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Quantitative Finance · शब्दावली

Leisen–Reimer tree क्या है?

अन्य नाम: Leisen--Reimer tree

Definition 2.8 Derivatives and Volatility · अध्याय 2 — The Binomial Model

The Leisen–Reimer tree uses an odd number of steps and chooses $p$ and $u$ so that the tree’s probabilities of finishing above the strike, under the risk-neutral and the share measures, equal $\Phi(d_2)$ and $\Phi(d_1)$ (through a normal-to-binomial inversion due to Peizer and Pratt). The tree is centred on the strike, and the error for European options falls like $1/n^2$ without oscillation.

Error of three trees for the one-year at-the-money European put (r=5\%, =20\%, formula 5.5735), even and odd step counts drawn separately. The Cox–Ross–Rubinstein error is negative for even n, positive for odd n, and shrinks like 1/n; the Leisen–Reimer error is invisible at this scale from 11 steps. Data: the tutorial. — Figure 2.3. Error of three trees for the one-year at-the-money European put ( $r=5\%$ , $\sigma=20\%$ , formula 5.5735), even and odd step counts drawn separately. The Cox–Ross–Rubinstein error is negative for even $n$ , positive for odd $n$ , and shrinks like $1/n$ ; the Leisen–Reimer error is invisible at this scale from 11 steps. Data: the tutorial.

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