Uses of Trigonometric Functions in Financial Modeling

# Are the sin, cos, tan functions used in some financial calculations?


# Are the sin, cos, tan functions used in some financial calculations?












I ask because those functions are on the TI BA II Plus financial calculator.

I saw some interesting answers but I don't think a calculator would be practical in their environment.

## Answer by user12348 (score 8)

https://quant.stackexchange.com/a/11239

Fourier methods use sine and cosine functions, and are used in calculating option prices, VaR, time series analysis etc. It is an alternative process for doing many things in finance. Some links Fourier Methods in trading on StackExchange and Wiki

## Answer by Marco Breitig (score 7)

https://quant.stackexchange.com/a/11219

One can use the Karhunen–Loève expansion to approximate a trajectory of a Wiener Process, which can be used to model the evolvement of returns in time. (http://en.wikipedia.org/wiki/Karhunen%E2%80%93Lo%C3%A8ve_theorem#The_Wiener_process)

Though the Karhunen–Loève expansion has theoretical advantages to other variants to generate a trajectory of a Wiener Process, many users will use different methods because on computers evaluation of trignometric is very expensive in terms of calculation time.

## Answer by Bob Jansen (score 5)

https://quant.stackexchange.com/a/11222

You can use $\sin$ or $\cos$ to model seasonality. If all you have is a calculator it might be the most practical way.

## Answer by wh0 (score 4)

https://quant.stackexchange.com/a/11281

When you do Monte Carlo simulation and would like to draw sample from the normal distribution $\mathcal{N}(\mu,\sigma^2)$, you may use Box-Muller transform and come up with formulas using $\sin$ and $\cos$.

## Answer by Felix (score 3)

https://quant.stackexchange.com/a/11292

Trigonometric functions show up in econometric models for business cycles. For example: the average length of a cycle of an AR(2) process is

$ k = \frac{2 \pi}{\cos^{-1}( \phi_1/ (2 \sqrt{-\phi_2}))}$

For an AR(2) model given by $ r_t = \phi_0 + \phi_1 r_{t-1} + \phi_2 r_{t-2} + a_t$

with complex roots, $\phi_1^2 + 4\phi_2 <0 $

## Answer by Tom Au (score 3)

https://quant.stackexchange.com/a/11565

Trigonometric functions are WAVE phenomena. As such, they are best used to model so-called periodic functions, that is, functions with cycles of a fixed period in length. That's why they are good for modelling, seasonal, annual, "blue moon" (once every two and half years), or other functions with set "periods."

## Answer by BCLC (score 2)

https://quant.stackexchange.com/a/11246

Solving some heat/diffusion equations under certain conditions needs trigonometric functions.

Black-Scholes reduces to a heat/diffusion equation by a change of variables.