Questions tagged [finance-mathematics]
The finance-mathematics tag has no usage guidance.
0
votes
1answer
12 views
Getting sets of random correlated variables
For the training of a machine learning model I need to add additional features (macro variables), and these features are correlated. I need to run the model N times adding these features with random ...
1
vote
1answer
29 views
What mathematical theory is required for high frequency trading?
I am an applied math postdoc and I have been presented with the option of leaving academia to work in high frequency trading. I wanted to get a feel for the field and the theory underlying it so I ...
1
vote
0answers
13 views
How is hypothesis testing work in population sampiling?
I am learning the basics of quant trading from quantconnect's tutorial Confidence Interval and Hypothesis Testing. I understood the first part of the article but I dont understand "Hypothesis Testing"...
3
votes
1answer
52 views
How to comprehend this notation?
I learned mathematical finance from Bjork's Arbitrage Theory in Continous Time, and never once did I encounter the "quadratic variation"-thingy with the angle brackets.
So now that I am reading ...
1
vote
1answer
22 views
Is the undiscounted value process of a Euro call option under Bachelier model a Martingale?
Assume that $c_t$ is the UNDISCOUNTED price process for a European call option in Bachelier model. In Bachelier model call option pricing formula the formulas is discussed. The undiscounted value ...
1
vote
1answer
54 views
Modeling mortgage loan defaults
I have a machine learning model trained with a list of mortgage features that include macro variables where the field to predict (the label) is "Mortgage Defaulted" = 1 or 0 (Yes or No).
Now, I need ...
0
votes
0answers
61 views
Derivative of the Black and Scholes equation [on hold]
What is the financial interpretation that the derivative of the Black and Scholes equation is equal to 0?
St n(d1) - Xe^-rt n(d2) = 0
0
votes
0answers
60 views
Term structure equation in the Vasicek model
Consider the SDE $$dr_t = (b-ar_t)dt +\sigma dW_t, \text{with } a; b > 0.$$ Let $$F(t; r) = E(\exp(-\int_{t}^{T}r_sds)| r_t = r).$$ (F can be interpreted as price of a zero coupon bond with ...
2
votes
0answers
71 views
Quantitative Finance books for Practitioners [duplicate]
Currently searching for some books on real options and option pricing. However, the vast majority of the books are quite theoretical, and if someone has been taught these subject in class, half of it ...
3
votes
1answer
140 views
Finding optimal trading of option on a foward
Assume you have a option on a forward $F$ with a payoff: $\max(F_T - K, 0)$.
Assume also, that you have a bullish view on the forward in such a way that $E_{0}[F_T] > F_0 = E_{0}^{*}[F_T]$ (where ...
1
vote
1answer
51 views
Finding the extrinsic value of an option with conditions
Background:
Consider a spread option with the payoff $\max (P_{T} - HR\times G_T, 0)$, where $P$, $G$ are underlying prices and $HR$ is a constant.
Let's also assume, that the correlation ...
1
vote
2answers
171 views
Are there any quant strategies which do not involve simultaneous buying and selling of two or more assets?
Whenever I read about quant strategies it leads me to stratergies which involve simultaneous buying and selling of two or more assets. Pairs trading, arbitrage, market neurtal or headging all these ...
2
votes
1answer
174 views
Forward Start Spread Options
Question:
We have a spread option with payoff: $\max (P_{T} - HR\times G_T, 0)$, where $P$, $G$ are underlying prices and $HR$ is a constant.
At time zero only contract $G$ is available for ...
1
vote
1answer
81 views
How to calculate Spot Rate with interest rate [closed]
You are a foreign exchange trader specialized in the US dollar Swiss franc market (USD/CHF). One morning, you notice that the one-year dollar interest rate is 4%, while the one-year interest rate on ...
2
votes
1answer
95 views
Fair price of a coupon paying bond
Consider a coupon paying bond with a maturity of $3$ years, that pays coupon annually. Let $c$ be the coupon rate (percentage) and let $F$ be the face value. This means that the holder of the bond ...
1
vote
1answer
58 views
Is it possible to create an instrument on the amount of beds sold within the real-estate market
I have been doing some research on the PBSA (purpose-built student accommodation) market around the globe. The market is growing year on year there is an index on this market the cbre.
What ...
1
vote
0answers
73 views
Errata for Mark Joshi's Concepts and practice of mathematical finance
I am wondering if anyone has a PDF copy of the errata for Mark Joshi's book "Concepts and practice of mathematical finance"? It seems that Mark's website markjoshi.com is not accessible anymore. I ...
3
votes
2answers
135 views
Verifying two properties of the Clayton Copula
So I'm trying to verify the first two properties of a copula for the Clayton model. The first two properties being:
$C(u_1,…,u_d)$ is non-decreasing in each component, $u_i$
The $i^{th}$ marginal ...
1
vote
0answers
18 views
Show that the variance of the portfolio market portfolio is function of the betas of its consituents [closed]
Let us assume that the market portfolio consists of n assets.
Given that the return of the market portfolio can be written as $r_m = \sum_{j=1}^{n} w_jr_j$, we have that $\sigma^2_m = E(\sum_{j=1}^{n} ...
4
votes
1answer
58 views
How to prove that the expected squared error associated with the optimal combination weight is smaller than the minimum of 2 forecast variances?
