Questions tagged [finance-mathematics]
The finance-mathematics tag has no usage guidance.
1
vote
1answer
53 views
How to modify binomial tree to incorporate one more asset?
I wonder, what would happen if we use the binomial tree to price exchange option, an option to exchange one asset for another at the expiry date. Payoff is $\max(S_1-S_2,0)$
For instance, I have two ...
4
votes
1answer
69 views
Barrier Option from binomial tree
What is the smallest information structure that is required for using the binomial tree to calculate the price of a barrier (up-and-in) option? My gut feeling is any node below the node that reaches ...
1
vote
0answers
25 views
Why no prepayment fee for the reverse mortgage?
I am currently studying the costs (to lender) of adding certain additional options to the reverse mortgage, including the option of prepayment. Would there be any scenarios of housing price/mortgage ...
1
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0answers
30 views
Is there a quantitative definition of a Quiet, Moderate or Accelerate market conditions?
i know the StdDev price technical indicator which is the standard deviation but this one has an absolute value.
The market conditions are:
Quiet: lower oscillation of price around a constant ...
2
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0answers
69 views
Pre-requisites for Finance Mathematics
I would like to pursue research in the areas of Financial Mathematics. Hoping to look into Operations Research, Risk Management and Stochastic Modeling. Anyone got some suggestions on useful resources ...
1
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0answers
45 views
Arbitrage argument and Market Quotes [closed]
Good day, I wanted to ask for help with a question from one of my exercise sheets.
For a share S the market quotes a given strike K in both european and
american styles. Use an arbitrage ...
2
votes
0answers
27 views
Stochastic integral representation of $F(T-s,X_s)$-type equations
For $T\in R$ given and fixed consider:
$$
{\rm d}F(T-t,X_t)=g(T-t,X_t)\,{\rm d}W_t.
$$
where $g(t,x)$ is a given functions and $X_t$ is a given process driven by a brownian motion ($dX_t=(...)dt+(...)...
0
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0answers
40 views
How to calculate this FRA
I'm not sure if FRAs should be calculated with annual interest or with monthly interest. Example:
Amount : 10.000
Interest rate contracted: 10% per annum.
Period-term to 3 months within 3 months.
...
2
votes
0answers
35 views
Transformation of random variables and second-order stochastic dominance
Suppose $X$ and $Y$ are two random variables where $X$ SOSD* $Y$. Let $g(\bullet)$ be a monotonic function and $X'=g(X)$ and $Y'=g(Y)$. Under what conditions of $g$ is
$X'$ SOSD $Y'$?
I know if $g$ ...
1
vote
1answer
53 views
How to check if $ E [\exp \{ \int_0^t \frac{Y_u^2}{1+Y_u^2}du \}]< \infty $
$dY_t=2Y_tdt+2\sqrt{1+Y_t^2}dW_t$ where $W_t$ is $P-$Brownian motion (Wiener process).
I have defined a new measure $Q$ where the Kernel density (In Girsanov theorem) is
$$ \phi_t = \frac{Y_t}{\sqrt{...
3
votes
2answers
169 views
Application of Ito's lemma
Let $X_t$ be some stochastic process driven by wiener process ($W_t)$ so it can be expressed as:
$$dX_t=(...)dt+(...)dW_t$$
Let $f(t,x)$ be some $C^2$ function. Define the process $Z_s=f(t-s,X_s)$ ...
0
votes
1answer
52 views
Monte Carlo simulated price and Black Scholes Price are giving a huge difference in my Matlab code
I have written a script for showing Monte Carlo Price for a increasing N.
But comparing with BS results , This indicates a huge difference. Where is the error?
Function :
function [cpay,ppay] = ...
1
vote
4answers
196 views
What are the benefits of publishing papers in mathematical finance/trading?
What are the benefits of publishing papers in mathematical finance and trading. Let us assume that the primary goal of a person/entity is to make money and reduce losses. Wouldn't publishing ...
2
votes
0answers
24 views
About buying and selling a cumulative parisian options
I ask my question here because I want to know more about the cumulative Parisian options introduced by M. Chesney, Mr. Jeanblanc-Picué and Mr. Yor in 1997, then developed by Hugonnier in 1999 and F. ...
1
vote
0answers
21 views
The deflator of reinsurance market is unique
How to prove that the deflator $\phi$ of the reinsurance market is unique when working in the equilibrium model?
That is, if we have a pricing function $\pi$, which satisfies:
$$\pi(Y)=E(\phi Y)$$
...
0
votes
1answer
56 views
Why do most interest rate formulas, and indeed finance in general, add 1 to a rate and then subtract afterwards? [closed]
For example, in the formula that shows the relationship between the nominal and effective interest rate shown below, 1 is first added to in/m and then 1 is subtracted from the result. What is the ...
3
votes
1answer
80 views
Hedging Value-Financial Mathematics
EXERCISE
We consider a free from arbitrage financial market $(Ω,F,P,S_0,S_1)$ with $α<S_0^{1}\cdot(1+r)<β$,where $$0<α:=min_{ω \in Ω} S_1^{1}(ω), β:=max_{ω \in Ω}S_1^{1}, α<β$$
Let ...
