ...
1
vote
1answer
75 views

derivation of heston pde in gatheral

Following Gather (the volatility surface, chapter 2) we assume the following process: $$ dS_t = S_t(\mu_t dt+\sqrt{\nu_t}dZ^1_t)$$ $$ d\nu_t= -\lambda(\nu_t-\bar{\nu})dt+\eta\sqrt{\nu_t}dZ^2_t$$ ...
0
votes
0answers
11 views

discounted price economic meaning

Could you please explain why we discount the prices using bank account or some numeraire, what is its economic meaning. Specifically The movement of the security prices relative to each other ...
1
vote
1answer
78 views

Arrow-Debreu Price in “The Volatility Smile and its implied Tree”

I was reading the old, but still interesting paper "The volatility smile and its implied tree" by Derman and Kani. I have a two questions about the derivation of the $2n+1$ equations, both of them ...
4
votes
3answers
219 views

How is stock data objectively different to this random walk?

I have a random walk that is generated as so using python, numpy, and matplotlib ...
1
vote
2answers
55 views

Weighting with restrictions, but no clear objective function?

I have 40 shares in an index and I want to weight them based on their market value, define the known value as $x_i$ In the traditional way, the weight of each share is calculated as: $w_i = x_i / ...
3
votes
2answers
182 views

Is linear programming important for quant?

I'm thinking about taking a course on Linear and Convex Programming, but I don't know how useful it is in the real world finance. Which areas in finance is mathematical programming used?
1
vote
0answers
47 views

Understanding Price Elasticities in Discrete Choice Models (Derivative)

I'am in the midst of a paper on mutual fund product differentiation by Li and Qiu. Here, the authors model the utility an investor derives from investing in a mutual fund using a Discrete Choice Model ...
0
votes
0answers
26 views

Real-World Cash Account Implementation and Return

Often in financial math, the concept of the risk-free cash account, with return R, is invoked as an instrument for calculating prices - when constructing an option-replicating portfolio, for example. ...
9
votes
2answers
1k views

Why Ito calculus?

Coming from physics, I am used to the fact that the Ito interpretation of most natural stochastic equations is wrong, and one should be using Stratonovich calculus instead (of course they are ...
-1
votes
1answer
72 views

Math basics of Equally-weighted Risk contributions

i'm writing my BA Thesis about "Equally-weighted Risk contributions". Can anyone recommend math books for further understanding of Risk contributions?
1
vote
0answers
30 views

Finding criteria for a household financial budget falsification

I’m working on a financial problem about budget of households. Households in a state fill a form about their net budget in every year and our insurance company investigate their financial status and ...
2
votes
1answer
91 views

Distribution of minimum of hazard functions

Suppose I have two random variables, $X_1$ and $X_2$, that are independent (but not identically distributed) and assume both have hazard functions $\lambda_1(s)$ and $\lambda_2(s)$, for $s > 0$. ...
3
votes
3answers
156 views

Budget Constraint in Sharpe Ratio Optimization

I am a math student and I am trying to understand the budget constraint in Sharpe Ratio optimization for portfolio design. Recall the budget constraint requires that the sum of the portfolio weights ...
3
votes
1answer
144 views

PDE pricing of barrier options in BS

Path-dependent options in BS framework is intuitive to price with monte-carlo under risk-neutral measure, however it appears that several kinds can be priced with PDEs. I understand how does the story ...
4
votes
1answer
77 views

backward Kolmogorov equations - Markov properties

I'm a physicist who's research has lead him into the theory of stochastic differential equations. If this question is not appropriate for this forum, please feel free to delete it. So I've been ...
1
vote
2answers
292 views

Why is that a risk averse consumer buys the optimum insurance when there is actuarially fair insurance?

I think I understand the fact that when marginal utilities of the same function are equal (a consequence of the actuarially fair insurance), the independent variables in it must be equal -- right? But ...
1
vote
0answers
71 views

Sampling and/or asymptotic distribution of a function

Assume we have the following function: $$f(p) = \frac{1}{(1-p)d}\ln\left(\frac{1}{T}\sum_{t=1}^{T}\left[\frac{1+X_t}{1+Y_t} \right]^{1-p} \right)$$ where $d$ is a constant $T$ is a constant $X_t$ ...
0
votes
0answers
23 views

How to rightfully balance the share of the organization between departments after variable changes?

This is an abstracted version of the problem I'm facing and I have to tell you first, my question might not be precise and or even correct, so I hope you understand and in that case can improve the ...
9
votes
2answers
512 views

Is it possible to understand financial theory without mathematics?

I am trying to develop a short course on financial theory, covering the fundamentals of forward and options pricing, and 'efficient market' theory. I want to reduce the amount of mathematics to a ...
3
votes
0answers
52 views

FTAP in the model independent case, paper by Schachermayer

I have a question about the following paper by Beatrice Acciaio, Mathias Beiglböck, Friedrich Penkner, Walter Schachermayer. At the very beginning of the paper, on page 3, there are two definitions ...
1
vote
0answers
122 views

What is the right group of durations?

It seems that the group of durations commonly used in quantitative analyse is $\mathbf{R}$ but it seems to me that $\mathbf{R_+^*}$ could also be an interesting choice. While I am not aware of ...
1
vote
1answer
72 views

Get discount factors with limited knowledge?

I am facing the problem of just having this information: 6% coupon bond with 2.5 years to maturity, traded at a 100% clean price 4% coupon bond with 1.5 years to maturity, traded at a 98% clean price ...
1
vote
1answer
51 views

Why is the discount function non increasing if pure cash holdings are feasible?

I am struggeling with the question, for example lets take a swap with rate of 3.2 for one year and 3.6 for 2 years and Discount Factor 0.96899 for the first year and 0.93158 for the second year. ...
6
votes
0answers
151 views

Proving the asymptotic distribution of Manipulation-Proof Performance Measure (MPPM) (Paper by Goetzmann et al.)