I am looking at linear combination of two forecasts (Bates and Granger, 1969). I would like to understand how to prove that the expected squared error associated with the optimal combination weight is ...
2
votes
1answer
92 views
Convert Geometric Direct Alpha PME to Arithmetic Excess IRR (PME Alpha / Implied Private Premium)
As a followup to this old question, Private Equity: Direct Alpha vs Excess IRR, I have a new one.
In automating PME calculations, the Direct Alpha (DA) approach is computationally simpler and ...
1
vote
0answers
56 views
Credit default swap replication by corporative bonds
I want to get literature or information related with the topic of CDS replication for those counterparties that do not hold. But that have traded bonds (with different degree of liquidity). What could ...
0
votes
2answers
76 views
Value-at-Risk theory papers
I am looking for some papers related to the value-at-risk theory. I would like to focus on mathematical aspects of VaR. I would like to read something about modern approaches to VaR (maybe using ...
4
votes
0answers
54 views
Why does risk-neutral price processes do not, in general, compose all arbitrage-free price processes?
I was reading reviewing my mathematical finance notes and I came across a remark I cant understand fully
Remark :Contrary to discrete time models, the risk-neutral price processes do not, in general, ...
2
votes
1answer
66 views
Finding the limit $\lim_{n \to \infty} P_0^n$ for a European Cash-or-Nothing put option with $P=K^2\cdot \mathbf{1}_{\{S_T < K\}}$
Exercise :
Let $K>0$. A European Cash-or-Nothing put option $P$ has the following pay-out profile :
$$P=K^2\cdot \mathbf{1}_{\{S_T < K\}}$$
Let $P_0^n$ be the no-arbitrage value at time $...
1
vote
1answer
62 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
78 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
26 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
vote
0answers
33 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
votes
0answers
79 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
vote
0answers
48 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 ...
3
votes
0answers
34 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+(...)...
2
votes
0answers
38 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
61 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
$$ \phi_t = \frac{Y_t}{\sqrt{...
3
votes
2answers
260 views
Application of Ito's lemma
Let $X_t$ be some stochastic process driven by wiener process ($W_t)$ so it can be expressed as:
$$dX_t=(...)dt+(...)dW_t$$
Let $f(t,x)$ be some $C^2$ function. Define the process $Z_s=f(t-s,X_s)$ ...
0
votes
1answer
61 views
Monte Carlo simulated price and Black Scholes Price are giving a huge difference in my Matlab code
I have written a script for showing Monte Carlo Price for a increasing N.
But comparing with BS results , This indicates a huge difference. Where is the error?
Function :
function [cpay,ppay] = ...
1
vote
4answers
217 views
What are the benefits of publishing papers in mathematical finance/trading?
What are the benefits of publishing papers in mathematical finance and trading. Let us assume that the primary goal of a person/entity is to make money and reduce losses. Wouldn't publishing ...
2
votes
0answers
29 views
About buying and selling a cumulative parisian options
I ask my question here because I want to know more about the cumulative Parisian options introduced by M. Chesney, Mr. Jeanblanc-Picué and Mr. Yor in 1997, then developed by Hugonnier in 1999 and F. ...
1
vote
0answers
24 views
The deflator of reinsurance market is unique
How to prove that the deflator $\phi$ of the reinsurance market is unique when working in the equilibrium model?
That is, if we have a pricing function $\pi$, which satisfies:
$$\pi(Y)=E(\phi Y)$$
...
0
votes
1answer
57 views
Why do most interest rate formulas, and indeed finance in general, add 1 to a rate and then subtract afterwards? [closed]
For example, in the formula that shows the relationship between the nominal and effective interest rate shown below, 1 is first added to in/m and then 1 is subtracted from the result. What is the ...
3
votes
1answer
83 views
Hedging Value-Financial Mathematics
EXERCISE
We consider a free from arbitrage financial market $(Ω,F,P,S_0,S_1)$ with $α<S_0^{1}\cdot(1+r)<β$,where $$0<α:=min_{ω \in Ω} S_1^{1}(ω), β:=max_{ω \in Ω}S_1^{1}, α<β$$
Let ...
3
votes
1answer
204 views
Equivalent martingale measure exists if and only if $a < S_0^1(1+r)< b$
Exercise :
We consider a market of one period $(\Omega, \mathcal{F}, \mathbb P, S^0, S^1)$, where the sample space $\Omega$ has a finite number of elements and the $\sigma-$algebra $\mathcal{F} = 2^...
2
votes
1answer
113 views
Showing that a market model has arbitrage and describing martingales
This is an exercise which I came upon while studying an introduction to financial mathematics.
Exercise :
Consider the finite sample space $\Omega = \{\omega_1,\omega_2,\omega_3\}$ and let $\...
3
votes
1answer
301 views
Total Returns From Adjusted Close Prices
I'm trying to understand why the total return (return including dividends) that I get from calculating return using adjusted close price, does not equal the total return calculated in another manner.
...
1
vote
1answer
73 views
Approximation of Forward Rates in discrete time
The forward rate from time $t$ to $T$ ($f_{t,T}$) can be approximated by:
$$
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
114 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
56 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
99 views
2
votes
1answer
104 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 ...
