Transcript Binomial Model

Lecturer: Jan R.
M. Röman
By: S.M. Nazmul Hoque
VecheakMony Heng
BINOMIAL MODEL
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A useful and very popular technique for pricing an option
Particularly useful for the holder having early exercise decisions
Different binomial models:Cox-Ross-Rubenstein (CRR), Tian,
Leisen-Reimer and Balck-Scholes smoothing
BACKGROUND
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Consider a financial market (from t = 0 to t = 1) with a security
with the stochastic process S(0) = s
S(1) = u.s with probability pu
d.s with probability pd
COX-ROSS-RUBENSTEIN MODEL
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u = exp^σSqr(δt)
d = 1/u = exp^σSqr(δt)
p = (exp^rσδt)/ (u-d), q = 1 – p
C = (exp^(-r)σδt) (pCu + qCd)
Tian Model
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u = MV/2 [V+1+Sqr(V2 + 2v -3)]
d = MV/2 [V+1-Sqr(V2 + 2v -3)]
M = exp^rδt), V = exp^σ2δt
LEISEN-REIMER MODEL
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A = exp^rδt
d1 = [ln(s/k) + (r+1/2σ2)(T-t)]/ (σSqr(T-t))
d2 = d1 - (σSqr(T-t)
p = B(d2, N) and p* = B(d2 + (σSqr(T-t), N)
BLACK-SCHOLES SMOOTHING
Three of the nodes closest to the strike price are used to
calculate the the Black-Scholes value.
Nodes to smooth