Questions tagged [finance-mathematics]

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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 ...
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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 ...
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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 ...
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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 $$\...
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1answer
455 views

Yield Curve Flattening Trade

Relatively simple question, but came upon it in class and have not been able to come up with an answer: The two-year bond yield is equal to 4% while the 10-year one is equal to 10%. You want to put ...
2
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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
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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 $...
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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. ...
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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 ...
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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 ...
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2answers
430 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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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1answer
100 views

Force Index EMA calculation for stock indicator

I am trying to smooth a 13 period EMA Elder Force Index in c++, and nobody really describes this as anything more than : ...
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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
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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 ...
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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 ...
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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 ...
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1answer
227 views

Stochastic Interest Rates in Option pricing

My lecturer has written the slide below. The function B^T(t) is a zero coupon bond. I don't understand how V(t) can be a negative integral from 0 to ...
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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
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1answer
192 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
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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 ...
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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 ...
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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
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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 ...
3
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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: ...
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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
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1answer
190 views

Reflection principle of the Brownian motion

really appreciate some guidance on how to get the following equality:
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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 ...
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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}...
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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 ...
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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
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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 ...
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1answer
2k views

Market Making Strategies Found by Hamilton-Jacobi-Bellman Equation

Im working my way through the book "Algorithmic and High-Frequency Trading" (AHFT) by Cartea, Jaimungal and Penalva and i'm curious to see how the market making model with an exponential utility ...
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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
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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 }} - \...
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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
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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 ...
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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 ...
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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 $\widehat{p}$ ...
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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 ...
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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}{...
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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 ...
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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 ...
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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 ...
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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}...
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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 ...
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1answer
2k views

Forward Contract Price on Zero Coupon Bond

I'm trying to calculate the forward contract on a zero coupon bond where the forward contract matures at t=4. The zero coupon bond matures at t=10 and has a face value of 100. The price of that bond ...

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