Questions tagged [finance-mathematics]

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4
votes
1answer
109 views

forward variances under rough bergomi

I have seen in several papers on rough volatility using the following expression for the forward variances $$ d\xi_t(u) = \xi_t(u) \eta \sqrt{2H} (u-t)^{H-1/2}dW_t $$ Can anyone explain to me how this ...
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0answers
30 views

How to calculate the longest expected losing streak for a system that trades all the index members simultaneously?

For a trading system that trades only one security we can easily compute the longest expected losing streak using this formula: where: n is the number of trades, ln is natural logarithm, P is the ...
1
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0answers
53 views

Regime-switching interest rate in Black-Cox model

Consider a modification of the time-homogeneous version of the model by Black and Cox (Journal of Finance, 1976). The firm value $V$ follows a Geometric Brownian motion: $$dV/V = \mu dt + \sigma dZ$$ ...
2
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0answers
135 views

How to compute standard errors of an estimator with antithetic variates?

I'm pricing American options using Longstaff and Schwartz Least square method. When using the following Python code, I obtain nearly the same prices and standard errors as in the Valuing American ...
5
votes
2answers
568 views

Relationship between Vega and Gamma in Black-Scholes model

my question is the following one: I don't manage to prove that, in Black-Scholes model, single-signed Gamma options have values that are monotonic in the volatility. I am looking for an exhaustive and ...
0
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0answers
16 views

How do I calculate inflation adjusted CAGR?

I'm running backtests with monthly data going back to the 1920's and I'd like to compare different strategies using inflation adjusted CAGR. But I don't know how to calculate it. Would any of these ...
4
votes
1answer
82 views

Default intensity in Black-Cox model

Consider the model by Black and Cox (Journal of Finance, 1976). The default intensity function is defined in the usual way: $$h(t) \equiv - \frac{\partial \log P[\tau > t| \mathcal{F}_t]}{\partial ...
0
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0answers
36 views

Real domestic return

I would like to calculate the real domestic return of a foreign asset What I know Real price is $$P_{Real, t} = \frac{P_{Nominal, t}}{CPI_t}$$ where CPI is consumer price index. And I know that the ...
1
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2answers
117 views

Affine Structure Resolution for the Vasicek model

I would like to now how to solve the PDE of the affine structure under Vasicek.I am delineating the steps: First let's posit the OU process under a Risk Neutral Measure such as : \begin{align*} \...
1
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1answer
231 views

Pricing of forwards contracts

Of the courses I am taking in college this semester, two are Financial Mathematics and Derivatives. In each course, we learn different formulas to calculate the forward price of a forward contract. ...
0
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0answers
147 views

Yield-to-maturity (YTM) vs effective annual rate (EAR)

If the yield-to-maturity (YTM) on a bond is 5%, is the effective annual rate (EAR) on the cash flows associated with the bond also 5%? I know that YTM does account for the present value of a bond's ...
0
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0answers
35 views

High Frequency financial data [duplicate]

I really need high frequency data for my thesis. The data should contain the following columns: Time with format: yyyy-mm-dd h:mm:ss; Price; Bid price; Ask price; Bid volume; Aks volume; volume I ...
0
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2answers
160 views

Starting Point for understanding Financial Theory for a Statistician

I am a Master’s student in Statistics who is interested in the field of Financial Modelling. I have very little experience or knowledge of Finance and have mostly worked on introductory projects in ...
0
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0answers
27 views

Calculating currency indexes weights?

I was looking at this formulas: USD_INDEX= 50.14348112 × EURUSD^-0.576 × USDJPY^0.136 × GBPUSD^-0.119 × USDCAD^0.091 × USDSEK^0.042 × USDCHF^0.036 and ...
4
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0answers
154 views

Summary of Stochastic Derivatives, Integrals, Expectations, and Variances

I wanted to make a summary table of stochastic functions to improve my understanding. Maybe the following should be a wiki page on this site so others can add functions and examples? Does the ...
0
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0answers
23 views

How can I calculate Total number of outstanding shares from a SEC 10Q report

I'm trying to calculate the total number of outstanding shares from a 10Q SEC repot. I dont see a field for that in the balance sheet. I noticed that there is As of November 12, 2020, 7,906,250 ...
1
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1answer
78 views

Investigating how rational price of European call option changes [closed]

Let S(0) = 100 be the initial price of the risky asset. Consider a European call option with exercise price K and expiry time T = 1 (year). Consider several binomial models and investigate how does ...
0
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0answers
30 views

Can LMSR be used in a decentralised way

I'm working on the link between Hanson's LMSR (Logarithmic Market Scoring Rule),[ref1][ref2], and I would like to know if it's possible to apply in some decentralised way. All whitepapers on AMMs (...
1
vote
1answer
154 views

What's the interpretation of the probability of default implied from CDS spreads?

