Questions tagged [finance-mathematics]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0 votes
0 answers
66 views

Should we use the conditional expectation to write the value of an option?

So, I've just started looking into financial mathematics and the following question keeps bugging me. From what I understood, if the market is arbitrage-free and a given contingent claim of value $h$ ...
user avatar
  • 1
0 votes
0 answers
29 views

Calculating market risk premium and expected excess return? [closed]

I need some help with this calculation. Suppose that the CAPM is valid and that the market portfolio consists of 60% stocks and 40% bonds. The standard deviation of the returns on stocks and bonds ...
user avatar
  • 1
0 votes
0 answers
42 views

How to measure the difference between the trend of two curves

I'm looking for a way to measure the trend of two curves. For example, the figure below is my forecast for the S&P 500. It can be seen that although I haven't predicted the exact index price, the ...
user avatar
1 vote
1 answer
66 views

Vasicek interest rate of T-forward measure [closed]

I know dr of risk-neutrual measure is There is a price of a pure-discount bond can be derived by computing the expectation, I get: where A and B are: why dr becomes to: under T-forward measure?
user avatar
  • 11
2 votes
1 answer
112 views

Macaulay Duration - Liability matching

Can someone provide a detailed example to prove the following statement: "When the investment horizon is equal to the Macaulay duration of the bond, coupon reinvestment risk offsets price risk.&...
user avatar
  • 23
2 votes
0 answers
91 views

How did Bachelier characterize the Brownian motion?

The model for a stock price $$ dS_t=\mu dt + \sigma dB_t $$ where $B_t$ is a Brownian motion on $(\Omega, \mathcal{F},P)$, is commonly attributed to the work that Bachelier has carried out in his PhD ...
user avatar
  • 221
0 votes
0 answers
26 views

What is the Accumulation/Distribution formula doing geometrically?

My understanding of the essence of the Accumulation/Distribution Index is that it tracks the closing price of a security during each period relative to its price range for that period, something like ...
user avatar
0 votes
0 answers
56 views

What could be a real-life example of sectors and instruments in a Financial Market in the context of this Portfolio Optimization Problem?

Recently I've been reading about mathematical models in finances and economics; however, I encountered this book chapter: Nagurney, A. (1993). Financial Equilibrium. In: Network Economics: A ...
user avatar
  • 101
1 vote
1 answer
51 views

Does a bond pay a coupon at maturity? [closed]

I know a bond pays an annuity cashflow of coupon payments and then at maturity it pays the face value. But, at maturity, does it pay an additional coupon payment on top of the face value or are we ...
user avatar
  • 11
0 votes
0 answers
61 views

Elliott and Kopp Mathematics of Financial Markets confusion about proof of Lemma 2.2.5

In the book "Mathematics of Financial Markets" by R. J. Elliott and P. E. Kopp, Second Edition there is a claim made in the proof of Lemma 2.2.5., namely that $V_0(\theta)=V_0(\phi)$. I don'...
user avatar
  • 1
1 vote
0 answers
48 views

Adapted Roll measure implementation

I'm currently trying to implement the roll measure adapted by Easley et al. (2020, p. 22). https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3345183 The adapted roll measure is given by the eq below....
user avatar
0 votes
0 answers
21 views

Counterparty Credit Risk - Reference book for a mathematical introduction [duplicate]

Which book would you recommend for an introduction to CCR from a mathematical perspective? I would like to complement the Jon Gregory's book "the XVA Challenge" with a more quant oriented ...
user avatar
  • 1
1 vote
1 answer
146 views

Game theoretic description of stock market

I read the book "Theory of Games and Economic Behavior" by John von Neumann and Oskar Morgenstern. I think that stock market may be described by game theory. But here are the problems: ...
user avatar
  • 279
1 vote
0 answers
61 views

Simultaneous Stochastic Differential Equations

I was thinking about cointegrated time series and came up with the following simultaneous equations model: $dY_t = \alpha (Y_t - \gamma X_t)dt + \sigma dB_t$ $dX_t = \beta (Y_t - \delta X_t)dt + \tau ...
user avatar
1 vote
0 answers
46 views

Heston model (closed-form moments of returns)

Are there closed form expressions for unconditional moments (first, second) for stock returns under Heston model? Most sources provide the moments for the variance process in Heston model, but not for ...
user avatar
  • 11
5 votes
1 answer
595 views

Where does 1/2 in Fourier Transform method of pricing options come from?

I am reading Jianwe Zhu's Applications of Fourier Transform to Smile Modeling. On page 26, the author is describing how to use the Fourier tranform to price vanilla European call options. If $f_j$ is ...
user avatar
1 vote
0 answers
73 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 ...
user avatar
  • 163
2 votes
0 answers
64 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 ...
user avatar
0 votes
0 answers
50 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 ...
user avatar
  • 101
1 vote
0 answers
41 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 $$\...
user avatar
2 votes
1 answer
173 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 ...
user avatar
  • 21
2 votes
1 answer
145 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 $...
user avatar
  • 65
0 votes
0 answers
62 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 ...
user avatar
  • 3
4 votes
0 answers
97 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 ...
user avatar
  • 41
0 votes
0 answers
73 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 ...
user avatar
0 votes
0 answers
43 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 ...
user avatar
  • 165
0 votes
0 answers
57 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 ...
user avatar
  • 23
0 votes
0 answers
43 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 ...
user avatar
  • 165
0 votes
1 answer
220 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. ...
user avatar
0 votes
1 answer
56 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 ...
user avatar
3 votes
0 answers
285 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 ...
user avatar
2 votes
0 answers
57 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 ...
user avatar
4 votes
1 answer
261 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, ...
user avatar
  • 243
3 votes
2 answers
417 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 ...
user avatar
0 votes
1 answer
84 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 ...
user avatar
  • 55
3 votes
0 answers
86 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 ...
user avatar
  • 55
0 votes
1 answer
499 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 ...
user avatar
3 votes
0 answers
70 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: ...
user avatar
0 votes
0 answers
15 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.
user avatar
  • 1
2 votes
1 answer
202 views

Reflection principle of the Brownian motion

really appreciate some guidance on how to get the following equality:
user avatar
0 votes
1 answer
239 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 ...
user avatar
2 votes
0 answers
42 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 ...
user avatar
  • 55
0 votes
0 answers
36 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}...
user avatar
  • 1
2 votes
1 answer
246 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 ...
user avatar
  • 165
0 votes
1 answer
281 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 ...
user avatar
8 votes
1 answer
266 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 $...
user avatar
  • 446
0 votes
0 answers
29 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) ...
user avatar
2 votes
1 answer
73 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 }} - \...
user avatar
  • 123
0 votes
0 answers
49 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 ...
user avatar
0 votes
1 answer
158 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 ...
user avatar
  • 43

1
2 3 4 5
9