# Binomial option pricing model help!Watch

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Binomial Option Pricing Model for Call Options
Single Period
- Assume European options
- Option has a life of one year
- Exercise price = £110
- Current market price at which option is written = £100
- 2 possible price changes: rise of 20% or fall of 10%
- No dividends
- RF = 10%

Stock Option
£120 £10

£90 £0

xxxx I dont understand a thing after this

To construct a risk-free portfolio of option and stock, buy one and short sell the other to make them move in opposite directions.

Either:
A. Buy stock and sell options
B. Short sell stock and buy options

Call ending value: = £10 if stock = £120
= £0 if stock = £90
£30 stock ending value difference
£10 option ending value difference
For exact match sell three options for every stock held.

No. of call options held = high-low spread (stock)

e.g. 120 – 90 = 3
10 – 0

STOCK OPTIONS PORTFOLIO
90 unexercised 90
120 -30 90

Whatever happens, the portfolio is worth £90; therefore it is a risk-free investment.

Portfolio should offer the risk-free rate of return in the absence of arbitrage.

Rp = year end portfolio value - 1
Price of 1 share – 3 x call option price

10% = £90 - 1
£100 – 3 x option price

Option price = £6.06

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