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Jumps: Merton jump-diffusion

Geometric Brownian motion plus Poisson jumps. Ring markers show where a jump hit; the daily returns grow fat tails that a normal curve misses.

Parameters

Jumps per year (λ)8

030

Mean log-jump (m)-0.04

-0.20.1

Jump std. dev. (δ)0.06

0.010.2

Volatility (σ)0.15

0.050.5

Random seed: 7

Metrics

Excess kurtosis (sample)

37.9

Excess kurtosis (exact)

37.3

Returns beyond 3 st. dev.

1.65%

Normal law

0.27%

3 price paths with jumps marked

50400 daily log-returns (in %) against the normal curve