Questions tagged [finance-mathematics]
The finance-mathematics tag has no usage guidance.
391
questions
1
vote
0answers
65 views
Mechanism design in continuous time models
I am interested in mechanism design and information design. Is there any part of the literature in financial mathematics that is associated with them. I mean could we bring somehow these topics under ...
2
votes
0answers
53 views
Zero coupon price using Vasiceks model under the Real-world P measure model
I'm wondering if there is a way to work out the formula for the price of the zero-coupon bond using the Vasicek's model (P measure). I have tried to find reference on it but could not, I don't know if ...
0
votes
0answers
36 views
Disecting a log diff transformation for time series analysis and prediction
I have been working in a predictive ML model that uses financial time-series as predictor variables. In one of the academic papers I used as reference, and to do feature engineering for building the ...
1
vote
0answers
38 views
Assymptotic behaviors of European options
In some of the numerical works on Black-Scholes generalized models, the boundary conditions on the truncated domain taken from the asymptotic behaviors of European call options, which is given by
$$\...
2
votes
1answer
124 views
Aggregating greeks to portfolio level
I have been asked to calculate/aggregate certain Greeks (delta, gamma, and vega) up to portfolio level for a portfolio consisting of a range of (long and short) equities, convertible bonds, and ...
2
votes
1answer
136 views
Interpolation of $\mu(t,X(t))dt+\sigma(t,X(t))dW(t)$
Let's assume that we have SDE
$$dX(t)=\mu(t,X(t))dt+\sigma(t,X(t))dW(t)$$
and we simulate it on a time grid which contains points $t_k$ and $t_{k+1}$. How can we then calculate value of $X$ at time $...
0
votes
0answers
50 views
Correlated Geometric Brownian Motion - Drift rate for different stocks from different countries
I am valuing a structured product where the payout function depends on the paths of two assets. The key in my valuation is to use Monte Carlo simulations of a payout function tied to a geometric ...
4
votes
0answers
87 views
Where is the Quadratic Variation Coming from in this One-Factor Cheyette Model?
I am having difficulty switching from a general interest rate model (the quasi-gaussian or cheyette model) and a specific version of this model. In particular, I assume the following instantaneous ...
0
votes
0answers
72 views
How do you do a geometric average if the numbers are unequally weighted?
If you have an investment of 54 months with the following returns,
year 1 = 15%
year 2 = -12%
year 3 = 14%
year 4 = 21%
last 6 months / year 4.5 = 8%,
what is the ...
0
votes
0answers
42 views
Difference between number of stocks and number of bonds: Predictable vs adapted
Let $\nu_k$ and $\eta_k$ denote the number of stocks and number of bonds in the portfolio. According to Schweizer, we need $\nu_k$ to be predictable and $\eta_k$ to be adapted. In the text, the ...
0
votes
0answers
49 views
How to calculate spot rate for maturity which does not have a zero-coupon bond?
How do I calculate zero-coupon yields for a maturity which does not have an equivalent zero-coupon bond?
For instance, let's say we have this spot rate curve:
t0.5=1%
t1=2%
And a bond which has a ...
0
votes
0answers
42 views
Difference between Risk minimization and local risk minimization
According to the survey paper "A Guided Tour through Quadratic Hedging Approaches" by Schweizer the risk function is defined by
$$R_t(\phi)=E[(C_T(\phi)-C_t(\phi))^2|\mathcal{F}_t]$$
When ...
0
votes
1answer
169 views
Game theory and stochastic calculus
Does anybody know any details of game theory literature combined with stochastic calculus in finance? If yes, please recommend some papers of any authors who are doing exceptional work on the filed. ...
0
votes
1answer
55 views
Evaluating principal and interest at different points in time [closed]
Consider simple interest and suppose we have a certain principal and interest at t=7 months, we want to find the value of that amount of money when t=3 months. I would like to do it in two different ...
3
votes
0answers
145 views
Deriving Bachelier Greeks
I am working on the Bachelier Model with r not equal to 0 as described in the first and most upvoted answer in following link:
Bachelier model call option pricing formula
This is fairly easy to code ...
2
votes
0answers
56 views
A question in information strucutres and probability measures - How are they connected?
Suppose that $\mathcal{I}=(X,\sigma^{\mathcal{X}},\mu)$ is an information strucutre, which is a probability space, where
$X=X^1\times X^2$ is the cartesian product of the individual finite sets of ...
4
votes
1answer
191 views
Mathematical solution to return decay of daily leveraged products (leveraged ETFs)
Daily leveraged ETFs have an inherent path dependence. An index performing (5%, -5%, 5%) on 3 days has an overall performance of 2.9%. A -1x leveraged ETF would perform -3.1%. At a higher volatility, ...
3
votes
2answers
408 views
How to derive this mathematical equation from the perspective of the mean-variance portfolio optimization?
Question
I found a simplified inequation to decide whether the new asset A should be added to my current portfolio B. If the following inequation is satisfied, the new asset A should be added to my ...
0
votes
1answer
69 views
Difference in pricing of American call and put
In Paul Wilmotts quantitative finance books he says that the the value of an American option satisfies the following
$$
\frac{\partial V}{\partial t}+\frac{1}{2}\sigma^2S^2 \frac{\partial^2V}{\partial ...
