Questions tagged [finance-mathematics]
The finance-mathematics tag has no usage guidance.
243
questions
0
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0answers
21 views
What NPV value to expect with X% success?
cross-posted from https://math.stackexchange.com/questions/3326309/what-value-to-expect-with-x-success
I'm trying to intuit the following statements based on the plot below, but I'm stuck on the ...
0
votes
1answer
51 views
Clarification on certain finance terms surrounding bonds
Whilst revising for my upcoming financial mathematics exam I've been struggling to get to grips with certain terms/ phrases used when studying Bonds. I am very new to Finance and get confused very ...
2
votes
2answers
94 views
How to Mathematically Prove Markets are Price-Discovering?
We all know that the Efficient Market Hypothesis is true if you're willing to make enough simplifying assumptions about the market participants. But where can I find a mathematical proof of this in ...
1
vote
1answer
69 views
Jensen’s Inequality for returns on short positions
this is puzzling me. Say you have an asset A, that on day t+1 returns 1%, and then on day t+2 returns 1% again.
If you invest $1 in A on day t (take a long position), then on day t+2 you have earned:...
0
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0answers
65 views
Stock prices and PCA
I'm trying to construct a portfolio using PCA based on a number of stocks. I was wondering what the best way to standardise the stock prices are.
Which method would be more appropriate? Standard ...
0
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0answers
19 views
Portfolio Values based on reference interest rates
How do I approach the following question?
A portfolio has 100 million invested in equities. It has also transacted an interest rate derivative issued by counterparty X, which the value is 0 if the ...
0
votes
1answer
121 views
Squared returns and volatility
Squared returns are considered pillars of GARCH/ARCH modelling and most used method for forecasting or studying volatility.
Can you tell me how to calculate it from simple stock price.
Is it better ...
0
votes
0answers
27 views
How Free Of Payment (FOP) trade works? How it impacts NAV and P&L?
I want to understand how the Free of Payment(FOP) trades work from accounting point of view. My questions are:
What data we collect while capturing FOP trade?
How it impacts NAV and P&L? e.g. say ...
1
vote
2answers
82 views
Find arbitrage opportunity in the given market model
Consider the following 3-period-market-model:
The discounted price of the risky asset $S$:
How can I find an arbitrage opportunity in this model?
I know that there would be no arbitrage if we ...
0
votes
1answer
97 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 ...
3
votes
3answers
193 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, and for each time I have to add ...
8
votes
3answers
6k 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
1answer
42 views
How is hypothesis testing work in population sampiling? [closed]
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
69 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
36 views
Is the undiscounted value process of a Euro call option under Bachelier model a Martingale? [duplicate]
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
71 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 ...
1
vote
0answers
81 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
81 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
146 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
55 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
191 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
179 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
83 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
104 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
62 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
131 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
20 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
105 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
73 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
81 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
57 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
67 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
85 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
27 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
36 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
86 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
39 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
40 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
65 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
$$ \phi_t = \frac{Y_t}{\sqrt{...
3
votes
2answers
289 views
Application of Ito's lemma
Let $X_t$ be some stochastic process driven by wiener process ($W_t)$ so it can be expressed as:
$$dX_t=(...)dt+(...)dW_t$$
Let $f(t,x)$ be some $C^2$ function. Define the process $Z_s=f(t-s,X_s)$ ...
0
votes
1answer
64 views
Monte Carlo simulated price and Black Scholes Price are giving a huge difference in my Matlab code
I have written a script for showing Monte Carlo Price for a increasing N.
But comparing with BS results , This indicates a huge difference. Where is the error?
Function :
function [cpay,ppay] = ...
1
vote
4answers
236 views
What are the benefits of publishing papers in mathematical finance/trading?
What are the benefits of publishing papers in mathematical finance and trading. Let us assume that the primary goal of a person/entity is to make money and reduce losses. Wouldn't publishing ...
2
votes
0answers
29 views
About buying and selling a cumulative parisian options
I ask my question here because I want to know more about the cumulative Parisian options introduced by M. Chesney, Mr. Jeanblanc-Picué and Mr. Yor in 1997, then developed by Hugonnier in 1999 and F. ...
1
vote
0answers
24 views
The deflator of reinsurance market is unique
How to prove that the deflator $\phi$ of the reinsurance market is unique when working in the equilibrium model?
That is, if we have a pricing function $\pi$, which satisfies:
$$\pi(Y)=E(\phi Y)$$
...
0
votes
1answer
57 views
Why do most interest rate formulas, and indeed finance in general, add 1 to a rate and then subtract afterwards? [closed]
For example, in the formula that shows the relationship between the nominal and effective interest rate shown below, 1 is first added to in/m and then 1 is subtracted from the result. What is the ...
3
votes
1answer
84 views
Hedging Value-Financial Mathematics
EXERCISE
We consider a free from arbitrage financial market $(Ω,F,P,S_0,S_1)$ with $α<S_0^{1}\cdot(1+r)<β$,where $$0<α:=min_{ω \in Ω} S_1^{1}(ω), β:=max_{ω \in Ω}S_1^{1}, α<β$$
Let ...
