The finance-mathematics tag has no usage guidance.
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16 views
Show that the effective rate of simple a interest rate, decreases over time
Could someone please give me an indication as to how I could show the following: Show that the effective rate of interest, when accumulating using a constant simple interest rate, decreases over time.
...
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4answers
160 views
Determine the right order size with market making strategy
In a market market strategy https://web.stanford.edu/class/msande448/2017/Final/Reports/gr4.pdf, how can we determine the right order size? Assuming I use a market making strategy and on a specific ...
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1answer
44 views
Cash Flow News and Discount Rate News + Return
I will appreciate If someone help me to understand how the final expansion is made. Specifically, how CF & DR are drived. This model is introduced by Chen et. al. (2013).What Drives Stock Price ...
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0answers
26 views
Arbitrage and state price formulation
I must be missing something really obvious due to my temporary obtuseness. Can someone please help me see the obvious? :-P Thank you.
I am just browsing Darrell Duffie's Dynamic Asset Pricing Theory. ...
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0answers
24 views
Utility Maximization on a finite Probability Space. Possible mistakes in a paper?
I am currently reading this paper on utility maximization in a financial market model. On page 5 the author starts with the case of a finite probability space and on page 19 he considers the ...
4
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1answer
169 views
Struggling with tau in Black-Litterman
According to the omega formula in B-L tau is used in the Omega estimation to determine the degree of uncertainty given to views of the investor:
So, if tau is given a low value then the inverse of ...
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0answers
67 views
Dubious math in Thorp's magnum opus
I started reading Thorp's "Beat the Market" book and stumbled on a formula I can't figure out:
https://imgur.com/a/xqfViKt
What's the point in adding time to price and the whole probabilites ...
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0answers
23 views
How to examine the impact of the parameters in the Hull White Model on the yield curve
I want to examine the yield curve resulting from the 2 Factor Hull-White model. Is there any way to examine the influence of the parameters on the yields curve without calibrating the model?
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24 views
Impact analysis of parameters in the 2 Factor Hull White Model
Through the 2-Factor-Hull White Model you can model the yield curve if you have the parameters $a, b, \sigma, \eta$ given.
Is there any way to measure the impact of these parameters on the yield ...
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1answer
176 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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1answer
38 views
Develop a pricing formula for an American digital put option
This problem comes from concepts and practice of mathematical finance by Joshi Chapter 8 problem 9.
Develop a pricing formula for an American digital put option
Joshi's solution - He states that ...
5
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1answer
177 views
Modelling EUR/USD rate with Ornstein-Uhlenbeck model
I have a data set of daily EUR/USD rate for time period 2000-2018.
My goal is to model future behaviour of this financial time series using Ornstein-Uhlenbeck model: $$d X_t = \alpha (\theta - X_t) ...
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1answer
101 views
Change of numeraire in options with currency exchange features
FV of an EUR denominated option under "COP" risk measure is given by:
$$V_t^{COP} = D^{COP} \mathbb{E}_t^{COP} \left[X_T(S_T -K)^+\right]$$ where $X_T$ is the exchange rate COP/EUR.
Pricing the ...
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1answer
64 views
Negative VaR equivalent Volatility (VEV) and its meaning?
Can a VaR equivalent Volatility (VEV) as defined by KID/PRIIPS law be negative and what does it mean if it has a negative value?
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0answers
33 views
Return / yield of an ATM-Call Option on a zero coupon bond
The zero-coupon bond with unit face value and maturity S for a call option with maturity T and strike K is given by:
The bond prices $P(t,T)$ and $P(t,S)$
$$\begin{aligned} ZBC(t,T,S,K) = & P(t,S) ...
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0answers
29 views
Literature recommendation subordinator models
I'm looking for relevant papers covering subordinator models for stock price modelling. I have alreay read the paper 'A Subordinated Stochastic Process Model with Finite Variance for Speculative ...
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0answers
58 views
are there quantitative tools to work with python pandas?
I have a code written in python and I have all my data in pandas dataframe. Are there quantitative tools to apply to these dataframes? For example, I want to calculate rsi, macd and other financial ...
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1answer
96 views
Finding the process of $X/Y$
This comes from Mark Joshi's concepts of mathematical finance exercise 4 chapter 11.
If
$$dX_t = \alpha X_t dt + \beta X_t dW_t$$
$$dY_t = \alpha Y_t dt + \gamma Y_t d\tilde{W}_t$$
with $W$ ...