3
votes
0answers
75 views
Independent variable in pricing of strongly path dependent options
I am reading Paul Wilmott on quantatative finance where he discuss the pricing of strongly path dependent options.The payoff at expiry T depends on the path taken by the asset in the sense that it ...
0
votes
1answer
187 views
How to derive the relationship between gamma and theta?
I am trying to derive this formula Θ = –0.5 × Γ × S^2 × σ^2 to see where it comes from.
My thinking is that PnL = delta dS + Vdσ + 0.5Γ(dS)^2 + Θdt.
Assume we delta hedged and vega hedged, first and ...
3
votes
0answers
59 views
Manual Computation of Python QuantLib's NPV for Pricing of a Forward Rate Agreement
Following the question that I have asked on this link and response obtained, I have managed to price a 3x6 FRA using QuantLib Python, using the following codes:
...
0
votes
0answers
13 views
net working capital impact on free cash flow
Why does net working capital impact cash (why is it included in free cash flow calculation)? NWC is found by subtracting current assets with current liabilities none of which impact cash.
2
votes
1answer
190 views
Reflection principle of the Brownian motion
really appreciate some guidance on how to get the following equality:
0
votes
1answer
98 views
Is IRR a Nominal or Effective Interest Rate?
The definition of the internal rate of return is the interest rate that causes the net present value to equal zero. However, interest rates can be given in two forms: nominal and effective. So, is the ...
2
votes
0answers
38 views
Equivalence of expectation condition for contingent claims attainable and contingent claims super replicable
We have the following definitions for set of contingent claims attainable and contingent claims super replicable
I want to prove the following result
How do I show iii $\implies $ ii.I understand ...
0
votes
0answers
29 views
In-sample forecast accuracy of Beta (Kalman filter) CAPM
One can calculate time-varying betas (known from the CAPM) using the Kalman filter.
For example, one can calculate the in-sample forecast accuracy using the MAE.
$MAE = \frac{1}{T}\sum_{t=1}^T|\hat{R}...
2
votes
1answer
195 views
Proving the discounted stock price is martingale
Let $\mathcal{K}_s$ be
$$ \mathcal{K}_s=\{\tilde{V}_t(\theta):0\leq t<\infty,\,\theta\text{ a simple strategy}\},$$
where $\tilde{V}_t(\theta)$ is the discounted value process of the self financing ...
0
votes
1answer
110 views
Explanation for Different Piecewise Yield Term Structures from QuantLib Python
I am new to QuantLib on Python, but as far as I understand, there are different types of piecewise yield term structures which exist on QuantLib which are bootstrapped on a number of interest rate ...
8
votes
1answer
227 views
Realised variance under simple rough volatility model
Using the Mandelbrot-Vann Ness representation of fractional Brownian motion in terms of Wiener integrals, increments of the logarithm of realized variance $v = \sigma^{2}$, under the physical measure $...
0
votes
0answers
24 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) ...
2
votes
1answer
69 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:
$${\underbrace U_{{\rm{investor's \ risk \ utility}}} \buildrel \Delta \over = {\bf{w}}_M^T{\bf{\Pi }} - \...
0
votes
0answers
48 views
Mathematical Model in Overlapping games
Does anybody know, where can I find more details about the mathematical model of Karatzas and Shubik A Stochastic Overlapping Generation Economy with Inheritance, July 2000? I need some help and ...
0
votes
1answer
98 views
In what cases characteristic function of (log-)price process is known?
Hey I know that we can use characteristic function of log-price process to price different options. But when we know the characteristic function? I know that we can take Levy processes and constant ...
0
votes
0answers
36 views
how can properties of transition matrix be applied in the transcation cost of option
I am currently reading the PP BOYLE's article ' Option Replication in Discrete Time with Transaction Costs' written in 1992. Here is one place i couldn't figure out:
Where does that $\widehat{p}$ ...
4
votes
0answers
132 views
Characteristic function of the Bates model
I have a misunderstanding concerning the derivation of the SVJ model :
Firsty,I understand how to reach the final differential equation from :
\begin{gather}
dS_t = (r - q - \lambda t (e^{m-\frac{\nu}{...
8
votes
0answers
148 views
Why were Laguerre polynomials a good choice of basis functions for American Monte Carlo?
I am implementing LSMC to price American options based on a custom model. I now need to make a choice of basis functions, so I am looking for the theoretical justification for using Laguerre ...
0
votes
0answers
23 views
Q determined by the market in Binomial Model
I read in a book about change of measure, so that the discounted stock price in a binomial model is equal to the current price. Namely:
$$E_{Q}[S_{1}/ \beta |S_{0}]= S_{0} $$
It then says: " Q is ...
0
votes
0answers
91 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 ...
0
votes
0answers
49 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 ...
3
votes
2answers
496 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 ...
1
vote
0answers
21 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}...
0
votes
1answer
206 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 ...
1
vote
1answer
98 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 ...
0
votes
0answers
75 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?
0
votes
0answers
47 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.
3
votes
0answers
95 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$
...
0
votes
1answer
144 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
votes
1answer
116 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)\...
2
votes
1answer
101 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 $&...