What's the time horizon of the probability of default implied from a CDS spread? Given CDS = PD*(1-R), if I use a 5yr CDS spread in the formula, is the implied PD the probability that that name ...
0
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0answers
26 views

Quantifying the difference between 2 Foward Curves

I'd like to quantify the difference between 2 Foward Curves. In particular, I'd like to get a single metric which represents the magnitude of change between curve A and curve B. I'd like to plot this ...
-2
votes
1answer
81 views

Efficient frontier portfolio's analytical solution for a given expected return $r$

$$\begin{equation} \boldsymbol{w}(r) = \frac{r\mathbf\Sigma^{-1} \boldsymbol{\mu}}{\boldsymbol{\mu}^{\top} \mathbf{\Sigma}^{-1}\boldsymbol{\mu}} \end{equation} $$ is the closed-form analytical ...
1
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0answers
51 views

Concentration of measure phenomena in financial mathematics

Concentration of measure is a small area of statistics and probability theory that proved inequalities regarding the statistical properties of sets of random variables that exclude one of those random ...
0
votes
1answer
70 views

Sensitivity to changes in the volatility

I have a sample payoff function shown below: How do I find a formula which gives the sensitivity to changes in the volatility of the underlying stock. In other words, I want to find a formula for $\...
0
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0answers
52 views

Derivative Pricing of an Asset

The Stochastic Differential Equation that models the change in an asset price is $$ dS = (12S-sin(S))dt+\frac{\sigma S}{S^2+1}dX $$ where dX's are random variables drawn from standard normal ...
0
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0answers
45 views

Escape Dynamics in financial economics or time series

These slides describe escape dynamics to be a type of, or having some relation to, rare event(s). Black swan events in business cycles was also included under the definition of rare events. My guess ...
3
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0answers
141 views

Large deviations theory in finance

In probability theory, the theory of large deviations concerns the asymptotic behavior of remote tails of sequences of probability distributions. A related post says: Large deviations theory is ...
3
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0answers
77 views

Application of Ito's lemma relating to bond price

I'm interested in solving the following questions but I am confused on the second part because I do not know how to define/calculate the interest per "unit time", which I'm guessing is ...
0
votes
1answer
32 views

is price of multiple option strategy linear under expectation? [closed]

I wonder if someone can confirm (or refute) that the expected payoff of several option (in a strategy such as a spread, condor, etc) behaves as "expection of a sum is sum of expectations". ...
2
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0answers
57 views

How can you interpret one of the parameters of optimal consumption at the Merton portfolio problem?

Statement: Let the dynamics of wealth of the agent satisfy $$dX_{t} = \pi_tX_t\Big(\mu dt+\sigma dB_{t}\Big)- c_t X_t dt, \qquad \textrm{with}\quad X_0=x_0 \in \mathbb{R},$$ where $(\pi,c)$ is an ...
0
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0answers
31 views

Estimating the XIRR of a very non uniform cash flows

It's my second post, so please bear my lack of experience in this field. I've a very irregular cash flow (here you can see the set of date - cumulative cash flow) The XIRR, calculated with Excel, is ...
2
votes
1answer
121 views

Delta neutrality (derivation)

I'm confused about the math for the delta-neutral portfolio. Assume we have a short position in a European call option with price $p(t,S_t)$ and want to hedge it with the stock with price $S_t$. The ...
2
votes
1answer
174 views

Inverse Covariance Matrix Transformation from CAPM

Beginning with the CAPM model we have (with a risk free rate of 0%): $r_i=\beta_i (r_m)+\varepsilon_i$ with $\varepsilon_i$ the diversifiable risks per assets The variance matrix: $\Omega = \beta'\...
0
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0answers
64 views

Option percentage quotation for structured products

I am having some trouble to understand how option premium can be a percentage for structured products. For example, in an Equity Linked Note, let's say the bond part cost 80% of notional we have 20% ...
-1
votes
1answer
107 views

