# Questions tagged [finance-mathematics]

The tag has no usage guidance.

287 questions
Filter by
Sorted by
Tagged with
20 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 ...
289 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 ...
60 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 ...
131 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 ...
131 views

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 ...
203 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 ...
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 ...
44 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"...
84 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 ...
49 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 ...
89 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 ...
122 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 ...
108 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 ...
154 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 ...
57 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 ...
216 views

### Are there any quant strategies which do not involve simultaneous buying and selling of two or more assets?

187 views

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 ...
98 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 ...
121 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 ...
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 ...
228 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 ...
141 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 ...
21 views

65 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 ...
145 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 ...
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 ...
38 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 ...
96 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 ...
57 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 ...