2
votes
1answer
80 views
Equivalent martingale measure exists if and only if $a < S_0^1(1+r)< b$
Exercise :
We consider a market of one period $(\Omega, \mathcal{F}, \mathbb P, S^0, S^1)$, where the sample space $\Omega$ has a finite number of elements and the $\sigma-$algebra $\mathcal{F} = 2^...
2
votes
1answer
91 views
Showing that a market model has arbitrage and describing martingales
This is an exercise which I came upon while studying an introduction to financial mathematics.
Exercise :
Consider the finite sample space $\Omega = \{\omega_1,\omega_2,\omega_3\}$ and let $\...
3
votes
1answer
154 views
Total Returns From Adjusted Close Prices
I'm trying to understand why the total return (return including dividends) that I get from calculating return using adjusted close price, does not equal the total return calculated in another manner.
...
1
vote
1answer
44 views
Approximation of Forward Rates in discrete time
The forward rate from time $t$ to $T$ ($f_{t,T}$) can be approximated by:
$$
f_{t,T}= \left[ \frac{(1+r_T)^T}{(1+r_t)^t} \right]^{\frac{1}{{T-t}}}-1
\sim
\frac{(1+r_T)^T-(1+r_t)^t}{T-t}
$$
Why is ...
1
vote
1answer
81 views
Replicating portfolios [closed]
Prices of a stock are modeled using a two-period binomial tree, with each period being six months.
The continuously compounded risk free interest rate is 7 %
The stock pays 2 % continuous dividend.
...
1
vote
0answers
51 views
Pricing methods in the real world when there is more than one free arbitrage price
Perhaps this question sounds trivial and obvious, but I am starting to study this new field. When we are in a complete market without arbitrage opportunities there is only one risk-neutral martingale ...
3
votes
0answers
52 views
Price of a stochastic game between an agent and the market
In the article Pricing via utility maximization and entropy from Richard Rouge and Nicole El Karoui, they define the value function of the optimization problem as
\begin{align}
V(x,C) = \dfrac{1}{\...
2
votes
1answer
83 views
2
votes
1answer
82 views
The duality of the free energy and relative entropy used to deduce deduce the stochastic game between an agent and the market
I am reading the article Pricing via utility maximization and entropy by Richard Rouge and Nicole El Karoui. They talk about the relative entropy of a probability measure $Q$ with respect to the ...
0
votes
1answer
43 views
standard brownian vs brownian motion
We say Xt with paramters (µ,σ) is brownian process if (Xt-s - X t) ~N (µs,σ2 s) AMONG other conditons .
Here we don't speak about any particular distribution for X t. We only say it is a brownian ...
2
votes
0answers
71 views
Pricing caplet with Bachelier (normal dynamic) using forward measure
I'm trying to price caplet with Bachelier under forward measure, but I can't find any solution.
Remind that Bachelier assumed rates follow a normal dynamic. So here what I was doing :
$C_t(T,T+d)$ ...
2
votes
4answers
263 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 ...
1
vote
1answer
92 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 ...
0
votes
0answers
30 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. ...
2
votes
0answers
28 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
votes
1answer
254 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 ...
1
vote
0answers
68 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 ...
0
votes
0answers
31 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?
0
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0answers
34 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 ...
10
votes
1answer
404 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 ...
0
votes
1answer
68 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
votes
1answer
246 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) ...
3
votes
1answer
305 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 ...
1
vote
1answer
145 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?
0
votes
0answers
45 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 $P(t,S)$
$$\begin{aligned} ZBC(t,T,S,K) = & P(t,S) ...
1
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0answers
34 views
Literature recommendation subordinator models
I'm looking for relevant papers covering subordinator models for stock price modelling. I have alreay read the paper 'A Subordinated Stochastic Process Model with Finite Variance for Speculative ...
0
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0answers
99 views
are there quantitative tools to work with python pandas?
I have a code written in python and I have all my data in pandas dataframe. Are there quantitative tools to apply to these dataframes? For example, I want to calculate rsi, macd and other financial ...
1
vote
1answer
104 views
Finding the process of $X/Y$
This comes from Mark Joshi's concepts of mathematical finance exercise 4 chapter 11.
If
$$dX_t = \alpha X_t dt + \beta X_t dW_t$$
$$dY_t = \alpha Y_t dt + \gamma Y_t d\tilde{W}_t$$
with $W$ ...
-2
votes
1answer
40 views
Calculate min. win ratio needed for a bet to be profitable [closed]
If a bet 12000 to win 4000 my risk/reward ratio is .33 .
How often must I win the bet to be profitable?
I know it's 75% but have not found the formula yet.
2
votes
1answer
82 views
Mathematical definition of a hedge?
For two given portfolios/trading strategies I want to know what criteria need to fulfilled in order to call the one portfolio a hedge to the other. In other words; what is the mathematical definition ...
7
votes
2answers
373 views
Stop-loss start-gain paradox: Why is it a 'paradox'?
The Stop-Loss Start-Gain Paradox and Option Valuation: A New Decomposition into Intrinsic and Time Value, by Peter P. Carr and Robert A. Jarrow, in The Review of Financial Studies, Volume 3, Issue 3, ...
0
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0answers
50 views
Computing the Expectation to a Max function
if $X_T$ is log-normally distributed and $k$ is a constant, how do I compute:
$$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[...
6
votes
2answers
2k 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 ...
