Use Algorithm 8 to construct several figures such as Fig. 2.4 and observe the extent to which correlated prices trend together (recall that it is the increments that are correlated, not the prices themselves). For each run, calculate the correlation between the prices.

Data given in Algorithm 8

Figure 2.4:

Transcribed Image Text:

inputs: p, om (market volatility) Hs, Os (equity parameters) generate a market scenario: mo, m1, ... De.g. quarterly prices manually assigned ▷generate preliminary market prices Pi = Pi-1(1 + 0m VdtZi) Zi ~ N(0, 1) • calculate the piecewise linear correction l(t) (pp 48) • calculate the market prices M₁ = Pi + l(i) ▷back out the market increments W₁ = (M₂ - M₁-1)/(om √dt Mi-1) label AA: ▷generate correlated N(0, 1) increments Y₁ = pW₁+√1-p²Z₁ Z₁ ~ N(0,1) ▷generate the correlated stock prices using the Yi Si = Si-1(1 + pędt +0,√dtY;)