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Quantitative Finance · Glossário

O que é Binomial model?

Definition 2.1 Derivatives and Volatility · Capítulo 2 — The Binomial Model

In the binomial model time runs in nn steps of length Δt=T/n\Delta t=T/n. Over each step the share price is multiplied by uu or by d<ud<u, and one unit of cash deposited grows to R=erΔtR=e^{r\Delta t} (with a continuous dividend yield qq, the share’s own growth is compared with e(r−q)Δte^{(r-q)\Delta t}). The model has no arbitrage if and only if d<e(r−q)Δt<ud<e^{(r-q)\Delta t}<u.

Exemplos

Example 2.2 (One step)

A share at 50 will be at 60 or 40; rates are zero. A call struck at 50 pays 10 or 0: Δ=10/20=0.5\Delta=10/20=0.5 share, and the deposit is b=(0−0.5×40)=−20b=(0-0.5\times40)=-20, a borrowing of 20. The call costs 0.5×50−20=50.5\times50-20=5, and p=(1−0.8)/0.4=0.5p=(1-0.8)/0.4=0.5.

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