Integral Calculus and Differential Equations › Key Parameters

The key parameters for integral calculus and differential equations in finance are:

• r: Interest rate or discount rate. Appears in continuous compounding $e^{rt}$ and determines how future cash flows are discounted to present value.
• T: Time horizon or maturity. At a fixed nonzero rate, a longer horizon increases the magnitude of compounding or discounting relative to the starting value; changing-sign rates can offset one another.
• κ (kappa): Positive mean reversion speed ($\kappa>0$) in models like Vasicek. Higher positive values mean faster reversion to the long-term mean, with half-life $\ln(2)/\kappa$.
• θ (theta): Long-term mean in models such as Vasicek. The conditional mean reverts toward this level; individual stochastic paths are not forced to converge to it.
• δ (delta): Continuous depreciation or decay rate. Positive decay and positive initial value give half-life $\ln(2)/\delta$; the effective annual loss is $1-e^{-\delta}$.
• K: Logistic limiting capacity. It bounds an increasing path started below $K$; a path started above it decreases toward it.
• μ (mu): Drift rate in growth models. Represents the expected rate of return or growth per unit time.
• σ (sigma): Volatility parameter. Measures the magnitude of random fluctuations in stochastic models.