Finance Knowledge Notes

Below are some finance notes.

DV01

DV01 (dollar value of 01) measures the change in the price of a bond for a 1 basis point (0.01%) change in yield.

(Sensitivity of bond price to yield change)

• Linear approximation of price sensitivity, non-linear if large yield changes.
• Used in fixed-income portfolio management.

It is calculated as:

$$DV01 = -\frac{\Delta P}{\Delta y} \times 10000$$

The dollar duration of a portfolio is the sum of the DV01 of each bond in the portfolio.

Value at Risk (VaR)

Given confidence level $\alpha$, the VaR is defined as

$$\alpha = \int_{-VaR}^{\infty} xf(x) dx$$

where $x$ is the dollar profit (loss) and $f(x)$ is the probability density function.

However, it is not-additive, i.e. if portfolio $C$ = $A + B$, it is not guaranteed that $VaR(C) < VaR(A) + VaR(B)$.

Forward and Futures

In the interest rate is deterministics, the forwards and futures prices are equivalent.

$$F = S_0 e^{(r + u - y)\tau},$$

where $u$ is the storages cost, $y$ is the divident yield for investment assets, covenience yield for commodities, and foreign risk-free interest rate for foreign exchange.

Interest Rate Model

Two categories:

1. Short rate models

   • Evolution of instantaneous interest rate is stochastic.

2. Forward rate models

Another classification

1. Arbitrage-free models

2. Equilibrium models