In Goetzmann et al.'s (2007) paper, the authors derive a "Manipulation-Proof Performance Measure" (MPPM), which is a performance measure that is impervious to performance manipulation by fund ...
0
votes
1answer
412 views

Determine state price vectors?

I have 3 states with two assets, stocks and bonds. The bond has a payoff of 1 in every state of the world. And the stock has a current price of $S_0 = 100$ and ...
1
vote
0answers
109 views

Does it make sense to apply complicated mathematics to calculate with precision when the margin of error is +/-10%? [closed]

This is more of a philosophical question than general question. Quantitative finance applies highly complicated mathematics and has attracted very smart people to this field lately given the high pay ...
1
vote
0answers
87 views

How to show that the risk contribution function is or is not injective?

Assume a portoflio $w \in \mathbb{R}^n$, you can get the total risk contribution $\psi_i$ of asset $i$ by doing: $$\psi_i = w_i \frac{\partial \sigma(w)}{\partial w_i}= \frac{1}{\sigma(w)} \left[ ...
6
votes
1answer
855 views

What is exactly Euler's decomposition?

I have often seen the following statement in different paper: As $\sigma$ is homogeneous and of degree 1, we use Euler decomposition and write $\sigma(x)=\sum_{i=1}^n x_i \frac{\partial ...
4
votes
1answer
136 views

What is the analytic value of an asset's risk contribution, if $n=2$?

The marginal risk contribution of asset $i$ is defined by Roncalli in his paper on ERC as follows: $$\frac{\partial \sigma(x)}{\partial x_i} = \frac{1}{\sigma(x)} \left( w_i \sigma_i^2 + ...
-1
votes
2answers
186 views

What's the first time-integral of price called?

In general I'm wondering about the names of time-derivatives of price. E.g. in physics the first few time-derivatives of position are: f(x) = displacement f'(x) = velocity f''(x) = acceleration ...
2
votes
0answers
536 views

How to correctly construct a value- and equally weighted portfolio consisting of property-types?

A problem of which I couldn’t find the answer on the forum is about the construction of equally-weighted and value-weighted portfolio. I want to compute the equally-weighted property-type portfolio ...
3
votes
1answer
176 views

Foward-start option pricing

Consider a probability filtred space $(\Omega, \mathcal F, \mathbb F, \mathbb P)$, where $\mathbb F = (\mathcal F_t)_{0\leq t\leq T}$ satisfing the habitual conditions and is generated by $1 d $- ...
6
votes
4answers
608 views

What are the options for a mathematician to break into QF without working for a fund?

I have a degree in mathematics, and I've worked as a statistician and done some programming work. I'm very strong in my math/stats/programming background and have browsed some QF books, and I'm very ...
3
votes
0answers
298 views

Monty Hall Model

Given a fixed time period,say 3 days, the stock/market can go up,down or stay sideways. A hedge fund can long, short or use rangebound(options strategy) to bet for that 3 days closing level. Hedge ...
2
votes
0answers
159 views

Measure change in a bond option problem

This is not a homework or assignment exercise. I'm trying to evaluate $\displaystyle \ \ I := E_\beta \big[\frac{1}{\beta(T_0)} K \mathbf{1}_{\{B(T_0,T_1) > K\}}\big]$, where $\beta$ is the ...
2
votes
1answer
3k views

Hurst Exponent Calculation

I am trying to calculate the Hurst Exponent using Excel. I am facing a problem where the exponent value sometime goes beyond 1. Can someone share a link / material so that it will help me to calculate ...
4
votes
2answers
282 views

What is Heston's equation?

This paper mentions the elliptic Heston operator: $Av:= -\frac y2(v_{xx}+2\rho\sigma v_{xy} + \sigma^2v_{yy}) - (c_0 - q - \frac y2)v_x + \kappa(\theta -y)v_y + c_0v$. Then boundary value problem ...
4
votes
2answers
619 views

Implications of the Riemann hypothesis in finance?

I was recently at a seminar by a top hedge fund manager at a top university for finance students, when one of the finance professors asked him what do you think are important areas of research for my ...
9
votes
1answer
257 views

Is a linear combination of GARCH processes also a GARCH process?

If two time series follow a GARCH process, and a third is a linear combination of them, is the third also GARCH process?
5
votes
2answers
2k views

How does one go from measure P to Q(risk-neutral) when modeling an asset paying dividends?

I am really having a terrible time applying Girsanov's theorem to go from the real-world measure $P$ to the risk-neutral measure $Q$. I want to determine the payoff of a derivative based an asset ...
7
votes
1answer
301 views

When pricing options, what precision should I work with?

I'm wondering if there's any point at all in double-precision calculations, or whether it's ok to just do everything in single-precision, seeing how the difference on non-Tesla GPUs for single and ...
7
votes
1answer
898 views

application of lie groups in finance

Can some one kindly go over some of the applications and use of Lie groups in finance? The math is very rigorous and I don't fully understand it or the potential it could have. Let me share some ...
2
votes
0answers
141 views

Optimal stop-loss reinsurance

What are some methods for optimizing stop-loss reinsurance? I've found an article on the minimization of the variance. I also know about the method of average-at-range. Can we apply a method for ...
11
votes
1answer
716 views

Any recommendations for textbooks for an undergraduate course in mathematical finance? [closed]

I'll teach an introductory course on mathematical finance in the near future. The course is intended to entertain and broaden some well-prepared advanced undergrad mathematics majors, some physics ...
25
votes
9answers
5k views

Recommendations for books to understand the math in quantitative finance papers?

Can anyone recommend books that explain the math used in quantitative finance academic papers?