Interest rate convexity in a Gaussian framework

Figures & data

Figure 1. Examples of rates curves over different days from the OptionMetrics rates data.

Figure 2. Top: Time series of the OptionMetrics rates for different maturities. Bottom: Estimation of the Hurst exponent for the OptionMetrics rates data.

Figure 3. Top: Time series of the US Treasury rates for different maturities. Bottom: Estimation of the Hurst exponent for the US Treasury rates.

Table 1. aaaa

$\mathrm{sgn}(\log {\mathfrak{C}}_t^{\tau }({\mathfrak{t}}_1,{\mathfrak{t}}_2\left)\right)$	${\mathfrak{t}}_1>{\mathfrak{t}}_2$	${\mathfrak{t}}_1<{\mathfrak{t}}_2$
$\tau <{\mathfrak{t}}_2$	negative	positive
$\tau >{\mathfrak{t}}_2$	positive	negative

Figure 4. Dynamics of the zero-coupon bond in the Exponential (left) and the Riemann-Liouville (right) kernel case.

Figure 5. Left: Impact of the exponential factor α on the convexity for the Exponential kernel from section 2.3.1. Right: Impact of the Hurst exponent H on the convexity for the power-law kernel from section 2.3.2.

Figure 6. Left: Impact of the exponential factor α on the convexity for the Exponential kernel with standard Brownian motion (black dashed) and with OU driver with different β parameters. Right: Same but with the power-law kernel.