Binomial option pricing model help! Watch
- 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%
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To construct a risk-free portfolio of option and stock, buy one and short sell the other to make them move in opposite directions.
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)
high-low spread (option)
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