What are some of the more Math-oriented professional certificates in Finance? (more math-oriented than CFA) [closed]

What are some of the more Math-oriented professional certificates in Finance? In particular, I'm interested in learning about professional certificates that are more Math/Statistics-oriented than the ...
1
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0answers
67 views

Advice for senior thesis [closed]

I'd like to get my degree in mathematical finance, or eventually in quantitative finance. Could you give me some (original) ideas, maybe transversal between the two, on which to focus my thesis? ...
0
votes
1answer
127 views

Need help with understanding the Mathematical notation in a research paper

Shown below is a snippet from the paper Arbitrage-free SVI volatility surfaces by Jim Gatheral and Antoine Jacquier (2013) (https://arxiv.org/pdf/1204.0646.pdf) . The formulae shown below are on page ...
0
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2answers
176 views

Utility Function with respect to Quantitative Finance

I am trying to understand utility function and its application in quantitative finance. I have done some preliminary research on the same (have gone through Paul Wilmott on Quantitative Finance) but ...
3
votes
2answers
274 views

Forward skew generated by Local Vol model

I'm digging into the properties of the Local Vol model and I become confused with statements made by authors in papers/textbooks (without explanations) like, "The forward skew in local vol model ...
1
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0answers
28 views

No Arbitrage condition for assets with different time frame

In the classic literature, one always assumes that the assets in the market are all available from the very beginning ($t=0$). And under such condition the market is arbitrage free iff there exists an ...
2
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0answers
300 views

Why does the Hurst exponent pseudo code not match the Python implementation?

I am working on understanding the Hurst exponent calculation by Ernest Chan; however, the description of the algorithm does not match the Python implementation. Chan [Algorithmic Trading: Winning ...
1
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0answers
52 views

Unique risk neutral measure for jumps or incomplete markets for jumps

I wanted to understand why the market is incomplete in jump-diffusion models. whereas if we have a model following geometric Brownian motion then we can get a risk-neutral measure and hence a complete ...
0
votes
1answer
102 views

How can we unwind a Index ( SPX ) Variance swap?

Client A comes to dealer to trade variance notional $1m at T=0. The trade is executed with dealer short volatility with strike of 20. term Payoff of dealer = notional*( Stike^2 - realized vol^2 ) now ...
1
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0answers
87 views

Is there a scientific significance to Fibonacci numbers in economics?

I am new to the field and have read popular articles on Fibonacci numbers, but I did not find it grounded in academic research and would love to know if there is a research basis for this and whether ...
1
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0answers
85 views

Proof of variance reduction of bagging

In Lecture 4 of the following course: Advances in Financial Machine Learning: 10 Lectures by Marcos Lopez de Prado link in the proof of variance reduction for a ...
1
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2answers
289 views

May someone please explain the intuition behind the Black-Scholes Equation?

Consider the Black-Scholes equation for a European Call Option, \begin{equation} \begin{cases}\frac{\partial V}{\partial t} + \frac{1}{2}\sigma^2 S^2 \frac{\partial^2 V}{\partial S^2} + r\frac{\...
0
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0answers
13 views

Derive the equilibrium of the economy Arrow Debreu Economy

Consider a competitive financial economy with two securities and two dates, i.e. date 0 and date 1. There is only one commodity (consumption good), and consumption takes place only at date 1, while ...
0
votes
1answer
157 views

How does Linear-Exponential Loss (Linex) function tend towards Quadratic Loss function?

Thank you for your help everyone, and I apologise beforehand if this is a lousy or dumb question. I am looking to read up more on Quadratic Loss & Linex Loss, and forecast optimality. In my ...
0
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4answers
180 views

Expected return rate greater than required return rate [closed]

I am a beginner to finance, today I found a question looks very simple that I am not quite sure about it. Question: Given I am paid \$50,000 now, growing at $6\%$ per year for a total of 10 years, ...
1
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0answers
98 views

How does negative performance of a portfolio constituent affect its weight?

This is an easy question, I hope. Suppose we have a swap A with a long position, which, originally, has a weight of 30%. Over time, it has a positive performance of 3%, meaning we have a multiplier ...
0
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0answers
47 views

CIR from the summation of Ornstein–Uhlenbeck processes with different parameters?

Here I see how the CIR developed from OU s with the same parameters. I wonder how the solution will change if we are adding squared of OU processes with different parameters? In this proof, it is ...

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