Questions tagged [finance-mathematics]

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92 views

Stock Volatility with Uncertain Probability

Suppose that the probability that determines the state of the economy is unknown. That is, you do not know whether the booms or recessions are more likely. Calculate the expected return and the ...
3
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1answer
43 views

Exposure/Factor Analysis on a loan portfolio?

I am working on performing factor analysis on a loan portfolio. This is my understanding so far, and I was hoping that some of the smart folks here might be able to chime and guide me through this ...
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0answers
23 views

Is it possible to price a double barrier option which one barrier is monitored continuously while another barrier discretely without using MCS?

I am thinking about pricing a down-and-in and up-and-out double barrier put option under Black-Scholes assumption. The upper barrier is monitored continuously and the lower barrier is monitored ...
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0answers
39 views

How to calculate the multiple integrals where the integral domain is based on the sum of normal distribution random variables?

The integral is shown below: And how to use python to calculate pi (better if we don't need to code for each pi)?
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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 ...
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1answer
54 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 ...
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2answers
108 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 ...
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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:...
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0answers
68 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 ...
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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 ...
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1answer
129 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 ...
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0answers
28 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 ...
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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 ...
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1answer
101 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
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3answers
196 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
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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
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1answer
43 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
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1answer
70 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 ...
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1answer
38 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
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1answer
76 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 ...
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0answers
90 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 ...
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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
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1answer
148 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
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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 ...
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2answers
192 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
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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
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1answer
84 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
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1answer
105 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
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1answer
63 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 ...
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0answers
149 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 ...
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2answers
136 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 ...
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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
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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
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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 ...
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0answers
82 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
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2answers
82 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
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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
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1answer
68 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
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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
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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
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0answers
28 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 ...
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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 ...
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0answers
87 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 ...
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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
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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+(...)...
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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 $g$ ...
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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
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2answers
296 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
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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
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4answers
243 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 ...