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 Binomial Model : Let's price with it !
Issued on October 01 2010 par Strategies-options.com
A simple way to price an european style option is to use the binomial model on a spreadsheet.
We saw how the binomial model is simple.
Let's look how it works out. I - VARIABLES AND PARAMETERS Variables Asset price S Maturity T Parameters Strike K Annualized volatilityσ in % risk free rate r in % per year Annualized dividend rateq in % Number of periods n II - FIRST STEEPS - One period is equal to total maturity divided by the number of periods - up factor u - down factor d=1/u - risk neutral probability p of an up move for each périod. - risk neutral probability p of an down move for each périod q=1-p III - SET UP We are going to price an 1 year call option struck at $100 with current underlying asset at $100, riskfree rate 5% volatility at 30% b- Let's go for column B and C: - In cells B2 "=Spot S", in cells C2 "=100" - In cells B3 "strike K", In cells C3 "=100" - In cells B4 "maturity T", In cells C4 "=1" - In cells B5 " =n", In cells C5 "=30" - In cells B6 "riskfree rate r", In cell C6 "=0.05" - In cells B7 "=dividend yield q", In cells C7 "=0" - In cells B8 "cost of carry b=r-q", In cells C8 "=C6-C7" - In cells B9 " dt", In cells C9 "=C4/C5" - In cells B10 "volatility sigma", In cells C10 "30%" - In cells B13 "up factor u", In cells C13 "=EXP(C10*RACINE(C9))" - In cells B14 "down factor d", In cells C14 "=1/C13" "Probabilities" - In cells B17 "p", In cells C17 "=(EXP(C8*C9)-C14)/(C13-C14)" - In cells B20 "1-p", In cells C20 "=1-C17"  Calculus - In cells E4, E5, E6, E7....E33, E34 "=$C$5" . In cells G4"=E4-F4". - In cells F5 "=F4+1", In cells G5 "=E5-F5". The same way F6 "=F5+1" ,G6 "=E6-F6"  - In cells I5 "=((FACT(E4)/(FACT(F4)*FACT(G4))))", In cells J5 "=(PUISSANCE($C$17;F4))" In cells K5 "=(PUISSANCE($C$20;G4))".  Finally, - In cells M4 "=I4*J4*K4*(MAX(($C$2*PUISSANCE($C$13;F4)*Power($C$14;G4))-$C$3;0))"  The outcome - In cells C24 "=sum(M4:M34)" - In cells C25 "=+EXP(-C6*C4)*C24"  14.1334. (Black & Scholes gives 14.2312 .) Next :Binomial Model: Let's Price With It ! ( The Revenge 2) Previous :Binomial Model : Simplest Option Pricing Model Related Pdf : - BINOMIAL MODEL OPTIONS PRICING MODEL - INDEX OPTIONS PRICING MODEL - INDEX OPTIONS PRICING MODEL - CHAPTER I OPTIONS PRICING MODEL - CHAPTER II OPTIONS PRICING MODEL - CHAPTER III Strategies-options.com |
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