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1answer
39 views
Calculate min. win ratio needed for a bet to be profitable [closed]
If a bet 12000 to win 4000 my risk/reward ratio is .33 .
How often must I win the bet to be profitable?
I know it's 75% but have not found the formula yet.
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1answer
75 views
Mathematical definition of a hedge?
For two given portfolios/trading strategies I want to know what criteria need to fulfilled in order to call the one portfolio a hedge to the other. In other words; what is the mathematical definition ...
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2answers
305 views
Stop-loss start-gain paradox: Why is it a 'paradox'?
The Stop-Loss Start-Gain Paradox and Option Valuation: A New Decomposition into Intrinsic and Time Value, by Peter P. Carr and Robert A. Jarrow, in The Review of Financial Studies, Volume 3, Issue 3, ...
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47 views
Computing the Expectation to a Max function
if $X_T$ is log-normally distributed and $k$ is a constant, how do I compute:
$$E[\max(X_T-k,0)]$$
I can compute $E[X_T-k]$ and $P(X_T-k>0)$. I was thinking that an approach will be compute to $$E[...
5
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2answers
455 views
Long Gamma vs Vega
What is the difference between being long gamma and being long Vega?
I understand that gamma is the vol of delta and that vega is the vol of the underlying. However, I have also found that being long ...
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0answers
34 views
Annuity calculcation
Let $A_k$ denote the annuity paid at the end of year $k.$ If $V_0$ is the amount borrowed during $n$ years with an annual interest rate $r$ and the borrower pays at the end of each period $k$ ...
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3answers
117 views
Does longer time horizon necessarily imply reduced risk?
Is there a mathematical/statistical basis for the commonly-held belief that the longer certain assets (particularly equities) are held, the less risk the investor is exposed to?
Alternatively, is ...
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0answers
37 views
Evaluating contract $D$ where the stock follows the Black Scholes assumption
Ch.7 Mark Joshi Problem 14
A contract, $D$, pays $30\%$ of the increase (if any) of a stock's value in a year. If $S_t$ follows Black-Scholes assumptions, give a formula in terms of the Black-...
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1answer
35 views
4-point Trapezium rule for numerical integration
Background:
This is in reference to Mark Joshi's concepts of mathematical finance ch.7 problem 11.
Question:
We have in the Black-Scholes model: $S_0 = 1, T = 1, \sigma = 0.1, r = 0$. A ...
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0answers
36 views
Anti-thetic sampling and second moment matching
Background:
This is in reference to ch 7 problem 10 of Mark Joshi's concepts of mathematical finance.
Question:
A normal random generator produces the following draws:
$$0.68, -0.31, -0.49, -0....
-2
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1answer
49 views
Withdrawing monthly from a bank for 40 years [closed]
Consider you have $\$104107.4099$ in the bank with a $.33\%$ monthly effective interest rate. You plan to withdraw a fixed amount X every month for 40 years, such that you make 480 withdrawals in ...
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1answer
59 views
Properties of Brownian motion and filtration, Exercise 6.22, Joshi Concepts and applications to mathematical finance
Let $W_t$ be a Brownian motion, and let $F_t$ be its filtration then for $t > s$ we are asked to compute
$$\mathbb{E}\left[W_t^2|F_s\right]$$
We have $$W_t = W_s + (W_t - W_s)$$
and
$$W_t^{2} ...
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1answer
79 views
Mark Joshi, The concepts and practice of mathematical finance chapter 6 exercise 20,21
Find the Black-Scholes price of an option paying
$$(S_T^{\alpha} - K)_{+}$$ at time $T$.
Solution - The forward price is given by
$$F_T(t) = e^{r(T-t)}S_t$$
So,
$$F_T(0) = e^{rT}S_0$$
and
$...
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1answer
75 views
Mark Joshi, The concepts and practice of mathematical finance chapter 6 exercise 6 [duplicate]
Suppose a stock allows a geometric Brownian motion in a Black-Scholes world. Develop an expression for the price of an option that pays $S^2 - K$ if $S^2 > K$ and zero otherwise. What PDE will this ...
2
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1answer
147 views
Mark Joshi, The concepts and practice of mathematical finance chapter 6 exercise 4
Let an asset follow a Brownian motion
$$dS = \mu dt + \sigma dW$$
with $\mu$ and $\sigma$ constant. The constant interest rate is $r$. What process does $S$ follow in the risk-neutral measure? ...
