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# Questions tagged [finance-mathematics]

Financial mathematics, or mathematical finance, is a set of mathematical tools allowing to express use cases on financial markets a way that can (or could) be solved using mathematics.

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### Intuitive Understanding of d1 in Black-Scholes [duplicate]

I am reading about the derivation of Black-Scholes using Future prices. I understand the mathematical steps of the derivation, which starts by separating it into the difference of two integrals, the ...
2 votes
1 answer
59 views

### Recover value function from its dual

I take as my reference Optimal Investment by Rogers (2013). Denote the agent's value function, which is convex, by $V(w)$, where $w$ is the state variable. Define the dual variable $z = V_w$, where ...
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### Fitting a multidimensional Ornstein-Uhlenbeck pProcess

If I have a dataset X, where each row is a time point and we have several variables, say 100, (so this is a multivariate time series), what is the best way to fit a multidimensional Ornstein-Uhlenbeck ...
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-2 votes
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### Simple arbitrage pricing of bond option

This is Tuckman fixed income security textbook. The text here is trying to price a 990 six month call on a six month zero bond. When we replicate the portfolio, where is the F_.5 coming from? My ...
5 votes
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### Predatory trading as a game of size

Predatory trading has been addressed in literature frequently. I have read for example Brunnemeier (2005) but that paper mostly addresses predatory trading surrounding a preexisting distressed trader. ...
1 vote
2 answers
106 views

### Calibrating CIR to bond prices

Consider the Hull-White model - $$dr_t = (\theta_t - kr_t)dt + \sigma_tdw_t$$ We can/have to calibrate $\theta_t$ to the current bond prices $P(0,t)$ and make it consistent with the HJM framework. For ...
2 votes
1 answer
239 views

### Preferred Option pricing model [closed]

I am at Uni studying mathematical finance and wanted to know which is most preferred /widely used model by Finance Industry Practitioners from the list below. Fourier Transform for option pricing ...
5 votes
2 answers
229 views

### Multicurrency holiday calendar math and combinations

Trade Example I have recently observed a trade which calculated spot (T+2) from Friday 16th June 2023 for a EURUSD FX product and derived the date Tuesday 20th June 2023. In EUR under the target ...
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2 votes
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### What is the proper way to derive risk definitions from utility functions?

In typical mean-variance analysis, the risk-adjusted relative value of an individual asset takes the general form $\frac{\mu}{\sigma^2}$, with further weighting and normalization depending on the ...
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3 votes
1 answer
275 views

### Calculating spread on a par rate curve given bond’s coupon and yield

In Tuckman and Serrat’s Fixed Income Securities, they give an example of a bond and state its coupon and yield. They also provide an HQM par rate curve and quote the bond’s spread to this curve. How ...
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### Fama-French Regression Output Interpretation (Intercept/Alpha)

I am currently doing a report regarding Fama and French 3 and 5 factors model. I was provided 3 companies with each of its daily stock return from 2015-2020, and the values of all 5 factors during ...
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1 answer
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### Is sorting stocks into portfolio mandatory in Fama-French model?

I am currently doing a report regarding Fama and French 3 and 5 factors model. I was provided 3 companies with each of its daily stock return from 2015-2020, and the values of all 5 factors during ...
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1 answer
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### How to analyse the resilience of banks during financial crises using linear regression and other statistical methods?

I am a student in finance and have to work on a project for the semester. I have to study the difference of resilience during financial crises between the 5 biggest US banks and the 5 biggest Canadian ...