Questions tagged [finance-mathematics]

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54 views

Calculation of divided in forward contract [closed]

I am reading the "Problems and Solutions in Mathematical Finance" from Eric Chin and Sverrir Olafsson and in page 15 they have a problem : Let the current price of a stock be $12.75$ that ...
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19 views

Simulating FX OPTION PRICE for Counterparty credit exposure under SA-CCR

I am looking to generate/simulate the prices for FX option price to calculate the counterparty credit exposure under SA-CCR. However, I have some doubt since I want to use PDE (Black-Scholes model) ...
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1answer
62 views

relation between risk averson coefficient and maximum Sharp ratio in Black-Litterman context

BL model compute the implied returns based on the reverse optimization where the objective is: $${\underbrace U_{{\rm{investor's \ risk \ utility}}} \buildrel \Delta \over = {\bf{w}}_M^T{\bf{\Pi }} - \...
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42 views

Mathematical Model in Overlapping games

Does anybody know, where can I find more details about the mathematical model of Karatzas and Shubik A Stochastic Overlapping Generation Economy with Inheritance, July 2000? I need some help and ...
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1answer
52 views

In what cases characteristic function of (log-)price process is known?

Hey I know that we can use characteristic function of log-price process to price different options. But when we know the characteristic function? I know that we can take Levy processes and constant ...
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Corporate finance equity valuation question (First year question)

Hi, This is a question from a first year finance course and I'm having trouble come up with the answer. I get so close but just not there. I unfortunately don't have the answers with me but if anyone ...
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36 views

how can properties of transition matrix be applied in the transcation cost of option

I am currently reading the PP BOYLE's article ' Option Replication in Discrete Time with Transaction Costs' written in 1992. Here is one place i couldn't figure out: Where does that $\widehat{p}$ ...
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106 views

Characteristic function of the Bates model

I have a misunderstanding concerning the derivation of the SVJ model : Firsty,I understand how to reach the final differential equation from : \begin{gather} dS_t = (r - q - \lambda t (e^{m-\frac{\nu}{...
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116 views

Why were Laguerre polynomials a good choice of basis functions for American Monte Carlo?

I am implementing LSMC to price American options based on a custom model. I now need to make a choice of basis functions, so I am looking for the theoretical justification for using Laguerre ...
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23 views

Q determined by the market in Binomial Model

I read in a book about change of measure, so that the discounted stock price in a binomial model is equal to the current price. Namely: $$E_{Q}[S_{1}/ \beta |S_{0}]= S_{0} $$ It then says: " Q is ...
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23 views

How to handle negative income tax when calculating EBIT

I am using the formula (Net income + interest expense + tax expense) to get my calculation What happens if the Income tax expense is negative for that year do you still add that negative number or do ...
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27 views

How to calculate NOPAT if the effective tax rate is 0 or negative

I am trying to calculate NOPAT for L S STARRETT CO. The effive tax rate I calculated for 2020 was -0.09% Operating Income was -5.3 mill. Using the NOPAT formula Operating Profit * (1 - tax rate) I got ...
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2answers
414 views

How do you derive this Carr-Madan-like equation?

How do you derive equation (3) below? The equation is tagged as equation (11) in this paper: http://janroman.dhis.org/finance/IR/Heston%E2%80%93Hull%E2%80%93White%20Model%20Part%20I.pdf There are ...
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158 views

Determining decomposition long bond yields via Fisher equation and the Expectations Hypothesis 2.0

I've started to get into the weed of UST pricing and was hoping to get some feedback on a "model" I thought about. It is presented in this blog post. https://nonlinearexpectations.blogspot....
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20 views

Additional requirement for the asset price and payoff to ensure the market is arbitrage-free

Suppose we have two risky assets and one risk-free asset in the market. The market is incomplete in that there are three assets and four states. The price vector at $t_0$ is: $\boldsymbol{p_0}=[p^s_{1}...
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1answer
97 views

Digital and binary put/call options

I'm looking for put-call parity for the call and put digital options, but I don't really know what is digital options and it's difference between ...
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1answer
52 views

Replicating Portfolio / Complete Market / Attainable Claim

Attempt So Far: 1) First Part: I have shown that the market is arbitrage-free since the only possible portfolio for which $V_1^h\geq0 \ $ given that $V_0^h=0 \ $ is $h=(0,0,0)$ and this clearly ...
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67 views

Expected value of P&L based on option prices

How can we compute the expected value of P&L assuming the option price is given? Do we need to have more information to calculate P&L?
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41 views

How does one transform the Black Scholes equation (u_t +0.5A^2 x^2 u_{tt} +Bxu_x - Cu= 0) to the heat equation [duplicate]

Given that A, B and C are constants, how does one transform (u_t +0.5A^2 x^2 u_{tt} +Bxu_x - Cu= 0) to the heat equation.
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88 views

Fractional Brownian Motion's Covariance Proof

Let's have the non independent Brownian motion such : $B_{H}(r)=\frac{1}{A(H)} \int_{R}\left[\left\{(r-s)_{+}\right\}^{H-1 / 2}-\left\{(-s)_{+}\right\}^{H-1 / 2}\right] \mathrm{d} B(s), \quad r \in R$ ...
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1answer
75 views

Coupon Adjusted Spread vs Z-Spread

Hi so I'm trying to figure out how to adjust for the coupon value in the Z-Spread of a given bond. For example we can take UKRAIN 9.75 11/28. The coupon is 9.75 which is quite a bit higher than the ...
3
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1answer
114 views

Justification for substituting “Itô differentials”

I'm reading Shreve's Stochastic Calculus for Finance, Volume II. In it, he uses the stochastic differential notation. For example, he may write $$\mathrm{d}X(t) = \sigma(t)\mathrm{d}W(t)+\alpha(t)\...
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1answer
92 views

Variance swaps and the Log-Moment formula

I was looking at the paper of Raval and Jaquier The Log Moment Formula For Implied Volatility available here : https://arxiv.org/pdf/2101.08145.pdf On the page 4 they wrote(with $<logS>_T$ and $&...
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1answer
84 views

ACT/360 and business day convention interest question

The question I've been stuck is: We have a deposit of 10 million on 2011-04-01 for 7 days at 4 percent, assume T+2 settlement, calculated with ACT/365 basis and following business day convention. (04-...
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59 views

Is the mean of a stationary timeseries the same everywhere?

Say for example I have the white noise process $Y_t\sim\text{WN}(\mu,\sigma^2)$. Is it true that $\mathbb{E}[Y_t]=\mathbb{E}[Y_{t-h}]$, where $h\in\mathbb{N}?$
4
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1answer
131 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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36 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 ...
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2answers
754 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 ...
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25 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
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1answer
102 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 ...
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40 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 ...
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2answers
147 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*} \...
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1answer
246 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. ...
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382 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 ...
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37 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 ...
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2answers
173 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 ...
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29 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 ...
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162 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 ...
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26 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 ...
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1answer
79 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 ...
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35 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 (...
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1answer
196 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 ...
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28 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 ...
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1answer
90 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 ...
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54 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 ...
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1answer
71 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 $\...
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54 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 ...
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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 ...
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165 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 ...
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80 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 ...

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