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1answer
409 views
What is an adapted process
I am reading Björk, Arbitrage theory in Continous Time and I have noticed that he uses the term adapted proces a lot. I can't seem to understand what an 'adapted proces' is by the wikipedia article. ...
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2answers
492 views
Implied Volatility of stock on Think or Swim
Think or swim has this thing where they have do a implied volatility of a stock. I have chatted with the TOS people but they aren't terribly helpful. Regardless they did send me two images of what ...
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1answer
58 views
How to calculate Chande Momentum Oscillator for FX
I am trying to calculate a momentum oscillator for the EUR/USD pair and am confused. A formula I read referenced the sum of previous up days. What is a "day" considered in Forex?
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1answer
85 views
Mark Joshi, Chapter 5 Problem 2 of The concepts and practice of mathematical finance
If $$dX_t = \mu(t,X_t)dt + \sigma(X_t)dW_t$$
with $\sigma$ positive, show there exists a function $f$ such that $$d\left(f(X_t)\right) = v(t,X_t)dt + V dW_t$$ where $V$ is constant. How unique is $f$...
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1answer
47 views
Problems with Money Weighted Rate of Return [closed]
The market value of a small pension fund’s assets was 2.7m on 1 January 2000 and 3.1 m
on 31 December 2000. During 2000 the only cash flows were:
Bank interest and dividends totalling 125,000 ...
1
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1answer
107 views
Can someone please verify or disprove this Sharpe Ratio math logic for me
I want to start by stating a problem that I wanted to figure out initially so that this all ties in somehow. I initially wanted to figure out if individual securities in an efficient portfolio all ...
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1answer
114 views
Joshi, Exercise 2.7 Concepts of Mathematical Finance
Let $D(K)$ pay $(S - K)^2$ if $S > K$, zero otherwise. Show that if $D(K)$ is differentiable function of $K$ then the third derivative w.r.t $K$ is non-negative.
From what the hint in the book, we ...
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0answers
21 views
Bond price formula, redemption yield and no arbitrage
Given the 1 year bond with a price 98 and C as 8% on face value 100.
I want to find the implied single compounding interest rate.
I can solve for r via the bond price formula or I can just set up ...
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0answers
37 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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0answers
52 views
Mathematical quantification of compensation for risk
I am learning about the CAPM, and still new to this. In this framework, given a market portfolio M, and a portfolio P, we regress the excess return of the portfolio $r_P$ versus the excess return of ...
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104 views
How to find a probability of VIX moving from one price to another
I asked a similar question on here with a bounty. I decided to modify the question to simplify what I am trying to do. Is there a package on MATLAB or some other tool where I can find the probability ...
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2answers
80 views
I need liquidity metrics of a portfolio (2-5 bonds) that takes into consideration difference in size of bonds and maturity profile
Context: I have bond A from say Apple, Apple also issued different types of bonds , namely B , C, D, E bonds.
Bonds A B C D E are all same, except, they were issued at different times, have ...
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1answer
358 views
Volatility Forecasting of VIX
Background:
As we know, volatility in the long run is mean reverting. Given that volatility is mean reverting, when volatility is low, it tends to go up. When it is high and going down, it tends to ...
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63 views
Interpretation of the stochastic integral as a wealth process
An agent has wealth $X(t)$ at time $t$ and invests an amount $\Delta(t)$ of money into a stock $S(t)$ given by
$$
dS(t) = \mu S(t) dt + \sigma S(t) dB(t).
$$
In other words, the wealth process has ...
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0answers
13 views
Expressing the value of the levered firm using the APV method as a function of the debt ratio instead of the debt dollar amount
I'm reading a paper titled Reconciling DCF Valuation Methodologies (Oded and Michel, 2007, available here). In Equation (9) on pg. 25, the authors define the value of the levered firm, $V_L$, in terms ...
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1answer
260 views
Types of programming languages used for optimization in finance
I'm currently taking graduate finance courses, and wish to pursue a career in finance - in particular $\textbf{optimization in finance}$. To date, I've only been taught the GAMS programming language (...
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68 views
Is there a mathematical way of showing the slowing down of economic markets?
I'm currently taking a introductory mathematical finance course in university and recently on the news (BBC, etc), it states that the economic markets are shown to be slowing down for the next few ...
